---
title: "Mathematical exploration and discovery at scale — Georgiev 2025"
description: "The authors test AlphaEvolve, an evolutionary coding agent from Google DeepMind. 305 references, cited by 13 papers here."
authors: ["Bogdan Georgiev", "Javier Gómez-Serrano", "Terence Tao", "Adam Zsolt Wagner"]
year: 2025
venue: "arXiv:2511.02864"
source: "https://arxiv.org/abs/2511.02864"
doi: "10.48550/arxiv.2511.02864"
arxiv: "2511.02864"
licence: "CC BY 4.0 (arXiv)"
licence_url: "http://creativecommons.org/licenses/by/4.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/georgiev-2025-mathematical-exploration-discovery-scale/"
---
[Elamur Research](https://md.research.elamur.ai/free/en/) · [this page in HTML](https://research.elamur.ai/free/en/papers/georgiev-2025-mathematical-exploration-discovery-scale/)

[home](https://md.research.elamur.ai/free/en/) / [papers](https://md.research.elamur.ai/free/en/papers/) / [2025](https://md.research.elamur.ai/free/en/papers/2025/page/7/) / Mathematical exploration and discovery at scale

# Mathematical exploration and discovery at scale

**Authors:** Bogdan Georgiev, Javier Gómez-Serrano, [Terence Tao](https://md.research.elamur.ai/free/en/authors/terence-tao/) and [Adam Zsolt Wagner](https://md.research.elamur.ai/free/en/authors/adam-zsolt-wagner/) · **Year:** 2025 · **Venue:** arXiv:2511.02864 · **Licence:** [CC BY 4.0 (arXiv)](http://creativecommons.org/licenses/by/4.0/)

**Links:** [Publisher's page](https://arxiv.org/abs/2511.02864) · [PDF](https://arxiv.org/pdf/2511.02864) · [DOI 10.48550/arxiv.2511.02864](https://doi.org/10.48550/arxiv.2511.02864) · [arXiv 2511.02864](https://arxiv.org/abs/2511.02864) · [OpenAlex](https://openalex.org/W4416017797)

**Citations:** 3 citations (OpenAlex, 2026-10-14) · [13](https://md.research.elamur.ai/free/en/papers/georgiev-2025-mathematical-exploration-discovery-scale/cited-by/) in our library, of the 149,439 papers whose bibliographies we read

## Summary
The paper asks whether an LLM-driven agent can help with constructive mathematics: building explicit objects (graphs, packings, functions, point sets) that reach strong numerical bounds on open problems. The authors test AlphaEvolve, an evolutionary coding agent from Google DeepMind. In AlphaEvolve, a language model repeatedly rewrites programs, and an automatic evaluator scores each program and keeps the best ones.

AlphaEvolve does not evolve objects directly. Its standard "search mode" evolves search heuristics. Each heuristic gets a fixed compute budget to improve the current best construction. A separate "generalizer mode" asks for one program that works for every input size n, so the system can turn small cases into a general formula.

They ran it on 67 problems from analysis, combinatorics, geometry and number theory. It matched the known records in most cases and beat them in several. Some outputs were later proved rigorously with Deep Think and AlphaProof. The work suggests that many problems can be explored at once with little expert setup.

## Key points
- The benchmark has 67 problems. AlphaEvolve recovered the best known constructions for most of them and improved on several, but it did not succeed on all.
- Compared with its predecessor FunSearch, AlphaEvolve evolves whole code files of up to hundreds of lines in any language. It needs only thousands of LLM samples rather than millions, and it gains from state-of-the-art LLMs.
- In search mode, each evolved program is an "improver" with a time limit (for example 100 seconds). Chaining such heuristics produces specialized stages, first broad exploration and then fine-tuning.
- In generalizer mode, a construction for the Nikodym problem led to a follow-up paper by Terence Tao (arXiv:2511.07721).
- Setting up a problem usually took a few hours at most. Deep Think and AlphaProof were added to the pipeline for proofs and formalization, and the authors are releasing a public Repository of Problems with code.

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

📚 Shelves (3): [🖥️ Computer Science](https://md.research.elamur.ai/free/en/shelves/computer-science/) · 19,503 works · [🤖 Artificial Intelligence](https://md.research.elamur.ai/free/en/shelves/computer-science/artificial-intelligence/) · 18,805 works · [🧮 Computational Theory and Mathematics](https://md.research.elamur.ai/free/en/shelves/computer-science/computational-theory-and-mathematics/) · 496 works

🧭 Topics (1): [🧮 Reasoning](https://md.research.elamur.ai/free/en/topics/reasoning/) · 1,948 works

## Cite

Cite as: Bogdan Georgiev, Javier Gómez-Serrano, Terence Tao and Adam Zsolt Wagner. 2025. Mathematical exploration and discovery at scale. arXiv:2511.02864.

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@misc{georgiev2025mathematical,
  title = {{Mathematical exploration and discovery at scale}},
  author = {Bogdan Georgiev, Javier Gómez-Serrano, Terence Tao and Adam Zsolt Wagner},
  year = {2025},
  doi = {10.48550/arxiv.2511.02864},
  eprint = {2511.02864},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2511.02864}
}
```

- [← previous LongRecipe: Recipe for Efficient Long Context Generalization in Large Language Models](https://md.research.elamur.ai/free/en/papers/hu-2025-longrecipe-recipe-efficient-long-context/)
- [next → Mind the Value-Action Gap: Do LLMs Act in Alignment with Their Values?](https://md.research.elamur.ai/free/en/papers/shen-2025-mind-value-action-gap-do/)
- [↑ back to papers of 2025](https://md.research.elamur.ai/free/en/papers/2025/page/7/)

## References

305 references, 11 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet.

1. Mathematical results Colab for AlphaEvolve paper. [https://colab.research.google.com/github/google-deepmind/](https://colab.research.google.com/github/google-deepmind/) alphaevolve_results/blob/master/mathematical_results.ipynb. Accessed: 2025-09-27. [↗](https://colab.research.google.com/github/google-deepmind/)
2. Problems from the workshop on “Low Eigenvalues of Laplace and Schrödinger Operators”. American Institute of Mathematics Workshop, May 2006. [find](https://scholar.google.com/scholar?q=Problems+from+the+workshop+on+%E2%80%9CLow+Eigenvalues+of+Laplace+and+Schr%C3%B6dinger+Operators%E2%80%9D%2E+American+Institute+of+Mathematics+Workshop%2C+May+2006%2E)
3. Problem \#106. [https://www.erdosproblems.com/106](https://www.erdosproblems.com/106), 2024. Erdős Problems database. [↗](https://www.erdosproblems.com/106)
4. J. M. Aldaz. Remarks on the Hardy–Littlewood maximal function. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 128(1):1–9, 1998. [find](https://scholar.google.com/scholar?q=J%2E+M%2E+Aldaz%2E+Remarks+on+the+Hardy%E2%80%93Littlewood+maximal+function%2E+Proceedings+of+the+Royal+Society+of+Edinburgh%3A+Section+A+Mathematics%2C+128%281%29%3A1%E2%80%939%2C+1998%2E)
5. Boris Alexeev, Evan Conway, Matthieu Rosenfeld, Andrew V. Sutherland, Terence Tao, Markus Uhr, and Kevin Ventullo. Decomposing a factorial into large factors, 2025. arXiv:2503.20170. — [arXiv:2503.20170](https://arxiv.org/abs/2503.20170) [find](https://scholar.google.com/scholar?q=Boris+Alexeev%2C+Evan+Conway%2C+Matthieu+Rosenfeld%2C+Andrew+V%2E+Sutherland%2C+Terence+Tao%2C+Markus+Uhr%2C+and+Kevin+Ventullo%2E+Decomposing+a+factorial+into+large+factors%2C+2025%2E+arXiv%3A2503%2E20170%2E+%E2%80%94+%5BarXiv%3A2503%2E201)
6. Alberto Alfarano, François Charton, and Amaury Hayat. [Global Lyapunov functions: a long-standing open problem in mathematics, with symbolic transformers](https://md.research.elamur.ai/free/en/papers/alfarano-2024-global-lyapunov-functions-long-standing/). In Advances in Neural Information Processing Systems, volume 37. Curran Associates, Inc., 2024.
7. Mark S. Ashbaugh, Rafael D. Benguria, Richard S. Laugesen, and Timo Weidl. Low Eigenvalues of Laplace and Schrödinger Operators. Oberwolfach Rep., 6(1):355–428, 2009. [find](https://scholar.google.com/scholar?q=Mark+S%2E+Ashbaugh%2C+Rafael+D%2E+Benguria%2C+Richard+S%2E+Laugesen%2C+and+Timo+Weidl%2E+Low+Eigenvalues+of+Laplace+and+Schr%C3%B6dinger+Operators%2E+Oberwolfach+Rep%2E%2C+6%281%29%3A355%E2%80%93428%2C+2009%2E)
8. Charles Audet, Xavier Fournier, Pierre Hansen, and Frédéric Messine. Extremal problems for convex polygons. Journal of Global Optimization, 38(2):163–179, 2010. [find](https://scholar.google.com/scholar?q=Charles+Audet%2C+Xavier+Fournier%2C+Pierre+Hansen%2C+and+Fr%C3%A9d%C3%A9ric+Messine%2E+Extremal+problems+for+convex+polygons%2E+Journal+of+Global+Optimization%2C+38%282%29%3A163%E2%80%93179%2C+2010%2E)
9. K. I. Babenko. An inequality in the theory of Fourier integrals. Izv. Akad. Nauk SSSR Ser. Mat., 25:531–542, 1961. [find](https://scholar.google.com/scholar?q=K%2E+I%2E+Babenko%2E+An+inequality+in+the+theory+of+Fourier+integrals%2E+Izv%2E+Akad%2E+Nauk+SSSR+Ser%2E+Mat%2E%2C+25%3A531%E2%80%93542%2C+1961%2E)
10. Jineon Baek. Optimality of Gerver’s Sofa, 2024. arXiv:2411.19826. — [arXiv:2411.19826](https://arxiv.org/abs/2411.19826) [find](https://scholar.google.com/scholar?q=Jineon+Baek%2E+Optimality+of+Gerver%E2%80%99s+Sofa%2C+2024%2E+arXiv%3A2411%2E19826%2E+%E2%80%94+%5BarXiv%3A2411%2E19826%5D%28https%3A%2F%2Farxiv%2Eorg%2Fabs%2F2411%2E19826%29)
11. Jineon Baek, Junnosuke Koizumi, and Takahiro Ueoro. A note on the Erdos conjecture about square packing, 2024. arXiv:2411.07274. — [arXiv:2411.07274](https://arxiv.org/abs/2411.07274) [find](https://scholar.google.com/scholar?q=Jineon+Baek%2C+Junnosuke+Koizumi%2C+and+Takahiro+Ueoro%2E+A+note+on+the+Erdos+conjecture+about+square+packing%2C+2024%2E+arXiv%3A2411%2E07274%2E+%E2%80%94+%5BarXiv%3A2411%2E07274%5D%28https%3A%2F%2Farxiv%2Eorg%2Fabs%2F2411%2E07274%29)
12. P. Balister, B. Bollobás, R. Morris, J. Sahasrabudhe, and M. Tiba. Flat Littlewood polynomials exist. Annals of Mathematics, 192(3):977–1004, 2020. [find](https://scholar.google.com/scholar?q=P%2E+Balister%2C+B%2E+Bollob%C3%A1s%2C+R%2E+Morris%2C+J%2E+Sahasrabudhe%2C+and+M%2E+Tiba%2E+Flat+Littlewood+polynomials+exist%2E+Annals+of+Mathematics%2C+192%283%29%3A977%E2%80%931004%2C+2020%2E)
13. Martin Balko, Adam Sheffer, and Ruiwen Tang. The constant of point-line incidence constructions. Comput. Geom., 114:14, 2023. Id/No 102009. [find](https://scholar.google.com/scholar?q=Martin+Balko%2C+Adam+Sheffer%2C+and+Ruiwen+Tang%2E+The+constant+of+point%2Dline+incidence+constructions%2E+Comput%2E+Geom%2E%2C+114%3A14%2C+2023%2E+Id%2FNo+102009%2E)
14. B. Ballinger, G. Blekherman, H. Cohn, N. Giansiracusa, E. Kelly, and A. Schürmann. Experimental study of energy-minimizing point configurations on spheres. Experimental Mathematics, 18:257–283, 2009. [find](https://scholar.google.com/scholar?q=B%2E+Ballinger%2C+G%2E+Blekherman%2C+H%2E+Cohn%2C+N%2E+Giansiracusa%2C+E%2E+Kelly%2C+and+A%2E+Sch%C3%BCrmann%2E+Experimental+study+of+energy%2Dminimizing+point+configurations+on+spheres%2E+Experimental+Mathematics%2C+18%3A257%E2%80%93283%2C+2009%2E)
15. Bradon Ballinger, Grigoriy Blekherman, Henry Cohn, Noah Giansiracusa, Elizabeth Kelly, and Achill Schürmann. Minimal Energy Configurations for N Points on a Sphere in n Dimensions. [https://aimath.org/data/paper/BBCGKS2006/](https://aimath.org/data/paper/BBCGKS2006/), 2006. [↗](https://aimath.org/data/paper/BBCGKS2006/)
16. Taras O Banakh and Volodymyr M Gavrylkiv. Difference bases in cyclic groups. Journal of Algebra and Its Applications, 18(05):1950081, 2019. [find](https://scholar.google.com/scholar?q=Taras+O+Banakh+and+Volodymyr+M+Gavrylkiv%2E+Difference+bases+in+cyclic+groups%2E+Journal+of+Algebra+and+Its+Applications%2C+18%2805%29%3A1950081%2C+2019%2E)
17. R. C. Barnard and S. Steinerberger. Three convolution inequalities on the real line with connections to additive combinatorics. Journal of Number Theory, 207:42–55, 2020. [find](https://scholar.google.com/scholar?q=R%2E+C%2E+Barnard+and+S%2E+Steinerberger%2E+Three+convolution+inequalities+on+the+real+line+with+connections+to+additive+combinatorics%2E+Journal+of+Number+Theory%2C+207%3A42%E2%80%9355%2C+2020%2E)
18. Paul Bateman and Paul Erdős. Geometrical extrema suggested by a lemma of Besicovitch. American Mathematical Monthly, 58:306– 314, 1951. [find](https://scholar.google.com/scholar?q=Paul+Bateman+and+Paul+Erd%C5%91s%2E+Geometrical+extrema+suggested+by+a+lemma+of+Besicovitch%2E+American+Mathematical+Monthly%2C+58%3A306%E2%80%93+314%2C+1951%2E)
19. A. F. Beardon, D. Minda, and T. W. Ng. Smale’s mean value conjecture and the hyperbolic metric. Mathematische Annalen, 332:623– 632, 2002. [find](https://scholar.google.com/scholar?q=A%2E+F%2E+Beardon%2C+D%2E+Minda%2C+and+T%2E+W%2E+Ng%2E+Smale%E2%80%99s+mean+value+conjecture+and+the+hyperbolic+metric%2E+Mathematische+Annalen%2C+332%3A623%E2%80%93+632%2C+2002%2E)
20. W. Beckner. Inequalities in Fourier analysis. Annals of Mathematics, 102(1):159–182, 1975. [find](https://scholar.google.com/scholar?q=W%2E+Beckner%2E+Inequalities+in+Fourier+analysis%2E+Annals+of+Mathematics%2C+102%281%29%3A159%E2%80%93182%2C+1975%2E)
21. Pierre C. Bellec and Tobias Fritz. Optimizing over iid distributions and the beat the average game, 2024. arXiv:2412.15179. — [arXiv:2412.15179](https://arxiv.org/abs/2412.15179) [find](https://scholar.google.com/scholar?q=Pierre+C%2E+Bellec+and+Tobias+Fritz%2E+Optimizing+over+iid+distributions+and+the+beat+the+average+game%2C+2024%2E+arXiv%3A2412%2E15179%2E+%E2%80%94+%5BarXiv%3A2412%2E15179%5D%28https%3A%2F%2Farxiv%2Eorg%2Fabs%2F2412%2E15179%29)
22. R. D. Benguria and M. Loss. Connection between the Lieb-Thirring conjecture for Schrödinger operators and an isoperimetric problem for ovals on the plane. Contemporary Mathematics, 362:53–61, 2004. [find](https://scholar.google.com/scholar?q=R%2E+D%2E+Benguria+and+M%2E+Loss%2E+Connection+between+the+Lieb%2DThirring+conjecture+for+Schr%C3%B6dinger+operators+and+an+isoperimetric+problem+for+ovals+on+the+plane%2E+Contemporary+Mathematics%2C+362%3A53%E2%80%9361%2C+2004%2E)
23. C. Berger. A strange dilation theorem. Notices of the American Mathematical Society, 12:590, 1965. Abstract 625–152. [find](https://scholar.google.com/scholar?q=C%2E+Berger%2E+A+strange+dilation+theorem%2E+Notices+of+the+American+Mathematical+Society%2C+12%3A590%2C+1965%2E+Abstract+625%E2%80%93152%2E)
24. J. D. Berman and K. Hanes. Volumes of polyhedra inscribed in the unit sphere in 𝐸 3 . Mathematische Annalen, 188:78–84, 1970. [find](https://scholar.google.com/scholar?q=J%2E+D%2E+Berman+and+K%2E+Hanes%2E+Volumes+of+polyhedra+inscribed+in+the+unit+sphere+in+%F0%9D%90%B8+3+%2E+Mathematische+Annalen%2C+188%3A78%E2%80%9384%2C+1970%2E)
25. Timo Berthold. Best Global Optimization Solver. FICO Blog, June 2025. Accessed September 5, 2025. [find](https://scholar.google.com/scholar?q=Timo+Berthold%2E+Best+Global+Optimization+Solver%2E+FICO+Blog%2C+June+2025%2E+Accessed+September+5%2C+2025%2E)
26. A. Bezdek. On the number of mutually touching cylinders. In Combinatorial and Computational Geometry, volume 52 of MSRI Publication, pages 121–127. 2005. [find](https://scholar.google.com/scholar?q=A%2E+Bezdek%2E+On+the+number+of+mutually+touching+cylinders%2E+In+Combinatorial+and+Computational+Geometry%2C+volume+52+of+MSRI+Publication%2C+pages+121%E2%80%93127%2E+2005%2E)
27. András Bezdek and Ferenc Fodor. Extremal point sets. Proceedings of the American Mathematical Society, 127(1):165–173, 1999. [find](https://scholar.google.com/scholar?q=Andr%C3%A1s+Bezdek+and+Ferenc+Fodor%2E+Extremal+point+sets%2E+Proceedings+of+the+American+Mathematical+Society%2C+127%281%29%3A165%E2%80%93173%2C+1999%2E)
28. A. Bezikovič. Sur deux questions de l’intégrabilité des fonctions. J. Soc. Phys. Math. Univ. Perm, 2:105–123, 1919. [find](https://scholar.google.com/scholar?q=A%2E+Bezikovi%C4%8D%2E+Sur+deux+questions+de+l%E2%80%99int%C3%A9grabilit%C3%A9+des+fonctions%2E+J%2E+Soc%2E+Phys%2E+Math%2E+Univ%2E+Perm%2C+2%3A105%E2%80%93123%2C+1919%2E)
29. R. Bhatia. Positive Definite Matrices. Princeton Series in Applied Mathematics. Princeton University Press, Princeton, NJ, 2007. [find](https://scholar.google.com/scholar?q=R%2E+Bhatia%2E+Positive+Definite+Matrices%2E+Princeton+Series+in+Applied+Mathematics%2E+Princeton+University+Press%2C+Princeton%2C+NJ%2C+2007%2E)
30. R. Bhatia and F. Kittaneh. The matrix arithmetic-geometric mean inequality revisited. Linear Algebra and its Applications, 428(8– 9):2177–2191, 2008. [find](https://scholar.google.com/scholar?q=R%2E+Bhatia+and+F%2E+Kittaneh%2E+The+matrix+arithmetic%2Dgeometric+mean+inequality+revisited%2E+Linear+Algebra+and+its+Applications%2C+428%288%E2%80%93+9%29%3A2177%E2%80%932191%2C+2008%2E)
31. A. Blokhuis, A. E. Brouwer, D. Jungnickel, V. Krčadinac, S. Rottey, L. Storme, T. Szőnyi, and P. Vandendriessche. Blocking sets of the classical unital. Finite Fields Appl., 35:1–15, 2015. [find](https://scholar.google.com/scholar?q=A%2E+Blokhuis%2C+A%2E+E%2E+Brouwer%2C+D%2E+Jungnickel%2C+V%2E+Kr%C4%8Dadinac%2C+S%2E+Rottey%2C+L%2E+Storme%2C+T%2E+Sz%C5%91nyi%2C+and+P%2E+Vandendriessche%2E+Blocking+sets+of+the+classical+unital%2E+Finite+Fields+Appl%2E%2C+35%3A1%E2%80%9315%2C+2015%2E)
32. Aart Blokhuis and Francesco Mazzocca. The finite field Kakeya problem. In Building bridges. Between mathematics and computer science. Selected papers of the conferences held in Budapest, Hungary, August 5–9, 2008 and Keszthely, Hungary, August 11–15, 2008 and other research papers dedicated to Lászl… [find](https://scholar.google.com/scholar?q=Aart+Blokhuis+and+Francesco+Mazzocca%2E+The+finite+field+Kakeya+problem%2E+In+Building+bridges%2E+Between+mathematics+and+computer+science%2E+Selected+papers+of+the+conferences+held+in+Budapest%2C+Hungary%2C+Augu)
33. Thomas F. Bloom. A history of the sum-product problem. [http://thomasbloom.org/notes/sumproduct.html](http://thomasbloom.org/notes/sumproduct.html), 2024. Online survey notes. [↗](http://thomasbloom.org/notes/sumproduct.html)
34. Thomas F. Bloom. Control and its applications in additive combinatorics, 2025. arXiv:2501.09470. — [arXiv:2501.09470](https://arxiv.org/abs/2501.09470) [find](https://scholar.google.com/scholar?q=Thomas+F%2E+Bloom%2E+Control+and+its+applications+in+additive+combinatorics%2C+2025%2E+arXiv%3A2501%2E09470%2E+%E2%80%94+%5BarXiv%3A2501%2E09470%5D%28https%3A%2F%2Farxiv%2Eorg%2Fabs%2F2501%2E09470%29)
35. B. D. Bojanov, Q. I. Rahman, and J. Szynal. On a conjecture of Sendov about the critical points of a polynomial. Mathematische Zeitschrift, 190(2):281–285, 1985. [find](https://scholar.google.com/scholar?q=B%2E+D%2E+Bojanov%2C+Q%2E+I%2E+Rahman%2C+and+J%2E+Szynal%2E+On+a+conjecture+of+Sendov+about+the+critical+points+of+a+polynomial%2E+Mathematische+Zeitschrift%2C+190%282%29%3A281%E2%80%93285%2C+1985%2E)
36. Béla Bollobás. Relations between sets of complete subgraphs. In C. St.J. A. Nash-Williams and J. Sheehan, editors, Proceedings of the Fifth British Combinatorial Conference, number XV in Congressus Numerantium, pages 79–84, Winnipeg, 1976. Utilitas Mathematica Publishing. [find](https://scholar.google.com/scholar?q=B%C3%A9la+Bollob%C3%A1s%2E+Relations+between+sets+of+complete+subgraphs%2E+In+C%2E+St%2EJ%2E+A%2E+Nash%2DWilliams+and+J%2E+Sheehan%2C+editors%2C+Proceedings+of+the+Fifth+British+Combinatorial+Conference%2C+number+XV+in+Congressus+Nu)
37. Andriy Bondarenko, Danylo Radchenko, and Maryna Viazovska. Optimal asymptotic bounds for spherical designs. Annals of Mathematics, 178(2):443–452, 2013. [find](https://scholar.google.com/scholar?q=Andriy+Bondarenko%2C+Danylo+Radchenko%2C+and+Maryna+Viazovska%2E+Optimal+asymptotic+bounds+for+spherical+designs%2E+Annals+of+Mathematics%2C+178%282%29%3A443%E2%80%93452%2C+2013%2E)
38. Iulius Borcea. The Sendov conjecture for polynomials with at most seven distinct zeros. Analysis, 16:137–159, 1996. [find](https://scholar.google.com/scholar?q=Iulius+Borcea%2E+The+Sendov+conjecture+for+polynomials+with+at+most+seven+distinct+zeros%2E+Analysis%2C+16%3A137%E2%80%93159%2C+1996%2E)
39. P. Borwein and M. J. Mossinghoff. Barker sequences and flat polynomials. In Number theory and polynomials, volume 352 of London Mathematical Society Lecture Note Series, pages 71–88. Cambridge University Press, Cambridge, 2008. [find](https://scholar.google.com/scholar?q=P%2E+Borwein+and+M%2E+J%2E+Mossinghoff%2E+Barker+sequences+and+flat+polynomials%2E+In+Number+theory+and+polynomials%2C+volume+352+of+London+Mathematical+Society+Lecture+Note+Series%2C+pages+71%E2%80%9388%2E+Cambridge+Univers)
40. J. Bourgain. Applications of the spaces of homogeneous polynomials to some problems on the ball algebra. Proceedings of the American Mathematical Society, 93(2):277–283, feb 1985. [find](https://scholar.google.com/scholar?q=J%2E+Bourgain%2E+Applications+of+the+spaces+of+homogeneous+polynomials+to+some+problems+on+the+ball+algebra%2E+Proceedings+of+the+American+Mathematical+Society%2C+93%282%29%3A277%E2%80%93283%2C+feb+1985%2E)
41. Jean Bourgain. On uniformly bounded bases in spaces of holomorphic functions. American Journal of Mathematics, 138(2):571–584, 2016. [find](https://scholar.google.com/scholar?q=Jean+Bourgain%2E+On+uniformly+bounded+bases+in+spaces+of+holomorphic+functions%2E+American+Journal+of+Mathematics%2C+138%282%29%3A571%E2%80%93584%2C+2016%2E)
42. Christopher Boyer and Zane Kun Li. An improved example for an autoconvolution inequality, 2025. arXiv:2506.16750. — [arXiv:2506.16750](https://arxiv.org/abs/2506.16750) [find](https://scholar.google.com/scholar?q=Christopher+Boyer+and+Zane+Kun+Li%2E+An+improved+example+for+an+autoconvolution+inequality%2C+2025%2E+arXiv%3A2506%2E16750%2E+%E2%80%94+%5BarXiv%3A2506%2E16750%5D%28https%3A%2F%2Farxiv%2Eorg%2Fabs%2F2506%2E16750%29)
43. Sándor Bozóki, Tsung-Lin Lee, and Lajos Rónyai. Seven mutually touching infinite cylinders. Computational Geometry, 48(2):87–93, 2014. [find](https://scholar.google.com/scholar?q=S%C3%A1ndor+Boz%C3%B3ki%2C+Tsung%2DLin+Lee%2C+and+Lajos+R%C3%B3nyai%2E+Seven+mutually+touching+infinite+cylinders%2E+Computational+Geometry%2C+48%282%29%3A87%E2%80%9393%2C+2014%2E)
44. Peter Brass, William O. J. Moser, and János Pach. Research Problems in Discrete Geometry. Springer, New York, 2005. Corrected 2nd printing 2006. [find](https://scholar.google.com/scholar?q=Peter+Brass%2C+William+O%2E+J%2E+Moser%2C+and+J%C3%A1nos+Pach%2E+Research+Problems+in+Discrete+Geometry%2E+Springer%2C+New+York%2C+2005%2E+Corrected+2nd+printing+2006%2E)
45. Peter Brass, William OJ Moser, and János Pach. Research problems in discrete geometry. Springer, 2005. [find](https://scholar.google.com/scholar?q=Peter+Brass%2C+William+OJ+Moser%2C+and+J%C3%A1nos+Pach%2E+Research+problems+in+discrete+geometry%2E+Springer%2C+2005%2E)
46. J. E. Brown. On the Sendov Conjecture for sixth degree polynomials. Proceedings of the American Mathematical Society, 113:939– 946, 1991. [find](https://scholar.google.com/scholar?q=J%2E+E%2E+Brown%2E+On+the+Sendov+Conjecture+for+sixth+degree+polynomials%2E+Proceedings+of+the+American+Mathematical+Society%2C+113%3A939%E2%80%93+946%2C+1991%2E)
47. J. E. Brown. A proof of the Sendov Conjecture for polynomials of degree seven. Complex Variables Theory and Application, 33:75–95, 1997. [find](https://scholar.google.com/scholar?q=J%2E+E%2E+Brown%2E+A+proof+of+the+Sendov+Conjecture+for+polynomials+of+degree+seven%2E+Complex+Variables+Theory+and+Application%2C+33%3A75%E2%80%9395%2C+1997%2E)
48. J. E. Brown and G. Xiang. Proof of the Sendov conjecture for polynomials of degree at most eight. Journal of Mathematical Analysis and Applications, 232:272–292, 1999. [find](https://scholar.google.com/scholar?q=J%2E+E%2E+Brown+and+G%2E+Xiang%2E+Proof+of+the+Sendov+conjecture+for+polynomials+of+degree+at+most+eight%2E+Journal+of+Mathematical+Analysis+and+Applications%2C+232%3A272%E2%80%93292%2C+1999%2E)
49. Boris Bukh and Ting-Wei Chao. Sharp density bounds on the finite field Kakeya problem. Discrete Anal., 2021:9, 2021. Id/No 26. [find](https://scholar.google.com/scholar?q=Boris+Bukh+and+Ting%2DWei+Chao%2E+Sharp+density+bounds+on+the+finite+field+Kakeya+problem%2E+Discrete+Anal%2E%2C+2021%3A9%2C+2021%2E+Id%2FNo+26%2E)
50. A. Burchard and L. E. Thomas. On the Cauchy problem for a dynamical Euler’s elastica. Communications in Partial Differential Equations, 28:271–300, 2003. [find](https://scholar.google.com/scholar?q=A%2E+Burchard+and+L%2E+E%2E+Thomas%2E+On+the+Cauchy+problem+for+a+dynamical+Euler%E2%80%99s+elastica%2E+Communications+in+Partial+Differential+Equations%2C+28%3A271%E2%80%93300%2C+2003%2E)
51. A. Burchard and L. E. Thomas. On an isoperimetric inequality for a Schrödinger operator depending on the curvature of a loop. The Journal of Geometric Analysis, 15(4), 2005. [find](https://scholar.google.com/scholar?q=A%2E+Burchard+and+L%2E+E%2E+Thomas%2E+On+an+isoperimetric+inequality+for+a+Schr%C3%B6dinger+operator+depending+on+the+curvature+of+a+loop%2E+The+Journal+of+Geometric+Analysis%2C+15%284%29%2C+2005%2E)
52. Connie M. Campbell and William Staton. A Square-Packing Problem of Erdős. The American Mathematical Monthly, 112(2):165– 167, 2005. [find](https://scholar.google.com/scholar?q=Connie+M%2E+Campbell+and+William+Staton%2E+A+Square%2DPacking+Problem+of+Erd%C5%91s%2E+The+American+Mathematical+Monthly%2C+112%282%29%3A165%E2%80%93+167%2C+2005%2E)
53. David Cantrell. Optimal configurations for the Heilbronn problem in convex regions, June 2007. [find](https://scholar.google.com/scholar?q=David+Cantrell%2E+Optimal+configurations+for+the+Heilbronn+problem+in+convex+regions%2C+June+2007%2E)
54. David Cantrell. Point configurations in 3D space minimizing maximum to minimum distance ratio, March 2009. [find](https://scholar.google.com/scholar?q=David+Cantrell%2E+Point+configurations+in+3D+space+minimizing+maximum+to+minimum+distance+ratio%2C+March+2009%2E)
55. David Cantrell. Point configurations minimizing maximum to minimum distance ratio, February 2009. [find](https://scholar.google.com/scholar?q=David+Cantrell%2E+Point+configurations+minimizing+maximum+to+minimum+distance+ratio%2C+February+2009%2E)
56. François Charton, Jordan S. Ellenberg, Adam Zsolt Wagner, and Geordie Williamson. PatternBoost: Constructions in Mathematics with a Little Help from AI. arXiv preprint arXiv:2411.00566, 2024. — [arXiv:2411.00566](https://arxiv.org/abs/2411.00566) [find](https://scholar.google.com/scholar?q=Fran%C3%A7ois+Charton%2C+Jordan+S%2E+Ellenberg%2C+Adam+Zsolt+Wagner%2C+and+Geordie+Williamson%2E+PatternBoost%3A+Constructions+in+Mathematics+with+a+Little+Help+from+AI%2E+arXiv+preprint+arXiv%3A2411%2E00566%2C+2024%2E+%E2%80%94+%5BarXiv)
57. P. L. Chebyshev. Mémoire sur les nombres premiers. Journal de Mathématiques Pures et Appliquées, 17:366–490, 1852. Also in Mémoires présentés à l’Académie Impériale des sciences de St.-Pétersbourg par divers savants 7 (1854), 15–33. Also in Oeuvres 1 (1899), 49–70. [find](https://scholar.google.com/scholar?q=P%2E+L%2E+Chebyshev%2E+M%C3%A9moire+sur+les+nombres+premiers%2E+Journal+de+Math%C3%A9matiques+Pures+et+Appliqu%C3%A9es%2C+17%3A366%E2%80%93490%2C+1852%2E+Also+in+M%C3%A9moires+pr%C3%A9sent%C3%A9s+%C3%A0+l%E2%80%99Acad%C3%A9mie+Imp%C3%A9riale+des+sciences+de+St%2E%2DP%C3%A9tersbourg+par)
58. W. Cheung and T. Ng. A companion matrix approach to the study of zeros and critical points of a polynomial. Journal of Mathematical Analysis and Applications, 319:690–707, 2006. [find](https://scholar.google.com/scholar?q=W%2E+Cheung+and+T%2E+Ng%2E+A+companion+matrix+approach+to+the+study+of+zeros+and+critical+points+of+a+polynomial%2E+Journal+of+Mathematical+Analysis+and+Applications%2C+319%3A690%E2%80%93707%2C+2006%2E)
59. A. Cloninger and S. Steinerberger. On suprema of autoconvolutions with an application to Sidon sets. Proceedings of the American Mathematical Society, 145(8):3191–3200, 2017. [find](https://scholar.google.com/scholar?q=A%2E+Cloninger+and+S%2E+Steinerberger%2E+On+suprema+of+autoconvolutions+with+an+application+to+Sidon+sets%2E+Proceedings+of+the+American+Mathematical+Society%2C+145%288%29%3A3191%E2%80%933200%2C+2017%2E)
60. Alex Cohen, Cosmin Pohoata, and Dmitrii Zakharov. Lower bounds for incidences, 2024. arXiv:2409.07658. — [arXiv:2409.07658](https://arxiv.org/abs/2409.07658) [find](https://scholar.google.com/scholar?q=Alex+Cohen%2C+Cosmin+Pohoata%2C+and+Dmitrii+Zakharov%2E+Lower+bounds+for+incidences%2C+2024%2E+arXiv%3A2409%2E07658%2E+%E2%80%94+%5BarXiv%3A2409%2E07658%5D%28https%3A%2F%2Farxiv%2Eorg%2Fabs%2F2409%2E07658%29)
61. H. Cohn and N. Elkies. New upper bounds on sphere packings I. Annals of Mathematics, 157(2):689–714, 2003. [find](https://scholar.google.com/scholar?q=H%2E+Cohn+and+N%2E+Elkies%2E+New+upper+bounds+on+sphere+packings+I%2E+Annals+of+Mathematics%2C+157%282%29%3A689%E2%80%93714%2C+2003%2E)
62. H. Cohn and F. Gonçalves. An optimal uncertainty principle in twelve dimensions via modular forms. Inventiones Mathematicae, 217(3):799–831, 2019. [find](https://scholar.google.com/scholar?q=H%2E+Cohn+and+F%2E+Gon%C3%A7alves%2E+An+optimal+uncertainty+principle+in+twelve+dimensions+via+modular+forms%2E+Inventiones+Mathematicae%2C+217%283%29%3A799%E2%80%93831%2C+2019%2E)
63. Harvey Cohn. Stability Configurations of Electrons on a Sphere. Mathematical Tables and Other Aids to Computation, 10(55):117– 120, 1956. [find](https://scholar.google.com/scholar?q=Harvey+Cohn%2E+Stability+Configurations+of+Electrons+on+a+Sphere%2E+Mathematical+Tables+and+Other+Aids+to+Computation%2C+10%2855%29%3A117%E2%80%93+120%2C+1956%2E)
64. Henry Cohn. Order and disorder in energy minimization. Proceedings of the International Congress of Mathematicians, 4:2416–2443, 2010. [find](https://scholar.google.com/scholar?q=Henry+Cohn%2E+Order+and+disorder+in+energy+minimization%2E+Proceedings+of+the+International+Congress+of+Mathematicians%2C+4%3A2416%E2%80%932443%2C+2010%2E)
65. Henry Cohn. Table of spherical codes. MIT DSpace, 2023. Dataset archiving spherical codes with up to 1024 points in up to 32 dimensions. [find](https://scholar.google.com/scholar?q=Henry+Cohn%2E+Table+of+spherical+codes%2E+MIT+DSpace%2C+2023%2E+Dataset+archiving+spherical+codes+with+up+to+1024+points+in+up+to+32+dimensions%2E)
66. Henry Cohn. Table of Kissing Number Bounds. MIT DSpace, 2025. [find](https://scholar.google.com/scholar?q=Henry+Cohn%2E+Table+of+Kissing+Number+Bounds%2E+MIT+DSpace%2C+2025%2E)
67. Henry Cohn and Abhinav Kumar. Universally Optimal Distribution of Points on Spheres. Journal of the American Mathematical Society, 20(1):99–148, 2007. [find](https://scholar.google.com/scholar?q=Henry+Cohn+and+Abhinav+Kumar%2E+Universally+Optimal+Distribution+of+Points+on+Spheres%2E+Journal+of+the+American+Mathematical+Society%2C+20%281%29%3A99%E2%80%93148%2C+2007%2E)
68. Henry Cohn, Abhinav Kumar, Stephen D. Miller, Danylo Radchenko, and Maryna Viazovska. The sphere packing problem in dimension 24. Annals of Mathematics, 185(3):1017–1033, 2017. [find](https://scholar.google.com/scholar?q=Henry+Cohn%2C+Abhinav+Kumar%2C+Stephen+D%2E+Miller%2C+Danylo+Radchenko%2C+and+Maryna+Viazovska%2E+The+sphere+packing+problem+in+dimension+24%2E+Annals+of+Mathematics%2C+185%283%29%3A1017%E2%80%931033%2C+2017%2E)
69. Henry Cohn and Anqi Li. Improved kissing numbers in seventeen through twenty-one dimensions. arXiv:2411.04916, 2024. — [arXiv:2411.04916](https://arxiv.org/abs/2411.04916) [find](https://scholar.google.com/scholar?q=Henry+Cohn+and+Anqi+Li%2E+Improved+kissing+numbers+in+seventeen+through+twenty%2Done+dimensions%2E+arXiv%3A2411%2E04916%2C+2024%2E+%E2%80%94+%5BarXiv%3A2411%2E04916%5D%28https%3A%2F%2Farxiv%2Eorg%2Fabs%2F2411%2E04916%29)
70. Katherine M. Collins, Albert Q. Jiang, Simon Frieder, Lionel Wong, Miri Zilka, Umang Bhatt, Thomas Lukasiewicz, Yuhuai Wu, Joshua B. Tenenbaum, William Hart, Timothy Gowers, Wenda Li, Adrian Weller, and Mateja Jamnik. [Evaluating language models for mathematics through interactions](https://md.research.elamur.ai/free/en/papers/collins-2023-evaluating-language-models-mathematics-through/). Proceedings of th…
71. Gheorghe Comanici, Eric Bieber, Mike Schaekermann, Ice Pasupat, Noveen Sachdeva, Inderjit Dhillon, Marcel Blistein, Ori Ram, Dan Zhang, Evan Rosen, et al. [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://md.research.elamur.ai/free/en/papers/comanici-2025-gemini-2-5-pushing-frontier/). arXiv preprint a…
72. David Conlon, Jacob Fox, and Benny Sudakov. An approximate version of Sidorenko’s conjecture. Geometric and Functional Analysis, 20:1354–1366, 2010. [find](https://scholar.google.com/scholar?q=David+Conlon%2C+Jacob+Fox%2C+and+Benny+Sudakov%2E+An+approximate+version+of+Sidorenko%E2%80%99s+conjecture%2E+Geometric+and+Functional+Analysis%2C+20%3A1354%E2%80%931366%2C+2010%2E)
73. David Conlon, Jeong Han Kim, Choongbum Lee, and Joonkyung Lee. Sidorenko’s conjecture for higher tree decompositions, 2018. Unpublished note. [find](https://scholar.google.com/scholar?q=David+Conlon%2C+Jeong+Han+Kim%2C+Choongbum+Lee%2C+and+Joonkyung+Lee%2E+Sidorenko%E2%80%99s+conjecture+for+higher+tree+decompositions%2C+2018%2E+Unpublished+note%2E)
74. David Conlon, Jeong Han Kim, Choongbum Lee, and Joonkyung Lee. Some advances on Sidorenko’s conjecture. Journal of the London Mathematical Society, 98(2):593–608, 2018. [find](https://scholar.google.com/scholar?q=David+Conlon%2C+Jeong+Han+Kim%2C+Choongbum+Lee%2C+and+Joonkyung+Lee%2E+Some+advances+on+Sidorenko%E2%80%99s+conjecture%2E+Journal+of+the+London+Mathematical+Society%2C+98%282%29%3A593%E2%80%93608%2C+2018%2E)
75. David Conlon and Joonkyung Lee. Sidorenko’s conjecture for blow-ups. Discrete Analysis, 2021(2):13, 2021. [find](https://scholar.google.com/scholar?q=David+Conlon+and+Joonkyung+Lee%2E+Sidorenko%E2%80%99s+conjecture+for+blow%2Dups%2E+Discrete+Analysis%2C+2021%282%29%3A13%2C+2021%2E)
76. A. Conte, E. Fujikawa, and N. Lakic. Smale’s mean value conjecture and the coefficients of univalent functions. Proceedings of the American Mathematical Society, 135(12):3819–3833, 2007. [find](https://scholar.google.com/scholar?q=A%2E+Conte%2C+E%2E+Fujikawa%2C+and+N%2E+Lakic%2E+Smale%E2%80%99s+mean+value+conjecture+and+the+coefficients+of+univalent+functions%2E+Proceedings+of+the+American+Mathematical+Society%2C+135%2812%29%3A3819%E2%80%933833%2C+2007%2E)
77. Kris Coolsaet, Sven D’hondt, and Jan Goedgebeur. House of Graphs 2.0: A database of interesting graphs and more. Discrete Applied Mathematics, 325:97–107, 2023. [find](https://scholar.google.com/scholar?q=Kris+Coolsaet%2C+Sven+D%E2%80%99hondt%2C+and+Jan+Goedgebeur%2E+House+of+Graphs+2%2E0%3A+A+database+of+interesting+graphs+and+more%2E+Discrete+Applied+Mathematics%2C+325%3A97%E2%80%93107%2C+2023%2E)
78. Antonio Cordoba. The Kakeya maximal function and the spherical summation multipliers. Am. J. Math., 99:1–22, 1977. [find](https://scholar.google.com/scholar?q=Antonio+Cordoba%2E+The+Kakeya+maximal+function+and+the+spherical+summation+multipliers%2E+Am%2E+J%2E+Math%2E%2C+99%3A1%E2%80%9322%2C+1977%2E)
79. Steve Cosares and Iraj Saniee. An optimization problem related to balancing loads on SONET rings. Telecommunication Systems, 3(2):165–181, 1994. [find](https://scholar.google.com/scholar?q=Steve+Cosares+and+Iraj+Saniee%2E+An+optimization+problem+related+to+balancing+loads+on+SONET+rings%2E+Telecommunication+Systems%2C+3%282%29%3A165%E2%80%93181%2C+1994%2E)
80. E. Crane. A bound for Smale’s mean value conjecture for complex polynomials. Bulletin of the London Mathematical Society, 39:781– 791, 2007. [find](https://scholar.google.com/scholar?q=E%2E+Crane%2E+A+bound+for+Smale%E2%80%99s+mean+value+conjecture+for+complex+polynomials%2E+Bulletin+of+the+London+Mathematical+Society%2C+39%3A781%E2%80%93+791%2C+2007%2E)
81. Hallard T. Croft, Kenneth J. Falconer, and Richard K. Guy. Unsolved Problems in Geometry, volume 2. Springer, New York, 1991. [find](https://scholar.google.com/scholar?q=Hallard+T%2E+Croft%2C+Kenneth+J%2E+Falconer%2C+and+Richard+K%2E+Guy%2E+Unsolved+Problems+in+Geometry%2C+volume+2%2E+Springer%2C+New+York%2C+1991%2E)
82. Michel Crouzeix. Bounds for Analytical Functions of Matrices. Integral √ Equations and Operator Theory, 48(4):461–477, 2004. [find](https://scholar.google.com/scholar?q=Michel+Crouzeix%2E+Bounds+for+Analytical+Functions+of+Matrices%2E+Integral+%E2%88%9A+Equations+and+Operator+Theory%2C+48%284%29%3A461%E2%80%93477%2C+2004%2E)
83. Michel Crouzeix and César Palencia. The Numerical Range is a (1 + 2)-Spectral Set. SIAM Journal on Matrix Analysis and Applications, 38:649–655, 2017. [find](https://scholar.google.com/scholar?q=Michel+Crouzeix+and+C%C3%A9sar+Palencia%2E+The+Numerical+Range+is+a+%281+%2B+2%29%2DSpectral+Set%2E+SIAM+Journal+on+Matrix+Analysis+and+Applications%2C+38%3A649%E2%80%93655%2C+2017%2E)
84. Orval R. Cruzan. Translational addition theorems for spherical vector wave functions. Quarterly of Applied Mathematics, 20(1):33–40, 1962. [find](https://scholar.google.com/scholar?q=Orval+R%2E+Cruzan%2E+Translational+addition+theorems+for+spherical+vector+wave+functions%2E+Quarterly+of+Applied+Mathematics%2C+20%281%29%3A33%E2%80%9340%2C+1962%2E)
85. Gabriel Currier. Sharp Szemerédi-Trotter constructions from arbitrary number fields, 2023. arXiv:2304.04900. — [arXiv:2304.04900](https://arxiv.org/abs/2304.04900) [find](https://scholar.google.com/scholar?q=Gabriel+Currier%2E+Sharp+Szemer%C3%A9di%2DTrotter+constructions+from+arbitrary+number+fields%2C+2023%2E+arXiv%3A2304%2E04900%2E+%E2%80%94+%5BarXiv%3A2304%2E04900%5D%28https%3A%2F%2Farxiv%2Eorg%2Fabs%2F2304%2E04900%29)
86. L. Danzer. Finite Point-Sets on 𝑆 2 with Minimum Distance as Large as Possible. Discrete Mathematics, 60:3–66, 1986. [find](https://scholar.google.com/scholar?q=L%2E+Danzer%2E+Finite+Point%2DSets+on+%F0%9D%91%86+2+with+Minimum+Distance+as+Large+as+Possible%2E+Discrete+Mathematics%2C+60%3A3%E2%80%9366%2C+1986%2E)
87. Alex Davies, Petar Veličković, Lars Buesing, Sam Blackwell, Daniel Zheng, Nenad Tomašev, Richard Tanburn, Peter Battaglia, Charles Blundell, András Juhász, Marc Lackenby, Geordie Williamson, Demis Hassabis, and Pushmeet Kohli. Advancing mathematics by guiding human intuition with AI. Nature, 600(788… [find](https://scholar.google.com/scholar?q=Alex+Davies%2C+Petar+Veli%C4%8Dkovi%C4%87%2C+Lars+Buesing%2C+Sam+Blackwell%2C+Daniel+Zheng%2C+Nenad+Toma%C5%A1ev%2C+Richard+Tanburn%2C+Peter+Battaglia%2C+Charles+Blundell%2C+Andr%C3%A1s+Juh%C3%A1sz%2C+Marc+Lackenby%2C+Geordie+Williamson%2C+Demis+Has)
88. Damek Davis. AlphaEvolve. [https://x.com/damekdavis/status/1923031798163857814](https://x.com/damekdavis/status/1923031798163857814), May 2025. Twitter/X thread. [↗](https://x.com/damekdavis/status/1923031798163857814)
89. M. G. de Bruin and A. Sharma. On a Schoenberg-type conjecture. Journal of Computational and Applied Mathematics, 105:221–228, 1999. Continued Fractions and Geometric Function Theory (CONFUN), Trondheim, 1997. [find](https://scholar.google.com/scholar?q=M%2E+G%2E+de+Bruin+and+A%2E+Sharma%2E+On+a+Schoenberg%2Dtype+conjecture%2E+Journal+of+Computational+and+Applied+Mathematics%2C+105%3A221%E2%80%93228%2C+1999%2E+Continued+Fractions+and+Geometric+Function+Theory+%28CONFUN%29%2C+Trondhei)
90. J. de Dios Pont and J. Madrid. On classical inequalities for autocorrelations and autoconvolutions, 2021. arXiv:2106.13873. — [arXiv:2106.13873](https://arxiv.org/abs/2106.13873) [find](https://scholar.google.com/scholar?q=J%2E+de+Dios+Pont+and+J%2E+Madrid%2E+On+classical+inequalities+for+autocorrelations+and+autoconvolutions%2C+2021%2E+arXiv%3A2106%2E13873%2E+%E2%80%94+%5BarXiv%3A2106%2E13873%5D%28https%3A%2F%2Farxiv%2Eorg%2Fabs%2F2106%2E13873%29)
91. P. Delsarte, J. M. Goethals, and J. J. Seidel. Spherical codes and designs. Geometriae Dedicata, 6(3):363–388, 1977. [find](https://scholar.google.com/scholar?q=P%2E+Delsarte%2C+J%2E+M%2E+Goethals%2C+and+J%2E+J%2E+Seidel%2E+Spherical+codes+and+designs%2E+Geometriae+Dedicata%2C+6%283%29%3A363%E2%80%93388%2C+1977%2E)
92. Philippe Delsarte. Bounds for unrestricted codes, by linear programming. Philips Research Reports, 27:272–289, 1972. [find](https://scholar.google.com/scholar?q=Philippe+Delsarte%2E+Bounds+for+unrestricted+codes%2C+by+linear+programming%2E+Philips+Research+Reports%2C+27%3A272%E2%80%93289%2C+1972%2E)
93. Erik D. Demaine, Sándor P. Fekete, and Robert J. Lang. Circle packing for origami design is hard. In Origami5: Proceedings of the 5th International Conference on Origami in Science, Mathematics and Education (OSME 2010), pages 609–626, Singapore, 2010. A K Peters. July 13–17, 2010. [find](https://scholar.google.com/scholar?q=Erik+D%2E+Demaine%2C+S%C3%A1ndor+P%2E+Fekete%2C+and+Robert+J%2E+Lang%2E+Circle+packing+for+origami+design+is+hard%2E+In+Origami5%3A+Proceedings+of+the+5th+International+Conference+on+Origami+in+Science%2C+Mathematics+and+Ed)
94. Arnaud Deza. Comment on: Seems a new circle packing result (2.635977) when reproducing your example. GitHub Comment, 2025. Comment \#3156455197 on Issue \#156, OpenEvolve repository by codelion. [find](https://scholar.google.com/scholar?q=Arnaud+Deza%2E+Comment+on%3A+Seems+a+new+circle+packing+result+%282%2E635977%29+when+reproducing+your+example%2E+GitHub+Comment%2C+2025%2E+Comment+%5C%233156455197+on+Issue+%5C%23156%2C+OpenEvolve+repository+by+codelion%2E)
95. H. Diamond. Elementary methods in the study of the distribution of prime numbers. Bulletin of the American Mathematical Society, 7(3):553–589, 1982. [find](https://scholar.google.com/scholar?q=H%2E+Diamond%2E+Elementary+methods+in+the+study+of+the+distribution+of+prime+numbers%2E+Bulletin+of+the+American+Mathematical+Society%2C+7%283%29%3A553%E2%80%93589%2C+1982%2E)
96. Travis Dillon, Junnosuke Koizumi, and Sammy Luo. At most 10 cylinders mutually touch: a ramsey-theoretic approach, 2025. [find](https://scholar.google.com/scholar?q=Travis+Dillon%2C+Junnosuke+Koizumi%2C+and+Sammy+Luo%2E+At+most+10+cylinders+mutually+touch%3A+a+ramsey%2Dtheoretic+approach%2C+2025%2E)
97. Michael R. Douglas, Subramanian Lakshminarasimhan, and Yidi Qi. Numerical Calabi-Yau metrics from holomorphic networks. In Joan Bruna, Jan Hesthaven, and Lenka Zdeborova, editors, Proceedings of the 2nd Mathematical and Scientific Machine Learning Conference, volume 145 of Proceedings of Machine Lea… [find](https://scholar.google.com/scholar?q=Michael+R%2E+Douglas%2C+Subramanian+Lakshminarasimhan%2C+and+Yidi+Qi%2E+Numerical+Calabi%2DYau+metrics+from+holomorphic+networks%2E+In+Joan+Bruna%2C+Jan+Hesthaven%2C+and+Lenka+Zdeborova%2C+editors%2C+Proceedings+of+the+2)
98. Andreas W. M. Dress, Lu Yang, and Zhenbing Zeng. Heilbronn problem for six points in a planar convex body. In Ding-Zhu Du and Panos M. Pardalos, editors, Minimax and Applications, volume 4 of Nonconvex Optimization and Its Applications, pages 173–190, Boston, MA, 1995. Springer. [find](https://scholar.google.com/scholar?q=Andreas+W%2E+M%2E+Dress%2C+Lu+Yang%2C+and+Zhenbing+Zeng%2E+Heilbronn+problem+for+six+points+in+a+planar+convex+body%2E+In+Ding%2DZhu+Du+and+Panos+M%2E+Pardalos%2C+editors%2C+Minimax+and+Applications%2C+volume+4+of+Nonconve)
99. J. Ducci. Commentary on “Towards a noncommutative arithmetic-geometric mean inequality” by B. Recht and C. Ré. In Proceedings of the 25th Annual Conference on Learning Theory, volume 23 of JMLR Workshop and Conference Proceedings. JMLR.org, 2012. [find](https://scholar.google.com/scholar?q=J%2E+Ducci%2E+Commentary+on+%E2%80%9CTowards+a+noncommutative+arithmetic%2Dgeometric+mean+inequality%E2%80%9D+by+B%2E+Recht+and+C%2E+R%C3%A9%2E+In+Proceedings+of+the+25th+Annual+Conference+on+Learning+Theory%2C+volume+23+of+JMLR+Worksh)
100. Jordan S. Ellenberg, Cristofero S. Fraser-Taliente, Thomas R. Harvey, Karan Srivastava, and Andrew V. Sutherland. Generative Modeling for Mathematical Discovery, 2025. arXiv:2503.11061. — [arXiv:2503.11061](https://arxiv.org/abs/2503.11061) [find](https://scholar.google.com/scholar?q=Jordan+S%2E+Ellenberg%2C+Cristofero+S%2E+Fraser%2DTaliente%2C+Thomas+R%2E+Harvey%2C+Karan+Srivastava%2C+and+Andrew+V%2E+Sutherland%2E+Generative+Modeling+for+Mathematical+Discovery%2C+2025%2E+arXiv%3A2503%2E11061%2E+%E2%80%94+%5BarXiv%3A2503%2E)
101. Jordan S Ellenberg and Lalit Jain. Convergence rates for ordinal embedding. arXiv:1904.12994, 2019. — [arXiv:1904.12994](https://arxiv.org/abs/1904.12994) [find](https://scholar.google.com/scholar?q=Jordan+S+Ellenberg+and+Lalit+Jain%2E+Convergence+rates+for+ordinal+embedding%2E+arXiv%3A1904%2E12994%2C+2019%2E+%E2%80%94+%5BarXiv%3A1904%2E12994%5D%28https%3A%2F%2Farxiv%2Eorg%2Fabs%2F1904%2E12994%29)
102. T. Erber and G. M. Hockney. Equilibrium configurations of N equal charges on a sphere. Journal of Physics A: Mathematical and General, 24(23):L1369, 1991. [find](https://scholar.google.com/scholar?q=T%2E+Erber+and+G%2E+M%2E+Hockney%2E+Equilibrium+configurations+of+N+equal+charges+on+a+sphere%2E+Journal+of+Physics+A%3A+Mathematical+and+General%2C+24%2823%29%3AL1369%2C+1991%2E)
103. P. Erdős. Problems and results in additive number theory. In Colloque sur la Théorie des Nombres, Bruxelles, 1955, pages 127–137. Georges Thone, Liège, 1956. [find](https://scholar.google.com/scholar?q=P%2E+Erd%C5%91s%2E+Problems+and+results+in+additive+number+theory%2E+In+Colloque+sur+la+Th%C3%A9orie+des+Nombres%2C+Bruxelles%2C+1955%2C+pages+127%E2%80%93137%2E+Georges+Thone%2C+Li%C3%A8ge%2C+1956%2E)
104. Paul Erdős. Some unsolved problems. Michigan Math. J., 4:299–300, 1957. Problems 2, 4, 23. [find](https://scholar.google.com/scholar?q=Paul+Erd%C5%91s%2E+Some+unsolved+problems%2E+Michigan+Math%2E+J%2E%2C+4%3A299%E2%80%93300%2C+1957%2E+Problems+2%2C+4%2C+23%2E)
105. Paul Erdős. Some of my favourite problems in various branches of combinatorics. Le Matematiche (Catania), 47:231–240, 1992. [find](https://scholar.google.com/scholar?q=Paul+Erd%C5%91s%2E+Some+of+my+favourite+problems+in+various+branches+of+combinatorics%2E+Le+Matematiche+%28Catania%29%2C+47%3A231%E2%80%93240%2C+1992%2E)
106. P. Erdős. An inequality for the maximum of trigonometric polynomials. Annales Polonici Mathematici, 12:151–154, 1962. [find](https://scholar.google.com/scholar?q=P%2E+Erd%C5%91s%2E+An+inequality+for+the+maximum+of+trigonometric+polynomials%2E+Annales+Polonici+Mathematici%2C+12%3A151%E2%80%93154%2C+1962%2E)
107. Pál Erdős. Some Unsolved problems in Geometry, Number Theory and Combinatorics. Eureka, 52:44–48, 1992. [find](https://scholar.google.com/scholar?q=P%C3%A1l+Erd%C5%91s%2E+Some+Unsolved+problems+in+Geometry%2C+Number+Theory+and+Combinatorics%2E+Eureka%2C+52%3A44%E2%80%9348%2C+1992%2E)
108. Paul Erdős. Some unsolved problems. Magyar Tud. Akad. Mat. Kutató Int. Közl., 6:221–254, 1961. [find](https://scholar.google.com/scholar?q=Paul+Erd%C5%91s%2E+Some+unsolved+problems%2E+Magyar+Tud%2E+Akad%2E+Mat%2E+Kutat%C3%B3+Int%2E+K%C3%B6zl%2E%2C+6%3A221%E2%80%93254%2C+1961%2E)
109. Paul Erdős. Some of my favourite unsolved problems. In A tribute to Paul Erdős, pages 467–478. Cambridge University Press, Cambridge, 1990. [find](https://scholar.google.com/scholar?q=Paul+Erd%C5%91s%2E+Some+of+my+favourite+unsolved+problems%2E+In+A+tribute+to+Paul+Erd%C5%91s%2C+pages+467%E2%80%93478%2E+Cambridge+University+Press%2C+Cambridge%2C+1990%2E)
110. Paul Erdős. Some of my favourite problems in number theory, combinatorics, and geometry. Resenhas do Instituto de Matemática e Estatística da Universidade de São Paulo, 2(2):165–186, 1995. [find](https://scholar.google.com/scholar?q=Paul+Erd%C5%91s%2E+Some+of+my+favourite+problems+in+number+theory%2C+combinatorics%2C+and+geometry%2E+Resenhas+do+Instituto+de+Matem%C3%A1tica+e+Estat%C3%ADstica+da+Universidade+de+S%C3%A3o+Paulo%2C+2%282%29%3A165%E2%80%93186%2C+1995%2E)
111. Paul Erdős. Some of my favourite unsolved problems. Mathematica Japonica, 46(1):527–537, 1997. [find](https://scholar.google.com/scholar?q=Paul+Erd%C5%91s%2E+Some+of+my+favourite+unsolved+problems%2E+Mathematica+Japonica%2C+46%281%29%3A527%E2%80%93537%2C+1997%2E)
112. Paul Erdős and Ronald L Graham. On packing squares with equal squares. Journal of Combinatorial Theory, Series A, 19(1):119–123, 1975. [find](https://scholar.google.com/scholar?q=Paul+Erd%C5%91s+and+Ronald+L+Graham%2E+On+packing+squares+with+equal+squares%2E+Journal+of+Combinatorial+Theory%2C+Series+A%2C+19%281%29%3A119%E2%80%93123%2C+1975%2E)
113. Paul Erdős and George Szekeres. A combinatorial problem in geometry. Compositio Mathematica, 2:463–470, 1935. [find](https://scholar.google.com/scholar?q=Paul+Erd%C5%91s+and+George+Szekeres%2E+A+combinatorial+problem+in+geometry%2E+Compositio+Mathematica%2C+2%3A463%E2%80%93470%2C+1935%2E)
114. Paul Erdős and George Szekeres. On some extremum problems in elementary geometry. Annales Universitatis Scientiarium Budapesti-nensis de Rolando Eötvös Nominatae, Sectio Mathematica, 3–4:53–63, 1960. [find](https://scholar.google.com/scholar?q=Paul+Erd%C5%91s+and+George+Szekeres%2E+On+some+extremum+problems+in+elementary+geometry%2E+Annales+Universitatis+Scientiarium+Budapesti%2Dnensis+de+Rolando+E%C3%B6tv%C3%B6s+Nominatae%2C+Sectio+Mathematica%2C+3%E2%80%934%3A53%E2%80%9363%2C+1960%2E)
115. Paul Erdős and E. Szemerédi. On sums and products of integers. Studies in Pure Mathematics, Mem. of P. Turán, 213-218 (1983)., 1983. [find](https://scholar.google.com/scholar?q=Paul+Erd%C5%91s+and+E%2E+Szemer%C3%A9di%2E+On+sums+and+products+of+integers%2E+Studies+in+Pure+Mathematics%2C+Mem%2E+of+P%2E+Tur%C3%A1n%2C+213%2D218+%281983%29%2E%2C+1983%2E)
116. Paul Erdős. Some problems in number theory, combinatorics and combinatorial geometry. Mathematica Pannonica, 5(2):261–269, 1994. [find](https://scholar.google.com/scholar?q=Paul+Erd%C5%91s%2E+Some+problems+in+number+theory%2C+combinatorics+and+combinatorial+geometry%2E+Mathematica+Pannonica%2C+5%282%29%3A261%E2%80%93269%2C+1994%2E)
117. Paul Erdős and Alexander Soifer. A Square-Packing Problem of Erdős. Geombinatorics, 4(4):110–114, 1995. [find](https://scholar.google.com/scholar?q=Paul+Erd%C5%91s+and+Alexander+Soifer%2E+A+Square%2DPacking+Problem+of+Erd%C5%91s%2E+Geombinatorics%2C+4%284%29%3A110%E2%80%93114%2C+1995%2E)
118. Erdős Problems Community. Erdős Problems. Website. Accessed December 23, 2025. [find](https://scholar.google.com/scholar?q=Erd%C5%91s+Problems+Community%2E+Erd%C5%91s+Problems%2E+Website%2E+Accessed+December+23%2C+2025%2E)
119. Siemion Fajtlowicz. On conjectures of Graffiti. In Annals of discrete mathematics, volume 38, pages 113–118. Elsevier, 1988. [find](https://scholar.google.com/scholar?q=Siemion+Fajtlowicz%2E+On+conjectures+of+Graffiti%2E+In+Annals+of+discrete+mathematics%2C+volume+38%2C+pages+113%E2%80%93118%2E+Elsevier%2C+1988%2E)
120. Alhussein Fawzi, Matej Balog, Aja Huang, Thomas Hubert, Bernardino Romera-Paredes, Mohammadamin Barekatain, Alexander Novikov, Francisco J R. Ruiz, Julian Schrittwieser, Grzegorz Swirszcz, et al. Discovering faster matrix multiplication algorithms with reinforcement learning. Nature, 610(7930):47–53… [find](https://scholar.google.com/scholar?q=Alhussein+Fawzi%2C+Matej+Balog%2C+Aja+Huang%2C+Thomas+Hubert%2C+Bernardino+Romera%2DParedes%2C+Mohammadamin+Barekatain%2C+Alexander+Novikov%2C+Francisco+J+R%2E+Ruiz%2C+Julian+Schrittwieser%2C+Grzegorz+Swirszcz%2C+et+al%2E+Disc)
121. László Fejes-Tóth. Regular Figures. The Macmillan Company, New York, 1964. [find](https://scholar.google.com/scholar?q=L%C3%A1szl%C3%B3+Fejes%2DT%C3%B3th%2E+Regular+Figures%2E+The+Macmillan+Company%2C+New+York%2C+1964%2E)
122. P. C. Fishburn and J. A. Reeds. Unit distances between vertices of a convex polygon. Computational Geometry, 2(2):81–91, 1992. [find](https://scholar.google.com/scholar?q=P%2E+C%2E+Fishburn+and+J%2E+A%2E+Reeds%2E+Unit+distances+between+vertices+of+a+convex+polygon%2E+Computational+Geometry%2C+2%282%29%3A81%E2%80%9391%2C+1992%2E)
123. D. Fisher. Lower bounds on the number of triangles in a graph. Journal of Graph Theory, 13(4):505–512, 1989. [find](https://scholar.google.com/scholar?q=D%2E+Fisher%2E+Lower+bounds+on+the+number+of+triangles+in+a+graph%2E+Journal+of+Graph+Theory%2C+13%284%29%3A505%E2%80%93512%2C+1989%2E)
124. Gerald B. Folland. Real Analysis: Modern Techniques and Their Applications. Pure and Applied Mathematics. John Wiley & Sons, Inc., New York, 2nd edition, 1999. A Wiley-Interscience Publication. [find](https://scholar.google.com/scholar?q=Gerald+B%2E+Folland%2E+Real+Analysis%3A+Modern+Techniques+and+Their+Applications%2E+Pure+and+Applied+Mathematics%2E+John+Wiley+%26+Sons%2C+Inc%2E%2C+New+York%2C+2nd+edition%2C+1999%2E+A+Wiley%2DInterscience+Publication%2E)
125. G. A. Freiman and V. P. Pigarev. The relation between the invariants R and T (russian). Kalinin. Gos. Univ., pages 172–174, 1973. [find](https://scholar.google.com/scholar?q=G%2E+A%2E+Freiman+and+V%2E+P%2E+Pigarev%2E+The+relation+between+the+invariants+R+and+T+%28russian%29%2E+Kalinin%2E+Gos%2E+Univ%2E%2C+pages+172%E2%80%93174%2C+1973%2E)
126. Erich Friedman. Packing Unit Squares in Squares: A Survey and New Results. The Electronic Journal of Combinatorics, 12(1):DS7, 2005. Dynamic Survey. [find](https://scholar.google.com/scholar?q=Erich+Friedman%2E+Packing+Unit+Squares+in+Squares%3A+A+Survey+and+New+Results%2E+The+Electronic+Journal+of+Combinatorics%2C+12%281%29%3ADS7%2C+2005%2E+Dynamic+Survey%2E)
127. Erich Friedman. The Heilbronn Problem for Convex Regions. [https://erich-friedman.github.io/packing/heilconvex/](https://erich-friedman.github.io/packing/heilconvex/), 2007. Webpage documenting optimal point configurations for the Heilbronn problem in general convex regions. [↗](https://erich-friedman.github.io/packing/heilconvex/)
128. Erich Friedman. Circles in Rectangles. [https://erich-friedman.github.io/packing/cirRrec/](https://erich-friedman.github.io/packing/cirRrec/), 2011. Webpage documenting n circles with the largest possible sum of radii packed inside a rectangle of perimeter 4. [↗](https://erich-friedman.github.io/packing/cirRrec/)
129. Erich Friedman. Circles in Squares. [https://erich-friedman.github.io/packing/cirRsqu/](https://erich-friedman.github.io/packing/cirRsqu/), 2012. Webpage documenting n circles with the largest possible sum of radii packed inside a unit square. [↗](https://erich-friedman.github.io/packing/cirRsqu/)
130. Erich Friedman. The Heilbronn Problem for Triangles. [https://erich-friedman.github.io/packing/heiltri/](https://erich-friedman.github.io/packing/heiltri/), 2015. Webpage documenting optimal point configurations for the Heilbronn problem in triangles of unit area. [↗](https://erich-friedman.github.io/packing/heiltri/)
131. Erich Friedman. Erich’s Packing Center. [https://erich-friedman.github.io/packing/](https://erich-friedman.github.io/packing/), 2019. Webpage documenting optimal configurations for various packing problems. [↗](https://erich-friedman.github.io/packing/)
132. Erich Friedman. Minimizing the Ratio of Maximum to Minimum Distance. [https://erich-friedman.github.io/packing/](https://erich-friedman.github.io/packing/) maxmin/, 2024. Webpage documenting optimal point configurations in 2D. [↗](https://erich-friedman.github.io/packing/)
133. Erich Friedman. Minimizing the Ratio of Maximum to Minimum Distance in 3 Dimensions. [https://erich-friedman.github.io/packing/maxmin3/](https://erich-friedman.github.io/packing/maxmin3/), 2024. Webpage documenting optimal point configurations in 3D. [↗](https://erich-friedman.github.io/packing/maxmin3/)
134. Erich Friedman. Cubes in Cubes. [https://erich-friedman.github.io/packing/cubincub/](https://erich-friedman.github.io/packing/cubincub/), [YEAR]. Accessed: [DATE]. [↗](https://erich-friedman.github.io/packing/cubincub/)
135. E. Fujikawa and T. Sugawa. Geometric function theory and smale’s mean value conjecture. Proceedings of the Japan Academy, Series A Mathematical Sciences, 82(7):97–100, 2006. [find](https://scholar.google.com/scholar?q=E%2E+Fujikawa+and+T%2E+Sugawa%2E+Geometric+function+theory+and+smale%E2%80%99s+mean+value+conjecture%2E+Proceedings+of+the+Japan+Academy%2C+Series+A+Mathematical+Sciences%2C+82%287%29%3A97%E2%80%93100%2C+2006%2E)
136. Harry Furstenberg. Ergodic behavior of diagonal measures and a theorem of Szemerédi on arithmetic progressions. J. Analyse Math., 31:204–256, 1977. [find](https://scholar.google.com/scholar?q=Harry+Furstenberg%2E+Ergodic+behavior+of+diagonal+measures+and+a+theorem+of+Szemer%C3%A9di+on+arithmetic+progressions%2E+J%2E+Analyse+Math%2E%2C+31%3A204%E2%80%93256%2C+1977%2E)
137. Mikhail Ganzhinov. Highly symmetric lines. Linear Algebra and its Applications, 2025. [find](https://scholar.google.com/scholar?q=Mikhail+Ganzhinov%2E+Highly+symmetric+lines%2E+Linear+Algebra+and+its+Applications%2C+2025%2E)
138. Robert Gerbicz. Sums and differences of sets (improvement over AlphaEvolve), 2025. arXiv:2505.16105. — [arXiv:2505.16105](https://arxiv.org/abs/2505.16105) [find](https://scholar.google.com/scholar?q=Robert+Gerbicz%2E+Sums+and+differences+of+sets+%28improvement+over+AlphaEvolve%29%2C+2025%2E+arXiv%3A2505%2E16105%2E+%E2%80%94+%5BarXiv%3A2505%2E16105%5D%28https%3A%2F%2Farxiv%2Eorg%2Fabs%2F2505%2E16105%29)
139. Joseph L. Gerver. On moving a sofa around a corner. Geometriae Dedicata, 42(3):267–283, 1992. [find](https://scholar.google.com/scholar?q=Joseph+L%2E+Gerver%2E+On+moving+a+sofa+around+a+corner%2E+Geometriae+Dedicata%2C+42%283%29%3A267%E2%80%93283%2C+1992%2E)
140. Anubhab Ghosal, Ritesh Goenka, and Peter Keevash. On subsets of lattice cubes avoiding affine and spherical degeneracies. arXiv preprint arXiv:2509.06935, 2025. — [arXiv:2509.06935](https://arxiv.org/abs/2509.06935) [find](https://scholar.google.com/scholar?q=Anubhab+Ghosal%2C+Ritesh+Goenka%2C+and+Peter+Keevash%2E+On+subsets+of+lattice+cubes+avoiding+affine+and+spherical+degeneracies%2E+arXiv+preprint+arXiv%3A2509%2E06935%2C+2025%2E+%E2%80%94+%5BarXiv%3A2509%2E06935%5D%28https%3A%2F%2Farxiv%2Eorg%2F)
141. L. Glasser and A. G. Every. Energies and spacings of point charges on a sphere. Journal of Physics A: Mathematical and General, 25(9):2473–2482, 1992. [find](https://scholar.google.com/scholar?q=L%2E+Glasser+and+A%2E+G%2E+Every%2E+Energies+and+spacings+of+point+charges+on+a+sphere%2E+Journal+of+Physics+A%3A+Mathematical+and+General%2C+25%289%29%3A2473%E2%80%932482%2C+1992%2E)
142. Jan Goedgebeur, Jorik Jooken, Gwenaël Joret, and Tibo Van den Eede. Improved lower bounds on the maximum size of graphs with girth 5. arXiv preprint arXiv:2508.05562, 2025. — [arXiv:2508.05562](https://arxiv.org/abs/2508.05562) [find](https://scholar.google.com/scholar?q=Jan+Goedgebeur%2C+Jorik+Jooken%2C+Gwena%C3%ABl+Joret%2C+and+Tibo+Van+den+Eede%2E+Improved+lower+bounds+on+the+maximum+size+of+graphs+with+girth+5%2E+arXiv+preprint+arXiv%3A2508%2E05562%2C+2025%2E+%E2%80%94+%5BarXiv%3A2508%2E05562%5D%28https%3A)
143. Marcel J. E. Golay. Notes on the representation of {1, 2, … , 𝑛} by differences. J. London Math. Soc. (2), 4:729–734, 1972. [find](https://scholar.google.com/scholar?q=Marcel+J%2E+E%2E+Golay%2E+Notes+on+the+representation+of+%7B1%2C+2%2C+%E2%80%A6+%2C+%F0%9D%91%9B%7D+by+differences%2E+J%2E+London+Math%2E+Soc%2E+%282%29%2C+4%3A729%E2%80%93734%2C+1972%2E)
144. Marcel J. E. Golay. Sieves for low autocorrelation binary sequences. IEEE Transactions on Information Theory, 23(1):43–51, 1977. [find](https://scholar.google.com/scholar?q=Marcel+J%2E+E%2E+Golay%2E+Sieves+for+low+autocorrelation+binary+sequences%2E+IEEE+Transactions+on+Information+Theory%2C+23%281%29%3A43%E2%80%9351%2C+1977%2E)
145. F. Gonçalves, D. Oliveira e Silva, and S. Steinerberger. Hermite polynomials, linear flows on the torus, and an uncertainty principle for roots. Journal of Mathematical Analysis and Applications, 451(2):678–711, 2017. [find](https://scholar.google.com/scholar?q=F%2E+Gon%C3%A7alves%2C+D%2E+Oliveira+e+Silva%2C+and+S%2E+Steinerberger%2E+Hermite+polynomials%2C+linear+flows+on+the+torus%2C+and+an+uncertainty+principle+for+roots%2E+Journal+of+Mathematical+Analysis+and+Applications%2C+451%28)
146. Felipe Gonçalves, Diogo Oliveira e Silva, and João Pedro Ramos. New sign uncertainty principles. Discrete Analysis, jul 21 2023. [find](https://scholar.google.com/scholar?q=Felipe+Gon%C3%A7alves%2C+Diogo+Oliveira+e+Silva%2C+and+Jo%C3%A3o+Pedro+Ramos%2E+New+sign+uncertainty+principles%2E+Discrete+Analysis%2C+jul+21+2023%2E)
147. A. W. Goodman. On sets of acquaintances and strangers at any party. American Mathematical Monthly, 66(9):778–783, 1959. [find](https://scholar.google.com/scholar?q=A%2E+W%2E+Goodman%2E+On+sets+of+acquaintances+and+strangers+at+any+party%2E+American+Mathematical+Monthly%2C+66%289%29%3A778%E2%80%93783%2C+1959%2E)
148. Google DeepMind. AI achieves silver-medal standard solving International Mathematical Olympiad problems. Google DeepMind Blog, July 2024. [find](https://scholar.google.com/scholar?q=Google+DeepMind%2E+AI+achieves+silver%2Dmedal+standard+solving+International+Mathematical+Olympiad+problems%2E+Google+DeepMind+Blog%2C+July+2024%2E)
149. Google DeepMind. Advanced version of Gemini with Deep Think officially achieves gold-medal standard at the International Mathematical Olympiad. Google DeepMind Blog, July 2025. [find](https://scholar.google.com/scholar?q=Google+DeepMind%2E+Advanced+version+of+Gemini+with+Deep+Think+officially+achieves+gold%2Dmedal+standard+at+the+International+Mathematical+Olympiad%2E+Google+DeepMind+Blog%2C+July+2025%2E)
150. B. Green. Open problems. [https://people.maths.ox.ac.uk/greenbj/papers/open-problems.pdf](https://people.maths.ox.ac.uk/greenbj/papers/open-problems.pdf). [↗](https://people.maths.ox.ac.uk/greenbj/papers/open-problems.pdf)
151. B. Green and I. Ruzsa. On the arithmetic Kakeya conjecture of Katz and Tao. Periodica Mathematica Hungarica, 78(2):135–151, 2019. [find](https://scholar.google.com/scholar?q=B%2E+Green+and+I%2E+Ruzsa%2E+On+the+arithmetic+Kakeya+conjecture+of+Katz+and+Tao%2E+Periodica+Mathematica+Hungarica%2C+78%282%29%3A135%E2%80%93151%2C+2019%2E)
152. Ben Green and Mehtaab Sawhney. Improved bounds for the Furstenberg-Sárközy theorem, 2024. arXiv:2411.17448. — [arXiv:2411.17448](https://arxiv.org/abs/2411.17448) [find](https://scholar.google.com/scholar?q=Ben+Green+and+Mehtaab+Sawhney%2E+Improved+bounds+for+the+Furstenberg%2DS%C3%A1rk%C3%B6zy+theorem%2C+2024%2E+arXiv%3A2411%2E17448%2E+%E2%80%94+%5BarXiv%3A2411%2E17448%5D%28https%3A%2F%2Farxiv%2Eorg%2Fabs%2F2411%2E17448%29)
153. Anne Greenbaum, Adrian S. Lewis, and Michael L. Overton. Variational analysis of the Crouzeix ratio. Mathematical Programming, 164:229–243, 2017. [find](https://scholar.google.com/scholar?q=Anne+Greenbaum%2C+Adrian+S%2E+Lewis%2C+and+Michael+L%2E+Overton%2E+Variational+analysis+of+the+Crouzeix+ratio%2E+Mathematical+Programming%2C+164%3A229%E2%80%93243%2C+2017%2E)
154. Anne Greenbaum, Adrian S Lewis, Michael L Overton, and Lloyd N Trefethen. Investigation of Crouzeix’s Conjecture via Optimization. In Householder Symposium XIX June 8-13, Spa Belgium, page 171, 2014. [find](https://scholar.google.com/scholar?q=Anne+Greenbaum%2C+Adrian+S+Lewis%2C+Michael+L+Overton%2C+and+Lloyd+N+Trefethen%2E+Investigation+of+Crouzeix%E2%80%99s+Conjecture+via+Optimization%2E+In+Householder+Symposium+XIX+June+8%2D13%2C+Spa+Belgium%2C+page+171%2C+2014%2E)
155. Anne Greenbaum and Michael L. Overton. Numerical investigation of Crouzeix’s conjecture. Linear Algebra and its Applications, 542:225–245, 2018. [find](https://scholar.google.com/scholar?q=Anne+Greenbaum+and+Michael+L%2E+Overton%2E+Numerical+investigation+of+Crouzeix%E2%80%99s+conjecture%2E+Linear+Algebra+and+its+Applications%2C+542%3A225%E2%80%93245%2C+2018%2E)
156. Alan Guo, Swastik Kopparty, and Madhu Sudan. New affine-invariant codes from lifting. In Proceedings of the 4th conference on innovations in theoretical computer science, ITCS’13, Berkeley, CA, USA, January 9–12, 2013, pages 529–539. New York, NY: Association for Computing Machinery (ACM), 2013. [find](https://scholar.google.com/scholar?q=Alan+Guo%2C+Swastik+Kopparty%2C+and+Madhu+Sudan%2E+New+affine%2Dinvariant+codes+from+lifting%2E+In+Proceedings+of+the+4th+conference+on+innovations+in+theoretical+computer+science%2C+ITCS%E2%80%9913%2C+Berkeley%2C+CA%2C+USA%2C+J)
157. Larry Guth and Olivine Silier. Sharp Szemerédi-Trotter constructions in the plane. Electron. J. Comb., 32(1):research paper p1.9, 11, 2025. [find](https://scholar.google.com/scholar?q=Larry+Guth+and+Olivine+Silier%2E+Sharp+Szemer%C3%A9di%2DTrotter+constructions+in+the+plane%2E+Electron%2E+J%2E+Comb%2E%2C+32%281%29%3Aresearch+paper+p1%2E9%2C+11%2C+2025%2E)
158. Katalin Gyarmati, François Hennecart, and Imre Z. Ruzsa. Sums and differences of finite sets. Functiones et Approximatio Commen-tarii Mathematici, 37(1):175–186, 2007. [find](https://scholar.google.com/scholar?q=Katalin+Gyarmati%2C+Fran%C3%A7ois+Hennecart%2C+and+Imre+Z%2E+Ruzsa%2E+Sums+and+differences+of+finite+sets%2E+Functiones+et+Approximatio+Commen%2Dtarii+Mathematici%2C+37%281%29%3A175%E2%80%93186%2C+2007%2E)
159. Thomas C. Hales. A proof of the Kepler conjecture. Annals of Mathematics, 162(3):1065–1185, 2005. [find](https://scholar.google.com/scholar?q=Thomas+C%2E+Hales%2E+A+proof+of+the+Kepler+conjecture%2E+Annals+of+Mathematics%2C+162%283%29%3A1065%E2%80%931185%2C+2005%2E)
160. Sylvia Halász. Packing a convex domain with similar convex domains. Journal of Combinatorial Theory, Series A, 37(1):85–90, 1984. [find](https://scholar.google.com/scholar?q=Sylvia+Hal%C3%A1sz%2E+Packing+a+convex+domain+with+similar+convex+domains%2E+Journal+of+Combinatorial+Theory%2C+Series+A%2C+37%281%29%3A85%E2%80%9390%2C+1984%2E)
161. R. H. Hardin and N. J. A. Sloane. Codes (Spherical) and Designs (Experimental). In A. R. Calderbank, editor, Different Aspects of Coding Theory, volume 50 of AMS Series Proceedings Symposia Applied Math., pages 179–206. American Mathematical Society, 1995. [find](https://scholar.google.com/scholar?q=R%2E+H%2E+Hardin+and+N%2E+J%2E+A%2E+Sloane%2E+Codes+%28Spherical%29+and+Designs+%28Experimental%29%2E+In+A%2E+R%2E+Calderbank%2C+editor%2C+Different+Aspects+of+Coding+Theory%2C+volume+50+of+AMS+Series+Proceedings+Symposia+Applied+Ma)
162. William B. Hart. FLINT: Fast Library for Number Theory: An Introduction. In Mathematical Software – ICMS 2010, volume 6327 of Lecture Notes in Computer Science, pages 88–91, Berlin, Heidelberg, 2010. Springer. [find](https://scholar.google.com/scholar?q=William+B%2E+Hart%2E+FLINT%3A+Fast+Library+for+Number+Theory%3A+An+Introduction%2E+In+Mathematical+Software+%E2%80%93+ICMS+2010%2C+volume+6327+of+Lecture+Notes+in+Computer+Science%2C+pages+88%E2%80%9391%2C+Berlin%2C+Heidelberg%2C+2010%2E+)
163. H. Hatami. Graph norms and Sidorenko’s conjecture. Israel Journal of Mathematics, 175:125–150, 2010. [find](https://scholar.google.com/scholar?q=H%2E+Hatami%2E+Graph+norms+and+Sidorenko%E2%80%99s+conjecture%2E+Israel+Journal+of+Mathematics%2C+175%3A125%E2%80%93150%2C+2010%2E)
164. J. K. Haugland. The minimum overlap problem revisited, 2016. arXiv:1609.08000. — [arXiv:1609.08000](https://arxiv.org/abs/1609.08000) [find](https://scholar.google.com/scholar?q=J%2E+K%2E+Haugland%2E+The+minimum+overlap+problem+revisited%2C+2016%2E+arXiv%3A1609%2E08000%2E+%E2%80%94+%5BarXiv%3A1609%2E08000%5D%28https%3A%2F%2Farxiv%2Eorg%2Fabs%2F1609%2E08000%29)
165. Yang-Hui He, Kyu-Hwan Lee, Thomas Oliver, and Alexey Pozdnyakov. Murmurations of elliptic curves. Experimental Mathematics, 34(3):528–540, 2025. [find](https://scholar.google.com/scholar?q=Yang%2DHui+He%2C+Kyu%2DHwan+Lee%2C+Thomas+Oliver%2C+and+Alexey+Pozdnyakov%2E+Murmurations+of+elliptic+curves%2E+Experimental+Mathematics%2C+34%283%29%3A528%E2%80%93540%2C+2025%2E)
166. F. Hennecart, G. Robert, and A. Yudin. On the number of sums and differences. In Structure theory of set addition, number 258 in Astérisque, pages 173–178. 1999. [find](https://scholar.google.com/scholar?q=F%2E+Hennecart%2C+G%2E+Robert%2C+and+A%2E+Yudin%2E+On+the+number+of+sums+and+differences%2E+In+Structure+theory+of+set+addition%2C+number+258+in+Ast%C3%A9risque%2C+pages+173%E2%80%93178%2E+1999%2E)
167. Andreas F. Holmsen, Hossein Nassajian Mojarrad, János Pach, and Gábor Tardos. Two extensions of the Erdős–Szekeres problem. Journal of the European Mathematical Society, 22(12):3981–3995, 2020. [find](https://scholar.google.com/scholar?q=Andreas+F%2E+Holmsen%2C+Hossein+Nassajian+Mojarrad%2C+J%C3%A1nos+Pach%2C+and+G%C3%A1bor+Tardos%2E+Two+extensions+of+the+Erd%C5%91s%E2%80%93Szekeres+problem%2E+Journal+of+the+European+Mathematical+Society%2C+22%2812%29%3A3981%E2%80%933995%2C+2020%2E)
168. Ákos G Horváth and Zsolt Lángi. Maximum volume polytopes inscribed in the unit sphere. Monatshefte für Mathematik, 181(2):341– 354, 2016. [find](https://scholar.google.com/scholar?q=%C3%81kos+G+Horv%C3%A1th+and+Zsolt+L%C3%A1ngi%2E+Maximum+volume+polytopes+inscribed+in+the+unit+sphere%2E+Monatshefte+f%C3%BCr+Mathematik%2C+181%282%29%3A341%E2%80%93+354%2C+2016%2E)
169. A. Israel, F. Krahmer, and R. Ward. An arithmetic-geometric mean inequality for products of three matrices. Linear Algebra and its Applications, 488:1–12, 2016. [find](https://scholar.google.com/scholar?q=A%2E+Israel%2C+F%2E+Krahmer%2C+and+R%2E+Ward%2E+An+arithmetic%2Dgeometric+mean+inequality+for+products+of+three+matrices%2E+Linear+Algebra+and+its+Applications%2C+488%3A1%E2%80%9312%2C+2016%2E)
170. Jonathan Jedwab, Daniel J. Katz, and Kai-Uwe Schmidt. Littlewood polynomials with small 𝐿 4 norm. Adv. Math., 241:127–136, 2013. [find](https://scholar.google.com/scholar?q=Jonathan+Jedwab%2C+Daniel+J%2E+Katz%2C+and+Kai%2DUwe+Schmidt%2E+Littlewood+polynomials+with+small+%F0%9D%90%BF+4+norm%2E+Adv%2E+Math%2E%2C+241%3A127%E2%80%93136%2C+2013%2E)
171. Fredrik Johansson. [Arb: Efficient Arbitrary-Precision Midpoint-Radius Interval Arithmetic](https://md.research.elamur.ai/free/en/papers/johansson-2016-arb-efficient-arbitrary-precision-midpoint/). IEEE Transactions on Computers, 66(8):1281–1292, August 2017.
172. J. Kalbfleisch, J. Kalbfleisch, and R. Stanton. A combinatorial problem on convex regions. In Proceedings of the Louisiana Conference on Combinatorics, Graph Theory and Computing, volume 1 of Congressus Numerantium, pages 180–188, Baton Rouge, Louisiana, 1970. Louisiana State University. [find](https://scholar.google.com/scholar?q=J%2E+Kalbfleisch%2C+J%2E+Kalbfleisch%2C+and+R%2E+Stanton%2E+A+combinatorial+problem+on+convex+regions%2E+In+Proceedings+of+the+Louisiana+Conference+on+Combinatorics%2C+Graph+Theory+and+Computing%2C+volume+1+of+Congress)
173. N. Katz and T. Tao. New bounds for Kakeya problems. Journal d’Analyse Mathématique, 87:231–263, 2002. [find](https://scholar.google.com/scholar?q=N%2E+Katz+and+T%2E+Tao%2E+New+bounds+for+Kakeya+problems%2E+Journal+d%E2%80%99Analyse+Math%C3%A9matique%2C+87%3A231%E2%80%93263%2C+2002%2E)
174. N. H. Katz and T. Tao. Bounds on arithmetic projections and applications to the Kakeya conjecture. Mathematical Research Letters, 6:625–630, 1999. [find](https://scholar.google.com/scholar?q=N%2E+H%2E+Katz+and+T%2E+Tao%2E+Bounds+on+arithmetic+projections+and+applications+to+the+Kakeya+conjecture%2E+Mathematical+Research+Letters%2C+6%3A625%E2%80%93630%2C+1999%2E)
175. Yitzhak Katznelson. An Introduction to Harmonic Analysis. John Wiley & Sons, New York, 1968. Awarded the American Mathematical Society Steele Prize for Mathematical Exposition. [find](https://scholar.google.com/scholar?q=Yitzhak+Katznelson%2E+An+Introduction+to+Harmonic+Analysis%2E+John+Wiley+%26+Sons%2C+New+York%2C+1968%2E+Awarded+the+American+Mathematical+Society+Steele+Prize+for+Mathematical+Exposition%2E)
176. Michael J Kearney and Peter Shiu. Efficient packing of unit squares in a square. the electronic journal of combinatorics, pages R14– R14, 2002. [find](https://scholar.google.com/scholar?q=Michael+J+Kearney+and+Peter+Shiu%2E+Efficient+packing+of+unit+squares+in+a+square%2E+the+electronic+journal+of+combinatorics%2C+pages+R14%E2%80%93+R14%2C+2002%2E)
177. Peter Keevash. Hypergraph Turán problems. Surveys in combinatorics, 392:83–140, 2011. [find](https://scholar.google.com/scholar?q=Peter+Keevash%2E+Hypergraph+Tur%C3%A1n+problems%2E+Surveys+in+combinatorics%2C+392%3A83%E2%80%93140%2C+2011%2E)
178. U. Keich. On 𝐿 𝑝 bounds for Kakeya maximal functions and the Minkowski dimension in ℝ 2 . Bulletin of the London Mathematical Society, 31(2):213–221, 1999. [find](https://scholar.google.com/scholar?q=U%2E+Keich%2E+On+%F0%9D%90%BF+%F0%9D%91%9D+bounds+for+Kakeya+maximal+functions+and+the+Minkowski+dimension+in+%E2%84%9D+2+%2E+Bulletin+of+the+London+Mathematical+Society%2C+31%282%29%3A213%E2%80%93221%2C+1999%2E)
179. N. Khadzhiivanov and V. Nikiforov. The Nordhaus-Stewart-Moon-Moser inequality. Serdica, 4:344–350, 1978. In Russian. [find](https://scholar.google.com/scholar?q=N%2E+Khadzhiivanov+and+V%2E+Nikiforov%2E+The+Nordhaus%2DStewart%2DMoon%2DMoser+inequality%2E+Serdica%2C+4%3A344%E2%80%93350%2C+1978%2E+In+Russian%2E)
180. Sanjeev Khanna. A polynomial time approximation scheme for the sonet ring loading problem. Bell Labs Technical Journal, 2(2):36– 41, 1997. [find](https://scholar.google.com/scholar?q=Sanjeev+Khanna%2E+A+polynomial+time+approximation+scheme+for+the+sonet+ring+loading+problem%2E+Bell+Labs+Technical+Journal%2C+2%282%29%3A36%E2%80%93+41%2C+1997%2E)
181. D. Khavinson, R. Pereira, M. Putinar, E. B. Saff, and S. Shimorin. Borcea’s variance conjectures on the critical points of polynomials. In P. Brändén, M. Passare, and M. Putinar, editors, Notions of Positivity and the Geometry of Polynomials, Trends in Mathematics. Springer, Basel, 2011. [find](https://scholar.google.com/scholar?q=D%2E+Khavinson%2C+R%2E+Pereira%2C+M%2E+Putinar%2C+E%2E+B%2E+Saff%2C+and+S%2E+Shimorin%2E+Borcea%E2%80%99s+variance+conjectures+on+the+critical+points+of+polynomials%2E+In+P%2E+Br%C3%A4nd%C3%A9n%2C+M%2E+Passare%2C+and+M%2E+Putinar%2C+editors%2C+Notions+of+P)
182. Jeong Han Kim, Choongbum Lee, and Joonkyung Lee. Two approaches to Sidorenko’s conjecture. Transactions of the American Mathematical Society, 368(7):5057–5074, 2016. [find](https://scholar.google.com/scholar?q=Jeong+Han+Kim%2C+Choongbum+Lee%2C+and+Joonkyung+Lee%2E+Two+approaches+to+Sidorenko%E2%80%99s+conjecture%2E+Transactions+of+the+American+Mathematical+Society%2C+368%287%29%3A5057%E2%80%935074%2C+2016%2E)
183. Boaz Klartag. Lattice packing of spheres in high dimensions using a stochastically evolving ellipsoid. 2025. arXiv:2504.05042. — [arXiv:2504.05042](https://arxiv.org/abs/2504.05042) [find](https://scholar.google.com/scholar?q=Boaz+Klartag%2E+Lattice+packing+of+spheres+in+high+dimensions+using+a+stochastically+evolving+ellipsoid%2E+2025%2E+arXiv%3A2504%2E05042%2E+%E2%80%94+%5BarXiv%3A2504%2E05042%5D%28https%3A%2F%2Farxiv%2Eorg%2Fabs%2F2504%2E05042%29)
184. János Komlós, János Pintz, and Endre Szemerédi. A lower bound for Heilbronn’s problem. J. Lond. Math. Soc., II. Ser., 25:13–24, 1982. [find](https://scholar.google.com/scholar?q=J%C3%A1nos+Koml%C3%B3s%2C+J%C3%A1nos+Pintz%2C+and+Endre+Szemer%C3%A9di%2E+A+lower+bound+for+Heilbronn%E2%80%99s+problem%2E+J%2E+Lond%2E+Math%2E+Soc%2E%2C+II%2E+Ser%2E%2C+25%3A13%E2%80%9324%2C+1982%2E)
185. Boris Konev and Alexei Lisitsa. Computer-aided proof of Erdős discrepancy properties. Artif. Intell., 224:103–118, 2015. [find](https://scholar.google.com/scholar?q=Boris+Konev+and+Alexei+Lisitsa%2E+Computer%2Daided+proof+of+Erd%C5%91s+discrepancy+properties%2E+Artif%2E+Intell%2E%2C+224%3A103%E2%80%93118%2C+2015%2E)
186. J. Korevaar and J. L. H. Meyers. Spherical Faraday cage for the case of equal point charges and Chebyshev-type quadrature on the sphere. Integral Transforms and Special Functions, 1(2):105–117, 1993. [find](https://scholar.google.com/scholar?q=J%2E+Korevaar+and+J%2E+L%2E+H%2E+Meyers%2E+Spherical+Faraday+cage+for+the+case+of+equal+point+charges+and+Chebyshev%2Dtype+quadrature+on+the+sphere%2E+Integral+Transforms+and+Special+Functions%2C+1%282%29%3A105%E2%80%93117%2C+1993%2E)
187. A. V. Kostochka. A class of constructions for Turán’s (3,4)-problem. Combinatorica, 2:187–192, 1982. [find](https://scholar.google.com/scholar?q=A%2E+V%2E+Kostochka%2E+A+class+of+constructions+for+Tur%C3%A1n%E2%80%99s+%283%2C4%29%2Dproblem%2E+Combinatorica%2C+2%3A187%E2%80%93192%2C+1982%2E)
188. Chun-Kit Lai and Adeline E. Wong. A non-sticky Kakeya set of Lebesgue measure zero, 2025. arXiv:2506.18142. — [arXiv:2506.18142](https://arxiv.org/abs/2506.18142) [find](https://scholar.google.com/scholar?q=Chun%2DKit+Lai+and+Adeline+E%2E+Wong%2E+A+non%2Dsticky+Kakeya+set+of+Lebesgue+measure+zero%2C+2025%2E+arXiv%3A2506%2E18142%2E+%E2%80%94+%5BarXiv%3A2506%2E18142%5D%28https%3A%2F%2Farxiv%2Eorg%2Fabs%2F2506%2E18142%29)
189. Xiangjing Lai, Dong Yue, Jin-Kao Hao, Fred Glover, and Zhipeng Lü. Iterated dynamic neighborhood search for packing equal circles on a sphere. Computers & Operations Research, 151:106121, 2023. [find](https://scholar.google.com/scholar?q=Xiangjing+Lai%2C+Dong+Yue%2C+Jin%2DKao+Hao%2C+Fred+Glover%2C+and+Zhipeng+L%C3%BC%2E+Iterated+dynamic+neighborhood+search+for+packing+equal+circles+on+a+sphere%2E+Computers+%26+Operations+Research%2C+151%3A106121%2C+2023%2E)
190. Robert Tjarko Lange. [ShinkaEvolve: Towards Open-Ended And Sample-Efficient Program Evolution](https://md.research.elamur.ai/free/en/papers/lange-2025-shinkaevolve-open-ended-sample/). arXiv:2509.19349, 2025.
191. Laszlo Hars. Numerical Solutions for the Tammes Problem, Numerical Solutions of the Thomson-P Problems. [https://www.hars.us/](https://www.hars.us/), 2025. [↗](https://www.hars.us/)
192. John Leech. On the representation of {1, 2, … , 𝑛} by differences. J. London Math. Soc., 31:160–169, 1956. [find](https://scholar.google.com/scholar?q=John+Leech%2E+On+the+representation+of+%7B1%2C+2%2C+%E2%80%A6+%2C+%F0%9D%91%9B%7D+by+differences%2E+J%2E+London+Math%2E+Soc%2E%2C+31%3A160%E2%80%93169%2C+1956%2E)
193. Nando Leijenhorst and David de Laat. Solving clustered low-rank semidefinite programs arising from polynomial optimization. Mathematical Programming Computation, 16(3):503–534, 2024. [find](https://scholar.google.com/scholar?q=Nando+Leijenhorst+and+David+de+Laat%2E+Solving+clustered+low%2Drank+semidefinite+programs+arising+from+polynomial+optimization%2E+Mathematical+Programming+Computation%2C+16%283%29%3A503%E2%80%93534%2C+2024%2E)
194. M. Lemm. New counterexamples for sums-differences. Proceedings of the American Mathematical Society, 143(9):3863–3868, 2015. [find](https://scholar.google.com/scholar?q=M%2E+Lemm%2E+New+counterexamples+for+sums%2Ddifferences%2E+Proceedings+of+the+American+Mathematical+Society%2C+143%289%29%3A3863%E2%80%933868%2C+2015%2E)
195. Vladimir I. Levenshtein. On bounds for packings in 𝑛-dimensional Euclidean space. Doklady Akademii Nauk SSSR, 245(6):1299–1303, 1979. English translation in Soviet Mathematics Doklady 20 (1979), 417–421. [find](https://scholar.google.com/scholar?q=Vladimir+I%2E+Levenshtein%2E+On+bounds+for+packings+in+%F0%9D%91%9B%2Ddimensional+Euclidean+space%2E+Doklady+Akademii+Nauk+SSSR%2C+245%286%29%3A1299%E2%80%931303%2C+1979%2E+English+translation+in+Soviet+Mathematics+Doklady+20+%281979%29%2C+417%E2%80%934)
196. Mark Lewko. An improved lower bound related to the Furstenberg-Sárközy theorem. Electronic Journal of Combinatorics, 22:Paper 1.32, 2015. [find](https://scholar.google.com/scholar?q=Mark+Lewko%2E+An+improved+lower+bound+related+to+the+Furstenberg%2DS%C3%A1rk%C3%B6zy+theorem%2E+Electronic+Journal+of+Combinatorics%2C+22%3APaper+1%2E32%2C+2015%2E)
197. J. X. Li and B. Szegedy. On the logarithmic calculus and Sidorenko’s conjecture, 2011. arXiv:1107.1153. — [arXiv:1107.1153](https://arxiv.org/abs/1107.1153) [find](https://scholar.google.com/scholar?q=J%2E+X%2E+Li+and+B%2E+Szegedy%2E+On+the+logarithmic+calculus+and+Sidorenko%E2%80%99s+conjecture%2C+2011%2E+arXiv%3A1107%2E1153%2E+%E2%80%94+%5BarXiv%3A1107%2E1153%5D%28https%3A%2F%2Farxiv%2Eorg%2Fabs%2F1107%2E1153%29)
198. Elliott H. Lieb and Michael Loss. Analysis, volume 14 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 2nd edition, 2001. [find](https://scholar.google.com/scholar?q=Elliott+H%2E+Lieb+and+Michael+Loss%2E+Analysis%2C+volume+14+of+Graduate+Studies+in+Mathematics%2E+American+Mathematical+Society%2C+Providence%2C+RI%2C+2nd+edition%2C+2001%2E)
199. Helmut Linde. A lower bound for the ground state energy of a Schrödinger operator on a loop. Proc. Amer. Math. Soc., 134(12):3629– 3635, 2006. ∑ ∑ [find](https://scholar.google.com/scholar?q=Helmut+Linde%2E+A+lower+bound+for+the+ground+state+energy+of+a+Schr%C3%B6dinger+operator+on+a+loop%2E+Proc%2E+Amer%2E+Math%2E+Soc%2E%2C+134%2812%29%3A3629%E2%80%93+3635%2C+2006%2E+%E2%88%91+%E2%88%91)
200. J. E. Littlewood. On polynomials ±𝑧 𝑚 , 𝑒 𝛼 𝑚 𝑖 𝑧 𝑚 , 𝑧 = 𝑒 𝜃𝑖 . Journal of the London Mathematical Society, 41:367–376, 1966. [find](https://scholar.google.com/scholar?q=J%2E+E%2E+Littlewood%2E+On+polynomials+%C2%B1%F0%9D%91%A7+%F0%9D%91%9A+%2C+%F0%9D%91%92+%F0%9D%9B%BC+%F0%9D%91%9A+%F0%9D%91%96+%F0%9D%91%A7+%F0%9D%91%9A+%2C+%F0%9D%91%A7+%3D+%F0%9D%91%92+%F0%9D%9C%83%F0%9D%91%96+%2E+Journal+of+the+London+Mathematical+Society%2C+41%3A367%E2%80%93376%2C+1966%2E)
201. J. E. Littlewood. Some problems in real and complex analysis. Heath Mathematical Monographs. Raytheon Education, Lexington, Massachusetts, 1968. [find](https://scholar.google.com/scholar?q=J%2E+E%2E+Littlewood%2E+Some+problems+in+real+and+complex+analysis%2E+Heath+Mathematical+Monographs%2E+Raytheon+Education%2C+Lexington%2C+Massachusetts%2C+1968%2E)
202. Gang Liu, Yihan Zhu, Jie Chen, and Meng Jiang. Scientific Algorithm Discovery by Augmenting AlphaEvolve with Deep Research, 2025. [find](https://scholar.google.com/scholar?q=Gang+Liu%2C+Yihan+Zhu%2C+Jie+Chen%2C+and+Meng+Jiang%2E+Scientific+Algorithm+Discovery+by+Augmenting+AlphaEvolve+with+Deep+Research%2C+2025%2E)
203. Hong Liu and Richard Montgomery. A solution to Erdős and Hajnal’s odd cycle problem. Journal of the American Mathematical Society, 36(4):1191–1234, 2023. [find](https://scholar.google.com/scholar?q=Hong+Liu+and+Richard+Montgomery%2E+A+solution+to+Erd%C5%91s+and+Hajnal%E2%80%99s+odd+cycle+problem%2E+Journal+of+the+American+Mathematical+Society%2C+36%284%29%3A1191%E2%80%931234%2C+2023%2E)
204. László Lovász and Miklós Simonovits. On the number of complete subgraphs of a graph, II. In Studies in Pure Mathematics, pages 459–495. Birkhäuser, 1983. [find](https://scholar.google.com/scholar?q=L%C3%A1szl%C3%B3+Lov%C3%A1sz+and+Mikl%C3%B3s+Simonovits%2E+On+the+number+of+complete+subgraphs+of+a+graph%2C+II%2E+In+Studies+in+Pure+Mathematics%2C+pages+459%E2%80%93495%2E+Birkh%C3%A4user%2C+1983%2E)
205. Ben Lund, Shubhangi Saraf, and Charles Wolf. Finite field Kakeya and Nikodym sets in three dimensions. SIAM J. Discrete Math., 32(4):2836–2849, 2018. [find](https://scholar.google.com/scholar?q=Ben+Lund%2C+Shubhangi+Saraf%2C+and+Charles+Wolf%2E+Finite+field+Kakeya+and+Nikodym+sets+in+three+dimensions%2E+SIAM+J%2E+Discrete+Math%2E%2C+32%284%29%3A2836%E2%80%932849%2C+2018%2E)
206. Thang Luong and Edward Lockhart. Advanced version of Gemini with Deep Think officially achieves gold-medal standard at the International Mathematical Olympiad. [https://deepmind.google/discover/blog/](https://deepmind.google/discover/blog/) advanced-version-of-gemini-with-deep-think-officially-achieves-gold-medal-standard-at-the-internation… [↗](https://deepmind.google/discover/blog/)
207. Filip Marić. Fast formal proof of the Erdős–Szekeres conjecture for convex polygons with at most 6 points. Journal of Automated Reasoning, 62:301–329, 2019. [find](https://scholar.google.com/scholar?q=Filip+Mari%C4%87%2E+Fast+formal+proof+of+the+Erd%C5%91s%E2%80%93Szekeres+conjecture+for+convex+polygons+with+at+most+6+points%2E+Journal+of+Automated+Reasoning%2C+62%3A301%E2%80%93329%2C+2019%2E)
208. MathOverflow Community. Sofa in a snaky 3D corridor. MathOverflow, 2022. Question 246914. [find](https://scholar.google.com/scholar?q=MathOverflow+Community%2E+Sofa+in+a+snaky+3D+corridor%2E+MathOverflow%2C+2022%2E+Question+246914%2E)
209. MathOverflow Community. How large can 𝐏[𝑥 1 + 𝑥 2 + 𝑥 3 \\< 2𝑥 4 ] get? MathOverflow, 2024. Question 474916. [find](https://scholar.google.com/scholar?q=MathOverflow+Community%2E+How+large+can+%F0%9D%90%8F%5B%F0%9D%91%A5+1+%2B+%F0%9D%91%A5+2+%2B+%F0%9D%91%A5+3+%5C%3C+2%F0%9D%91%A5+4+%5D+get%3F+MathOverflow%2C+2024%2E+Question+474916%2E)
210. M. Matolcsi and C. J. Vinuesa. Improved bounds on the supremum of autoconvolutions. Journal of Mathematical Analysis and Applications, 372(2):439–447, 2010. [find](https://scholar.google.com/scholar?q=M%2E+Matolcsi+and+C%2E+J%2E+Vinuesa%2E+Improved+bounds+on+the+supremum+of+autoconvolutions%2E+Journal+of+Mathematical+Analysis+and+Applications%2C+372%282%29%3A439%E2%80%93447%2C+2010%2E)
211. A. Meir and A. Sharma. On Ilyeff’s conjecture. Pacific Journal of Mathematics, 31:459–467, 1969. [find](https://scholar.google.com/scholar?q=A%2E+Meir+and+A%2E+Sharma%2E+On+Ilyeff%E2%80%99s+conjecture%2E+Pacific+Journal+of+Mathematics%2C+31%3A459%E2%80%93467%2C+1969%2E)
212. A. Melas. On the centered Hardy–Littlewood maximal operator. Transactions of the American Mathematical Society, 354:3263–3273, 2002. [find](https://scholar.google.com/scholar?q=A%2E+Melas%2E+On+the+centered+Hardy%E2%80%93Littlewood+maximal+operator%2E+Transactions+of+the+American+Mathematical+Society%2C+354%3A3263%E2%80%933273%2C+2002%2E)
213. A. D. Melas. The best constant for the centered Hardy–Littlewood maximal inequality. Annals of Mathematics, 157:647–688, 2003. [find](https://scholar.google.com/scholar?q=A%2E+D%2E+Melas%2E+The+best+constant+for+the+centered+Hardy%E2%80%93Littlewood+maximal+inequality%2E+Annals+of+Mathematics%2C+157%3A647%E2%80%93688%2C+2003%2E)
214. Ali Mohammadi and Sophie Stevens. Attaining the exponent 5/4 for the sum-product problem in finite fields. Int. Math. Res. Not., 2023(4):3516–3532, 2023. [find](https://scholar.google.com/scholar?q=Ali+Mohammadi+and+Sophie+Stevens%2E+Attaining+the+exponent+5%2F4+for+the+sum%2Dproduct+problem+in+finite+fields%2E+Int%2E+Math%2E+Res%2E+Not%2E%2C+2023%284%29%3A3516%E2%80%933532%2C+2023%2E)
215. J. W. Moon and L. Moser. On a problem of Turán. Magyar. Tud. Akad. Mat. Kutató Int. Közl, 7:283–286, 1962. [find](https://scholar.google.com/scholar?q=J%2E+W%2E+Moon+and+L%2E+Moser%2E+On+a+problem+of+Tur%C3%A1n%2E+Magyar%2E+Tud%2E+Akad%2E+Mat%2E+Kutat%C3%B3+Int%2E+K%C3%B6zl%2C+7%3A283%E2%80%93286%2C+1962%2E)
216. Leo Moser. Moving furniture through a hallway. SIAM Review, 8(3):381–381, 1966. [find](https://scholar.google.com/scholar?q=Leo+Moser%2E+Moving+furniture+through+a+hallway%2E+SIAM+Review%2C+8%283%29%3A381%E2%80%93381%2C+1966%2E)
217. O. R. Musin and A. S. Tarasov. The strong thirteen spheres problem. Discrete & Computational Geometry, 48(1):128–141, 2012. [find](https://scholar.google.com/scholar?q=O%2E+R%2E+Musin+and+A%2E+S%2E+Tarasov%2E+The+strong+thirteen+spheres+problem%2E+Discrete+%26+Computational+Geometry%2C+48%281%29%3A128%E2%80%93141%2C+2012%2E)
218. Oleg R Musin. The kissing number in four dimensions. Annals of Mathematics, pages 1–32, 2008. [find](https://scholar.google.com/scholar?q=Oleg+R+Musin%2E+The+kissing+number+in+four+dimensions%2E+Annals+of+Mathematics%2C+pages+1%E2%80%9332%2C+2008%2E)
219. Oleg R. Musin and Alexey S. Tarasov. The Tammes Problem for 𝑁 = 14. Experimental Mathematics, 24(4):460–468, 2015. [find](https://scholar.google.com/scholar?q=Oleg+R%2E+Musin+and+Alexey+S%2E+Tarasov%2E+The+Tammes+Problem+for+%F0%9D%91%81+%3D+14%2E+Experimental+Mathematics%2C+24%284%29%3A460%E2%80%93468%2C+2015%2E)
220. Nobuaki Mutoh. The Polyhedra of Maximal Volume Inscribed in the Unit Sphere and of Minimal Volume Circumscribed about the Unit Sphere. In Jin Akiyama and Mikio Kano, editors, Discrete and Computational Geometry, volume 2866 of Lecture Notes in Computer Science, pages 204–214. Springer, Berlin, Heide… [find](https://scholar.google.com/scholar?q=Nobuaki+Mutoh%2E+The+Polyhedra+of+Maximal+Volume+Inscribed+in+the+Unit+Sphere+and+of+Minimal+Volume+Circumscribed+about+the+Unit+Sphere%2E+In+Jin+Akiyama+and+Mikio+Kano%2C+editors%2C+Discrete+and+Computationa)
221. Ansh Nagda, Prabhakar Raghavan, and Abhradeep Thakurta. Reinforced Generation of Combinatorial Structures: Applications to Complexity Theory. arXiv:2509.18057, 2025. — [arXiv:2509.18057](https://arxiv.org/abs/2509.18057) [find](https://scholar.google.com/scholar?q=Ansh+Nagda%2C+Prabhakar+Raghavan%2C+and+Abhradeep+Thakurta%2E+Reinforced+Generation+of+Combinatorial+Structures%3A+Applications+to+Complexity+Theory%2E+arXiv%3A2509%2E18057%2C+2025%2E+%E2%80%94+%5BarXiv%3A2509%2E18057%5D%28https%3A%2F%2Farxiv)
222. Arnold Neumaier. Interval Methods for Systems of Equations, volume 37 of Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge, 1990. [find](https://scholar.google.com/scholar?q=Arnold+Neumaier%2E+Interval+Methods+for+Systems+of+Equations%2C+volume+37+of+Encyclopedia+of+Mathematics+and+its+Applications%2E+Cambridge+University+Press%2C+Cambridge%2C+1990%2E)
223. E. A. Nordhaus and B. M. Stewart. Triangles in an ordinary graph. Canadian J. Math., 15:33–41, 1963. [find](https://scholar.google.com/scholar?q=E%2E+A%2E+Nordhaus+and+B%2E+M%2E+Stewart%2E+Triangles+in+an+ordinary+graph%2E+Canadian+J%2E+Math%2E%2C+15%3A33%E2%80%9341%2C+1963%2E)
224. Alexander Novikov, Ngân Vu, Marvin Eisenberger, Emilien Dupont, Po-Sen Huang, Adam Zsolt Wagner, Sergey Shirobokov, Borislav Kozlovskii, Francisco J. R. Ruiz, Abbas Mehrabian, M. Pawan Kumar, Abigail See, Swarat Chaudhuri, George Holland, Alex Davies, Sebastian Nowozin, Pushmeet Kohli, and Matej Bal… — [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://md.research.elamur.ai/free/en/papers/novikov-2025-alphaevolve-coding-agent-scientific-algorithmic/)
225. Andrew Odlyzko. Search for ultraflat polynomials with plus and minus one coefficients. In Connections in discrete mathematics. 2018. [find](https://scholar.google.com/scholar?q=Andrew+Odlyzko%2E+Search+for+ultraflat+polynomials+with+plus+and+minus+one+coefficients%2E+In+Connections+in+discrete+mathematics%2E+2018%2E)
226. Andrew M. Odlyzko and Neil J. A. Sloane. New bounds on the number of unit spheres that can touch a unit sphere in 𝑛 dimensions. Journal of Combinatorial Theory, Series A, 26(2):210–214, 1979. [find](https://scholar.google.com/scholar?q=Andrew+M%2E+Odlyzko+and+Neil+J%2E+A%2E+Sloane%2E+New+bounds+on+the+number+of+unit+spheres+that+can+touch+a+unit+sphere+in+%F0%9D%91%9B+dimensions%2E+Journal+of+Combinatorial+Theory%2C+Series+A%2C+26%282%29%3A210%E2%80%93214%2C+1979%2E)
227. Tom Packebusch and Stephan Mertens. Low autocorrelation binary sequences. J. Phys. A, Math. Theor., 49(16):18, 2016. Id/No 165001. [find](https://scholar.google.com/scholar?q=Tom+Packebusch+and+Stephan+Mertens%2E+Low+autocorrelation+binary+sequences%2E+J%2E+Phys%2E+A%2C+Math%2E+Theor%2E%2C+49%2816%29%3A18%2C+2016%2E+Id%2FNo+165001%2E)
228. C. Pearcy. An elementary proof of the power inequality for the numerical radius. Michigan Mathematical Journal, 13:289–291, 1966. [find](https://scholar.google.com/scholar?q=C%2E+Pearcy%2E+An+elementary+proof+of+the+power+inequality+for+the+numerical+radius%2E+Michigan+Mathematical+Journal%2C+13%3A289%E2%80%93291%2C+1966%2E)
229. D. Phelps and R. S. Rodriguez. Some properties of extremal polynomials for the Ilieff conjecture. Kodai Mathematical Seminar Reports, 24:172–175, 1972. [find](https://scholar.google.com/scholar?q=D%2E+Phelps+and+R%2E+S%2E+Rodriguez%2E+Some+properties+of+extremal+polynomials+for+the+Ilieff+conjecture%2E+Kodai+Mathematical+Seminar+Reports%2C+24%3A172%E2%80%93175%2C+1972%2E)
230. P. V. Pikhitsa, M. Choi, H.-J. Kim, and S.-H. Ahn. Auxetic lattice of multipods. Physica Status Solidi B, 246(9):2098–2101, 2009. [find](https://scholar.google.com/scholar?q=P%2E+V%2E+Pikhitsa%2C+M%2E+Choi%2C+H%2E%2DJ%2E+Kim%2C+and+S%2E%2DH%2E+Ahn%2E+Auxetic+lattice+of+multipods%2E+Physica+Status+Solidi+B%2C+246%289%29%3A2098%E2%80%932101%2C+2009%2E)
231. Peter V. Pikhitsa. Regular Network of Contacting Cylinders with Implications for Materials with Negative Poisson Ratios. Physical Review Letters, 93(1):015505, 2004. [find](https://scholar.google.com/scholar?q=Peter+V%2E+Pikhitsa%2E+Regular+Network+of+Contacting+Cylinders+with+Implications+for+Materials+with+Negative+Poisson+Ratios%2E+Physical+Review+Letters%2C+93%281%29%3A015505%2C+2004%2E)
232. Iwan Praton. The Erdos and Campbell-Staton conjectures about square packing, 2005. arXiv:0504341. [find](https://scholar.google.com/scholar?q=Iwan+Praton%2E+The+Erdos+and+Campbell%2DStaton+conjectures+about+square+packing%2C+2005%2E+arXiv%3A0504341%2E)
233. Danylo Radchenko and Maryna Viazovska. Fourier interpolation on the real line. Publications mathématiques de l’IHÉS, 129(1):51– 81, 2019. [find](https://scholar.google.com/scholar?q=Danylo+Radchenko+and+Maryna+Viazovska%2E+Fourier+interpolation+on+the+real+line%2E+Publications+math%C3%A9matiques+de+l%E2%80%99IH%C3%89S%2C+129%281%29%3A51%E2%80%93+81%2C+2019%2E)
234. E. A. Rakhmanov, E. B. Saff, and Y. M. Zhou. Minimal discrete energy on the sphere. Mathematical Research Letters, 1(5):647–662, 1994. √ [find](https://scholar.google.com/scholar?q=E%2E+A%2E+Rakhmanov%2C+E%2E+B%2E+Saff%2C+and+Y%2E+M%2E+Zhou%2E+Minimal+discrete+energy+on+the+sphere%2E+Mathematical+Research+Letters%2C+1%285%29%3A647%E2%80%93662%2C+1994%2E+%E2%88%9A)
235. Thomas Ransford and Felix Schwenninger. Remarks on the Crouzeix-Palencia proof that the numerical range is a (1 + 2)-spectral set. SIAM Journal on Matrix Analysis and Applications, 39(1):342–345, 2018. [find](https://scholar.google.com/scholar?q=Thomas+Ransford+and+Felix+Schwenninger%2E+Remarks+on+the+Crouzeix%2DPalencia+proof+that+the+numerical+range+is+a+%281+%2B+2%29%2Dspectral+set%2E+SIAM+Journal+on+Matrix+Analysis+and+Applications%2C+39%281%29%3A342%E2%80%93345%2C+2018)
236. A. Razborov. On 3-hypergraphs with forbidden 4-vertex configurations. SIAM Journal on Discrete Mathematics, 24(3):946–963, 2010. [find](https://scholar.google.com/scholar?q=A%2E+Razborov%2E+On+3%2Dhypergraphs+with+forbidden+4%2Dvertex+configurations%2E+SIAM+Journal+on+Discrete+Mathematics%2C+24%283%29%3A946%E2%80%93963%2C+2010%2E)
237. Alexander A. Razborov. On the minimal density of triangles in graphs. Combinatorics, Probability and Computing, 17(4):603–618, 2008. [find](https://scholar.google.com/scholar?q=Alexander+A%2E+Razborov%2E+On+the+minimal+density+of+triangles+in+graphs%2E+Combinatorics%2C+Probability+and+Computing%2C+17%284%29%3A603%E2%80%93618%2C+2008%2E)
238. Ingo Rechenberg. Point configurations with minimal distance ratio, 2006. [find](https://scholar.google.com/scholar?q=Ingo+Rechenberg%2E+Point+configurations+with+minimal+distance+ratio%2C+2006%2E)
239. Benjamin Recht and Christopher Ré. Beneath the valley of the noncommutative arithmetic-geometric mean inequality: conjectures, case-studies, and consequences, 2012. arXiv:1202.4184. — [arXiv:1202.4184](https://arxiv.org/abs/1202.4184) [find](https://scholar.google.com/scholar?q=Benjamin+Recht+and+Christopher+R%C3%A9%2E+Beneath+the+valley+of+the+noncommutative+arithmetic%2Dgeometric+mean+inequality%3A+conjectures%2C+case%2Dstudies%2C+and+consequences%2C+2012%2E+arXiv%3A1202%2E4184%2E+%E2%80%94+%5BarXiv%3A1202%2E4184)
240. L. Rédei and A. Rényi. On the representation of the numbers {1, 2, … , 𝑁} by means of differences. Mat. Sbornik N.S., 24/66:385–389, 1949. [find](https://scholar.google.com/scholar?q=L%2E+R%C3%A9dei+and+A%2E+R%C3%A9nyi%2E+On+the+representation+of+the+numbers+%7B1%2C+2%2C+%E2%80%A6+%2C+%F0%9D%91%81%7D+by+means+of+differences%2E+Mat%2E+Sbornik+N%2ES%2E%2C+24%2F66%3A385%E2%80%93389%2C+1949%2E)
241. R. M. Robinson. Arrangement of 24 Circles on a Sphere. Mathematische Annalen, 144:17–48, 1961. [find](https://scholar.google.com/scholar?q=R%2E+M%2E+Robinson%2E+Arrangement+of+24+Circles+on+a+Sphere%2E+Mathematische+Annalen%2C+144%3A17%E2%80%9348%2C+1961%2E)
242. Bernardino Romera-Paredes, Mohammadamin Barekatain, Alexander Novikov, Matej Balog, M. Pawan Kumar, Emilien Dupont, Francisco J. R. Ruiz, Jordan Ellenberg, Pengming Wang, Omar Fawzi, Pushmeet Kohli, and Alhussein Fawzi. [Mathematical discoveries from program search with large language models](https://md.research.elamur.ai/free/en/papers/paredes-2023-mathematical-discoveries-program-search-large/). Nature,…
243. D. Romik. Differential equations and exact solutions in the moving sofa problem. Experimental Mathematics, 27:316–330, 2018. [find](https://scholar.google.com/scholar?q=D%2E+Romik%2E+Differential+equations+and+exact+solutions+in+the+moving+sofa+problem%2E+Experimental+Mathematics%2C+27%3A316%E2%80%93330%2C+2018%2E)
244. I. Ruzsa. Sums of finite sets. In D. V. Chudnovsky, G. V. Chudnovsky, and M. B. Nathanson, editors, Number Theory: New York Seminar. Springer-Verlag, 1996. [find](https://scholar.google.com/scholar?q=I%2E+Ruzsa%2E+Sums+of+finite+sets%2E+In+D%2E+V%2E+Chudnovsky%2C+G%2E+V%2E+Chudnovsky%2C+and+M%2E+B%2E+Nathanson%2C+editors%2C+Number+Theory%3A+New+York+Seminar%2E+Springer%2DVerlag%2C+1996%2E)
245. Imre Z. Ruzsa. Difference sets without squares. Periodica Mathematica Hungarica, 15:205–209, 1984. [find](https://scholar.google.com/scholar?q=Imre+Z%2E+Ruzsa%2E+Difference+sets+without+squares%2E+Periodica+Mathematica+Hungarica%2C+15%3A205%E2%80%93209%2C+1984%2E)
246. E. B. Saff and A. B. J. Kuijlaars. Distributing many points on a sphere. The Mathematical Intelligencer, 19(1):5–11, 1997. [find](https://scholar.google.com/scholar?q=E%2E+B%2E+Saff+and+A%2E+B%2E+J%2E+Kuijlaars%2E+Distributing+many+points+on+a+sphere%2E+The+Mathematical+Intelligencer%2C+19%281%29%3A5%E2%80%9311%2C+1997%2E)
247. A. Sárk˝ ozy. On difference sets of sequences of integers. I. Acta Math. Acad. Sci. Hungar., 31(1-2):125–149, 1978. [find](https://scholar.google.com/scholar?q=A%2E+S%C3%A1rk%CB%9D+ozy%2E+On+difference+sets+of+sequences+of+integers%2E+I%2E+Acta+Math%2E+Acad%2E+Sci%2E+Hungar%2E%2C+31%281%2D2%29%3A125%E2%80%93149%2C+1978%2E)
248. Mehtaab Sawhney. On 𝑎 ⊂ [𝑛] such that 𝑎𝑏 + 1 is never squarefree for 𝑎, 𝑏 ∈ 𝑎. [https://www.math.columbia.edu/~msawhney/](https://www.math.columbia.edu/~msawhney/) Problem_848.pdf, 2025. [↗](https://www.math.columbia.edu/~msawhney/)
249. Johann Schellhorn. Personal communication, September 2025. Email to the authors of the AlphaEvolve whitepaper, analyzing the published hexagon packing constructions. [find](https://scholar.google.com/scholar?q=Johann+Schellhorn%2E+Personal+communication%2C+September+2025%2E+Email+to+the+authors+of+the+AlphaEvolve+whitepaper%2C+analyzing+the+published+hexagon+packing+constructions%2E)
250. Manfred Scheucher. Two disjoint 5-holes in point sets. Computational Geometry, 91:101670, 2020. [find](https://scholar.google.com/scholar?q=Manfred+Scheucher%2E+Two+disjoint+5%2Dholes+in+point+sets%2E+Computational+Geometry%2C+91%3A101670%2C+2020%2E)
251. G. Schmeisser. On Ilieff’s conjecture. Mathematische Zeitschrift, 156:165–173, 1977. [find](https://scholar.google.com/scholar?q=G%2E+Schmeisser%2E+On+Ilieff%E2%80%99s+conjecture%2E+Mathematische+Zeitschrift%2C+156%3A165%E2%80%93173%2C+1977%2E)
252. Gerhard Schmeisser. Bemerkungen zu einer Vermutung von Ilieff. Mathematische Zeitschrift, 111:121–125, 1969. [find](https://scholar.google.com/scholar?q=Gerhard+Schmeisser%2E+Bemerkungen+zu+einer+Vermutung+von+Ilieff%2E+Mathematische+Zeitschrift%2C+111%3A121%E2%80%93125%2C+1969%2E)
253. Alexander Schrijver, Paul Seymour, and Peter Winkler. The ring loading problem. SIAM review, 41(4):777–791, 1999. [find](https://scholar.google.com/scholar?q=Alexander+Schrijver%2C+Paul+Seymour%2C+and+Peter+Winkler%2E+The+ring+loading+problem%2E+SIAM+review%2C+41%284%29%3A777%E2%80%93791%2C+1999%2E)
254. K. Schütte and B. L. van der Waerden. Auf welcher Kugel haben 5,6,7,8 oder 9 Punkte mit Mindestabstand 1 Platz? Mathematische Annalen, 123:96–124, 1951. [find](https://scholar.google.com/scholar?q=K%2E+Sch%C3%BCtte+and+B%2E+L%2E+van+der+Waerden%2E+Auf+welcher+Kugel+haben+5%2C6%2C7%2C8+oder+9+Punkte+mit+Mindestabstand+1+Platz%3F+Mathematische+Annalen%2C+123%3A96%E2%80%93124%2C+1951%2E)
255. Richard Evan Schwartz. The Five-Electron Case of Thomson’s Problem. Experimental Mathematics, 22(2):157–186, 2013. [find](https://scholar.google.com/scholar?q=Richard+Evan+Schwartz%2E+The+Five%2DElectron+Case+of+Thomson%E2%80%99s+Problem%2E+Experimental+Mathematics%2C+22%282%29%3A157%E2%80%93186%2C+2013%2E)
256. Bl. Sendov. On the critical points of a polynomial. East Journal on Approximations, 1(2):255–258, 1995. [find](https://scholar.google.com/scholar?q=Bl%2E+Sendov%2E+On+the+critical+points+of+a+polynomial%2E+East+Journal+on+Approximations%2C+1%282%29%3A255%E2%80%93258%2C+1995%2E)
257. Asankhaya Sharma. Openevolve: an open-source evolutionary coding agent. [https://github.com/codelion/openevolve](https://github.com/codelion/openevolve), 2025. Open-source implementation of AlphaEvolve. [↗](https://github.com/codelion/openevolve)
258. F Bruce Shepherd. Single-sink multicommodity flow with side constraints. In Research Trends in Combinatorial Optimization: Bonn 2008, pages 429–450. Springer, 2009. [find](https://scholar.google.com/scholar?q=F+Bruce+Shepherd%2E+Single%2Dsink+multicommodity+flow+with+side+constraints%2E+In+Research+Trends+in+Combinatorial+Optimization%3A+Bonn+2008%2C+pages+429%E2%80%93450%2E+Springer%2C+2009%2E)
259. Alexander Sidorenko. A correlation inequality for bipartite graphs. Graphs and Combinatorics, 9:201–204, 1993. [find](https://scholar.google.com/scholar?q=Alexander+Sidorenko%2E+A+correlation+inequality+for+bipartite+graphs%2E+Graphs+and+Combinatorics%2C+9%3A201%E2%80%93204%2C+1993%2E)
260. James Singer. A theorem in finite projective geometry and some applications to number theory. Transactions of the American Mathematical Society, 43(3):377–385, 1938. [find](https://scholar.google.com/scholar?q=James+Singer%2E+A+theorem+in+finite+projective+geometry+and+some+applications+to+number+theory%2E+Transactions+of+the+American+Mathematical+Society%2C+43%283%29%3A377%E2%80%93385%2C+1938%2E)
261. Martin Skutella. A note on the ring loading problem. SIAM Journal on Discrete Mathematics, 30(1):327–342, 2016. [find](https://scholar.google.com/scholar?q=Martin+Skutella%2E+A+note+on+the+ring+loading+problem%2E+SIAM+Journal+on+Discrete+Mathematics%2C+30%281%29%3A327%E2%80%93342%2C+2016%2E)
262. N. J. A. Sloane. Maximal Volume Spherical Codes. Online tables, 1994. Part of ongoing work on spherical codes with R. H. Hardin and W. D. Smith. [find](https://scholar.google.com/scholar?q=N%2E+J%2E+A%2E+Sloane%2E+Maximal+Volume+Spherical+Codes%2E+Online+tables%2C+1994%2E+Part+of+ongoing+work+on+spherical+codes+with+R%2E+H%2E+Hardin+and+W%2E+D%2E+Smith%2E)
263. N. J. A. Sloane, R. H. Hardin, W. D. Smith, et al. Tables of Spherical Codes. Published electronically at [http://neilsloane.com/](http://neilsloane.com/) packings/, 1994–2024. Copyright R. H. Hardin, N. J. A. Sloane & W. D. Smith, 1994–1996. [↗](http://neilsloane.com/)
264. Neil J. A. Sloane. Spherical Designs. [find](https://scholar.google.com/scholar?q=Neil+J%2E+A%2E+Sloane%2E+Spherical+Designs%2E)
265. S. Smale. The fundamental theorem of algebra and complexity theory. Bulletin of the American Mathematical Society, 4(1):1–36, 1981. [find](https://scholar.google.com/scholar?q=S%2E+Smale%2E+The+fundamental+theorem+of+algebra+and+complexity+theory%2E+Bulletin+of+the+American+Mathematical+Society%2C+4%281%29%3A1%E2%80%9336%2C+1981%2E)
266. Stephen Smale. Mathematical Problems for the Next Century. The Mathematical Intelligencer, 20(2):7–15, 1998. [find](https://scholar.google.com/scholar?q=Stephen+Smale%2E+Mathematical+Problems+for+the+Next+Century%2E+The+Mathematical+Intelligencer%2C+20%282%29%3A7%E2%80%9315%2C+1998%2E)
267. Raymond Smullyan. What is the name of this book? Touchstone Books Guildford, UK, 1986. [find](https://scholar.google.com/scholar?q=Raymond+Smullyan%2E+What+is+the+name+of+this+book%3F+Touchstone+Books+Guildford%2C+UK%2C+1986%2E)
268. József Solymosi. Triangles in the integer grid [𝑛] × [𝑛]. 2023. [find](https://scholar.google.com/scholar?q=J%C3%B3zsef+Solymosi%2E+Triangles+in+the+integer+grid+%5B%F0%9D%91%9B%5D+%C3%97+%5B%F0%9D%91%9B%5D%2E+2023%2E)
269. József Solymosi. On Perles’ Configuration. SIAM Journal on Discrete Mathematics, 39(2):912–920, 2025. [find](https://scholar.google.com/scholar?q=J%C3%B3zsef+Solymosi%2E+On+Perles%E2%80%99+Configuration%2E+SIAM+Journal+on+Discrete+Mathematics%2C+39%282%29%3A912%E2%80%93920%2C+2025%2E)
270. Andrew Suk and Ethan Patrick White. A note on the no-(𝑑 + 2)-on-a-sphere problem. arXiv:2412.02866, 2024. — [arXiv:2412.02866](https://arxiv.org/abs/2412.02866) [find](https://scholar.google.com/scholar?q=Andrew+Suk+and+Ethan+Patrick+White%2E+A+note+on+the+no%2D%28%F0%9D%91%91+%2B+2%29%2Don%2Da%2Dsphere+problem%2E+arXiv%3A2412%2E02866%2C+2024%2E+%E2%80%94+%5BarXiv%3A2412%2E02866%5D%28https%3A%2F%2Farxiv%2Eorg%2Fabs%2F2412%2E02866%29)
271. Grzegorz Swirszcz, Adam Zsolt Wagner, Geordie Williamson, Sam Blackwell, Bogdan Georgiev, Alex Davies, Ali Eslami, Sebastien Racaniere, Theophane Weber, and Pushmeet Kohli. Advancing geometry with AI: Multi-agent generation of polytopes. arXiv preprint arXiv:2502.05199, 2025. — [arXiv:2502.05199](https://arxiv.org/abs/2502.05199) [find](https://scholar.google.com/scholar?q=Grzegorz+Swirszcz%2C+Adam+Zsolt+Wagner%2C+Geordie+Williamson%2C+Sam+Blackwell%2C+Bogdan+Georgiev%2C+Alex+Davies%2C+Ali+Eslami%2C+Sebastien+Racaniere%2C+Theophane+Weber%2C+and+Pushmeet+Kohli%2E+Advancing+geometry+with+AI%3A)
272. J. Sylvester. On Tchebycheff’s theory of the totality of the prime numbers comprised within given limits. In The collected mathematical papers of James Joseph Sylvester. Vol. 3, (1870-1883), pages 530–549. Cambridge University Press, Cambridge, 1909. [find](https://scholar.google.com/scholar?q=J%2E+Sylvester%2E+On+Tchebycheff%E2%80%99s+theory+of+the+totality+of+the+prime+numbers+comprised+within+given+limits%2E+In+The+collected+mathematical+papers+of+James+Joseph+Sylvester%2E+Vol%2E+3%2C+%281870%2D1883%29%2C+pages+530)
273. B. Szegedy. An information theoretic approach to Sidorenko’s conjecture, 2014. arXiv:1406.6738. — [arXiv:1406.6738](https://arxiv.org/abs/1406.6738) [find](https://scholar.google.com/scholar?q=B%2E+Szegedy%2E+An+information+theoretic+approach+to+Sidorenko%E2%80%99s+conjecture%2C+2014%2E+arXiv%3A1406%2E6738%2E+%E2%80%94+%5BarXiv%3A1406%2E6738%5D%28https%3A%2F%2Farxiv%2Eorg%2Fabs%2F1406%2E6738%29)
274. George Szekeres and Lindsay Peters. Computer solution to the 17-point Erdős–Szekeres problem. ANZIAM Journal, 48(2):151–164, 2006. [find](https://scholar.google.com/scholar?q=George+Szekeres+and+Lindsay+Peters%2E+Computer+solution+to+the+17%2Dpoint+Erd%C5%91s%E2%80%93Szekeres+problem%2E+ANZIAM+Journal%2C+48%282%29%3A151%E2%80%93164%2C+2006%2E)
275. Endre Szemerédi and William T. jun. Trotter. Extremal problems in discrete geometry. Combinatorica, 3:381–392, 1983. [find](https://scholar.google.com/scholar?q=Endre+Szemer%C3%A9di+and+William+T%2E+jun%2E+Trotter%2E+Extremal+problems+in+discrete+geometry%2E+Combinatorica%2C+3%3A381%E2%80%93392%2C+1983%2E)
276. Tamás Szőnyi, Antonello Cossidente, András Gács, Csaba Mengyán, Alessandro Siciliano, and Zsuzsa Weiner. On large minimal blocking sets in PG(2, 𝑞). J. Comb. Des., 13(1):25–41, 2005. [find](https://scholar.google.com/scholar?q=Tam%C3%A1s+Sz%C5%91nyi%2C+Antonello+Cossidente%2C+Andr%C3%A1s+G%C3%A1cs%2C+Csaba+Mengy%C3%A1n%2C+Alessandro+Siciliano%2C+and+Zsuzsa+Weiner%2E+On+large+minimal+blocking+sets+in+PG%282%2C+%F0%9D%91%9E%29%2E+J%2E+Comb%2E+Des%2E%2C+13%281%29%3A25%E2%80%9341%2C+2005%2E)
277. R. M. L. Tammes. On the Origin Number and Arrangement of the Places of Exits on the Surface of Pollengrains. Recueil des Travaux Botaniques Néerlandais, 27:1–84, 1930. [find](https://scholar.google.com/scholar?q=R%2E+M%2E+L%2E+Tammes%2E+On+the+Origin+Number+and+Arrangement+of+the+Places+of+Exits+on+the+Surface+of+Pollengrains%2E+Recueil+des+Travaux+Botaniques+N%C3%A9erlandais%2C+27%3A1%E2%80%9384%2C+1930%2E)
278. Quanyu Tang. Sharp schoenberg type inequalities and the de bruin–sharma problem. arXiv preprint arXiv:2508.10341, 2025. 21 pages, 1 figure. v2: major revision; added Sections 5–6 confirming two conjectures and providing a complete solution to the de Bruin–Sharma problem. — [arXiv:2508.10341](https://arxiv.org/abs/2508.10341) [find](https://scholar.google.com/scholar?q=Quanyu+Tang%2E+Sharp+schoenberg+type+inequalities+and+the+de+bruin%E2%80%93sharma+problem%2E+arXiv+preprint+arXiv%3A2508%2E10341%2C+2025%2E+21+pages%2C+1+figure%2E+v2%3A+major+revision%3B+added+Sections+5%E2%80%936+confirming+two+conjec)
279. T. Tao. Sendov’s conjecture for sufficiently high degree polynomials. Acta Mathematica, 229(2):347–392, 2022. [find](https://scholar.google.com/scholar?q=T%2E+Tao%2E+Sendov%E2%80%99s+conjecture+for+sufficiently+high+degree+polynomials%2E+Acta+Mathematica%2C+229%282%29%3A347%E2%80%93392%2C+2022%2E)
280. Terence Tao. The Erdős discrepancy problem. Discrete Anal., 2016:29, 2016. Id/No 1. [find](https://scholar.google.com/scholar?q=Terence+Tao%2E+The+Erd%C5%91s+discrepancy+problem%2E+Discrete+Anal%2E%2C+2016%3A29%2C+2016%2E+Id%2FNo+1%2E)
281. Terence Tao. New nikodym set constructions over finite fields. arXiv preprint arXiv:2511.07721, 2025. — [arXiv:2511.07721](https://arxiv.org/abs/2511.07721) [find](https://scholar.google.com/scholar?q=Terence+Tao%2E+New+nikodym+set+constructions+over+finite+fields%2E+arXiv+preprint+arXiv%3A2511%2E07721%2C+2025%2E+%E2%80%94+%5BarXiv%3A2511%2E07721%5D%28https%3A%2F%2Farxiv%2Eorg%2Fabs%2F2511%2E07721%29)
282. Terence Tao. Sum-difference exponents for boundedly many slopes, and rational complexity. arXiv preprint arXiv:2511.15135, 2025. — [arXiv:2511.15135](https://arxiv.org/abs/2511.15135) [find](https://scholar.google.com/scholar?q=Terence+Tao%2E+Sum%2Ddifference+exponents+for+boundedly+many+slopes%2C+and+rational+complexity%2E+arXiv+preprint+arXiv%3A2511%2E15135%2C+2025%2E+%E2%80%94+%5BarXiv%3A2511%2E15135%5D%28https%3A%2F%2Farxiv%2Eorg%2Fabs%2F2511%2E15135%29)
283. Amitayush Thakur, George Tsoukalas, Yeming Wen, Jimmy Xin, and Swarat Chaudhuri. [An in-context learning agent for formal theorem-proving](https://md.research.elamur.ai/free/en/papers/thakur-2023-context-learning-agent-formal-theorem/). In Conference on Language Models, 2024.
284. Torsten Thiele. Geometric selection problems and hypergraphs. PhD thesis, Citeseer, 1995. [find](https://scholar.google.com/scholar?q=Torsten+Thiele%2E+Geometric+selection+problems+and+hypergraphs%2E+PhD+thesis%2C+Citeseer%2C+1995%2E)
285. J. J. Thomson. On the structure of the atom. Philosophical Magazine, 7:237–265, 1904. [find](https://scholar.google.com/scholar?q=J%2E+J%2E+Thomson%2E+On+the+structure+of+the+atom%2E+Philosophical+Magazine%2C+7%3A237%E2%80%93265%2C+1904%2E)
286. L. Fejes Tóth. Über die Abschätzung des kürzesten Abstandes zweier Punkte eines auf einer Kugelfläche liegenden Punktsystems. Jahresbericht der Deutschen Mathematiker-Vereinigung, 53:66–68, 1943. [find](https://scholar.google.com/scholar?q=L%2E+Fejes+T%C3%B3th%2E+%C3%9Cber+die+Absch%C3%A4tzung+des+k%C3%BCrzesten+Abstandes+zweier+Punkte+eines+auf+einer+Kugelfl%C3%A4che+liegenden+Punktsystems%2E+Jahresbericht+der+Deutschen+Mathematiker%2DVereinigung%2C+53%3A66%E2%80%9368%2C+1943%2E)
287. Trieu H. Trinh, Yuhuai Wu, Quoc V. Le, He He, and Thang Luong. [Solving Olympiad Geometry without Human Demonstrations](https://md.research.elamur.ai/free/en/papers/trinh-2024-solving-olympiad-geometry-without-human/). Nature, 625(7995):476–482, 2024.
288. S.-H. Tso and P.-Y. Wu. Matricial ranges of quadratic operators. Rocky Mountain Journal of Mathematics, 29(3):1139–1152, 1999. [find](https://scholar.google.com/scholar?q=S%2E%2DH%2E+Tso+and+P%2E%2DY%2E+Wu%2E+Matricial+ranges+of+quadratic+operators%2E+Rocky+Mountain+Journal+of+Mathematics%2C+29%283%29%3A1139%E2%80%931152%2C+1999%2E)
289. M. S. Viazovska. The sphere packing problem in dimension 8. Annals of Mathematics, 185:991–1015, 2017. [find](https://scholar.google.com/scholar?q=M%2E+S%2E+Viazovska%2E+The+sphere+packing+problem+in+dimension+8%2E+Annals+of+Mathematics%2C+185%3A991%E2%80%931015%2C+2017%2E)
290. Adam Zsolt Wagner. Constructions in combinatorics via neural networks. arXiv:2104.14516, 2021. — [arXiv:2104.14516](https://arxiv.org/abs/2104.14516) [find](https://scholar.google.com/scholar?q=Adam+Zsolt+Wagner%2E+Constructions+in+combinatorics+via+neural+networks%2E+arXiv%3A2104%2E14516%2C+2021%2E+%E2%80%94+%5BarXiv%3A2104%2E14516%5D%28https%3A%2F%2Farxiv%2Eorg%2Fabs%2F2104%2E14516%29)
291. G. Wagner. On mean distances on the surface of the sphere (lower bounds). Pacific Journal of Mathematics, 144(2):389–398, 1990. [find](https://scholar.google.com/scholar?q=G%2E+Wagner%2E+On+mean+distances+on+the+surface+of+the+sphere+%28lower+bounds%29%2E+Pacific+Journal+of+Mathematics%2C+144%282%29%3A389%E2%80%93398%2C+1990%2E)
292. G. Wagner. On mean distances on the surface of the sphere II. upper bounds. Pacific Journal of Mathematics, 154(2):381–396, 1992. [find](https://scholar.google.com/scholar?q=G%2E+Wagner%2E+On+mean+distances+on+the+surface+of+the+sphere+II%2E+upper+bounds%2E+Pacific+Journal+of+Mathematics%2C+154%282%29%3A381%E2%80%93396%2C+1992%2E)
293. Hong Wang and Joshua Zahl. Volume estimates for unions of convex sets, and the Kakeya set conjecture in three dimensions, 2025. arXiv:2502.17655. — [arXiv:2502.17655](https://arxiv.org/abs/2502.17655) [find](https://scholar.google.com/scholar?q=Hong+Wang+and+Joshua+Zahl%2E+Volume+estimates+for+unions+of+convex+sets%2C+and+the+Kakeya+set+conjecture+in+three+dimensions%2C+2025%2E+arXiv%3A2502%2E17655%2E+%E2%80%94+%5BarXiv%3A2502%2E17655%5D%28https%3A%2F%2Farxiv%2Eorg%2Fabs%2F2502%2E17655%29)
294. Yongji Wang, Mehdi Bennani, James Martens, Sébastien Racanière, Sam Blackwell, Alex Matthews, Stanislav Nikolov, Gonzalo Cao-Labora, Daniel S. Park, Martin Arjovsky, Daniel Worrall, Chongli Qin, Ferran Alet, Borislav Kozlovskii, Nenad Tomašev, Alex Davies, Pushmeet Kohli, Tristan Buckmaster, Bogdan… [find](https://scholar.google.com/scholar?q=Yongji+Wang%2C+Mehdi+Bennani%2C+James+Martens%2C+S%C3%A9bastien+Racani%C3%A8re%2C+Sam+Blackwell%2C+Alex+Matthews%2C+Stanislav+Nikolov%2C+Gonzalo+Cao%2DLabora%2C+Daniel+S%2E+Park%2C+Martin+Arjovsky%2C+Daniel+Worrall%2C+Chongli+Qin%2C+Ferra)
295. Yongji Wang, Ching-Yao Lai, Javier Gómez-Serrano, and Tristan Buckmaster. Asymptotic Self-Similar Blow-Up Profile for Three-Dimensional Axisymmetric Euler Equations Using Neural Networks. Physical Review Letters, 130(24):244002, 2023. [find](https://scholar.google.com/scholar?q=Yongji+Wang%2C+Ching%2DYao+Lai%2C+Javier+G%C3%B3mez%2DSerrano%2C+and+Tristan+Buckmaster%2E+Asymptotic+Self%2DSimilar+Blow%2DUp+Profile+for+Three%2DDimensional+Axisymmetric+Euler+Equations+Using+Neural+Networks%2E+Physical+Rev)
296. Alexander Wei. Gold medal-level performance on the world’s most prestigious math competition—the International Math Olympiad (IMO). [https://x.com/alexwei_/status/1946477742855532918](https://x.com/alexwei_/status/1946477742855532918), 2025. [↗](https://x.com/alexwei_/status/1946477742855532918)
297. M. I. Weinstein. Nonlinear Schrödinger equations and sharp interpolation estimates. Communications in Mathematical Physics, 87:567–576, 1983. [find](https://scholar.google.com/scholar?q=M%2E+I%2E+Weinstein%2E+Nonlinear+Schr%C3%B6dinger+equations+and+sharp+interpolation+estimates%2E+Communications+in+Mathematical+Physics%2C+87%3A567%E2%80%93576%2C+1983%2E)
298. E. White. A new bound for Erdős’ minimum overlap problem. Acta Arithmetica, 208(3):235–255, 2023. [find](https://scholar.google.com/scholar?q=E%2E+White%2E+A+new+bound+for+Erd%C5%91s%E2%80%99+minimum+overlap+problem%2E+Acta+Arithmetica%2C+208%283%29%3A235%E2%80%93255%2C+2023%2E)
299. Chai Wah Wu. Counting the number of isosceles triangles in rectangular regular grids. arXiv:1605.00180, 2016. — [arXiv:1605.00180](https://arxiv.org/abs/1605.00180) [find](https://scholar.google.com/scholar?q=Chai+Wah+Wu%2E+Counting+the+number+of+isosceles+triangles+in+rectangular+regular+grids%2E+arXiv%3A1605%2E00180%2C+2016%2E+%E2%80%94+%5BarXiv%3A1605%2E00180%5D%28https%3A%2F%2Farxiv%2Eorg%2Fabs%2F1605%2E00180%29)
300. Kaiyu Yang, Gabriel Poesia, Jingxuan He, Wenda Li, Kristin Lauter, Swarat Chaudhuri, and Dawn Song. [Formal mathematical reasoning: A new frontier in AI](https://md.research.elamur.ai/free/en/papers/yang-2024-formal-mathematical-reasoning-new-frontier/), 2024.
301. Kaiyu Yang, Aidan Swope, Alex Gu, Rahul Chalamala, Peiyang Song, Shixing Yu, Saad Godil, Ryan J. Prenger, and Animashree Anandkumar. [Leandojo: Theorem proving with retrieval-augmented language models](https://md.research.elamur.ai/free/en/papers/yang-2023-leandojo-theorem-proving-retrieval-augmented/). In Advances in Neural Information Processing Systems, volume 36, pages 21573–21612, 2023.
302. Lu Yang and Zhenbing Zeng. Heilbronn problem for seven points in a planar convex body. In Ding-Zhu Du and Panos M. Pardalos, editors, Minimax and Applications, volume 4 of Nonconvex Optimization and Its Applications, pages 191–218, Boston, MA, 1995. Springer. Proved optimal solution for 7 points wit… [find](https://scholar.google.com/scholar?q=Lu+Yang+and+Zhenbing+Zeng%2E+Heilbronn+problem+for+seven+points+in+a+planar+convex+body%2E+In+Ding%2DZhu+Du+and+Panos+M%2E+Pardalos%2C+editors%2C+Minimax+and+Applications%2C+volume+4+of+Nonconvex+Optimization+and+I)
303. Lu Yang, Jingzhong Zhang, and Zhenbing Zeng. On a conjecture on and computation of the first Heilbronn numbers. Chin. Ann. Math., Ser. A, 13(4):503–515, 1992. [find](https://scholar.google.com/scholar?q=Lu+Yang%2C+Jingzhong+Zhang%2C+and+Zhenbing+Zeng%2E+On+a+conjecture+on+and+computation+of+the+first+Heilbronn+numbers%2E+Chin%2E+Ann%2E+Math%2E%2C+Ser%2E+A%2C+13%284%29%3A503%E2%80%93515%2C+1992%2E)
304. V. A. Yudin. Minimum Potential Energy of a Point System of Charges. Diskret. Mat., 4:115–121, 1992. in Russian; English translation in Discrete Math. Appl. 3 (1993) 75–81. [find](https://scholar.google.com/scholar?q=V%2E+A%2E+Yudin%2E+Minimum+Potential+Energy+of+a+Point+System+of+Charges%2E+Diskret%2E+Mat%2E%2C+4%3A115%E2%80%93121%2C+1992%2E+in+Russian%3B+English+translation+in+Discrete+Math%2E+Appl%2E+3+%281993%29+75%E2%80%9381%2E)
305. Fan Zheng. Sums and differences of sets: a further improvement over AlphaEvolve, 2025. arXiv:2506.01896. (Bogdan Georgiev) G OOGLE D EEP M IND , H ANDYSIDE S TREET , K INGS C ROSS , L ONDON N1C 4UZ, UK Email address: bogeorgiev@google.com (Javier Gómez-Serrano) D EPARTMENT OF M ATHEMATICS , B ROWN U… — [arXiv:2506.01896](https://arxiv.org/abs/2506.01896) [find](https://scholar.google.com/scholar?q=Fan+Zheng%2E+Sums+and+differences+of+sets%3A+a+further+improvement+over+AlphaEvolve%2C+2025%2E+arXiv%3A2506%2E01896%2E+%28Bogdan+Georgiev%29+G+OOGLE+D+EEP+M+IND+%2C+H+ANDYSIDE+S+TREET+%2C+K+INGS+C+ROSS+%2C+L+ONDON+N1C+4UZ%2C+U)

*Updated 3 November 2026*