---
title: "Why Machines Cannot Learn Mathematics, Yet (2019)"
description: "As a concrete step, they propose Mathematical Objects of Interest (MOI), a… 48.60% precision. 36 references, cited by 7 papers here."
authors: ["André Greiner-Petter", "Terry Ruas", "Moritz Schubotz", "Akiko Aizawa", "William Grosky", "Bela Gipp"]
year: 2019
venue: "arXiv:1905.08359 (2019 http://ceur-ws.org/Vol-2414/paper14.pdf)"
source: "https://arxiv.org/abs/1905.08359"
doi: "10.48550/arxiv.1905.08359"
arxiv: "1905.08359"
licence: "arXiv — non-exclusive licence to distribute"
licence_url: "https://arxiv.org/licenses/nonexclusive-distrib/1.0/license.html"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/petter-2019-why-machines-cannot-learn-mathematics/"
---
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# Why Machines Cannot Learn Mathematics, Yet

**Authors:** [André Greiner-Petter](https://md.research.elamur.ai/free/en/authors/andre-greiner-petter/), [Terry Ruas](https://md.research.elamur.ai/free/en/authors/terry-ruas/), [Moritz Schubotz](https://md.research.elamur.ai/free/en/authors/moritz-schubotz/), [Akiko Aizawa](https://md.research.elamur.ai/free/en/authors/akiko-aizawa/), William Grosky and [Bela Gipp](https://md.research.elamur.ai/free/en/authors/bela-gipp/) · **Year:** 2019 · **Venue:** arXiv:1905.08359 (2019 http://ceur-ws.org/Vol-2414/paper14.pdf) · **Licence:** [arXiv — non-exclusive licence to distribute](https://arxiv.org/licenses/nonexclusive-distrib/1.0/license.html)

**Links:** [Publisher's page](https://arxiv.org/abs/1905.08359) · [PDF](https://arxiv.org/pdf/1905.08359v1) · [DOI 10.48550/arxiv.1905.08359](https://doi.org/10.48550/arxiv.1905.08359) · [arXiv 1905.08359](https://arxiv.org/abs/1905.08359) · [OpenAlex](https://openalex.org/W2945597847)

**Citations:** 5 citations (OpenAlex, 2026-10-14) · [7](https://md.research.elamur.ai/free/en/papers/petter-2019-why-machines-cannot-learn-mathematics/cited-by/) in our library, of the 149,439 papers whose bibliographies we read

## Summary
The paper asks why machine learning, especially text embedding methods, has done so poorly at capturing the meaning of mathematical notation in STEM documents. The authors argue that formulas are short, ambiguous and dependent on context. For example, in W(2,k) the symbol W may be a function or a variable. Formulas are also defined only loosely in the surrounding prose, so embeddings trained on raw text cannot reliably tie symbols to their definitions.

To test this, they applied word2vec and Paragraph Vectors to the arXMLiv 2018 collection of arXiv papers. They also reviewed related embedding work (EqEmb, symbol embeddings, math-aware topic models) and found that it shows appealing examples but lacks rigorous MIR evaluation.

They identify several missing ingredients:
- a lexical resource for mathematics, comparable to WordNet,
- staged training that starts from educational texts before moving to research papers,
- shared evaluation standards.

As a concrete step, they propose Mathematical Objects of Interest (MOI), a recursive tree representation intended to unify how the semantics of expressions are interpreted. The work matters because it explains why current results in this area are often overstated.

## Key points
- Experiments trained word2vec (skip-gram/CBOW) and Paragraph Vectors (DM/DBOW) on the arXMLiv 2018 dataset. The motivating examples come from the MathMLBen benchmark, which converts LaTeX to MathML.
- The authors treat an earlier identifier–definiens extraction method (POS patterns, distance scoring and SVM) as the MIR baseline. It reached 48.60% precision and 28.06% recall.
- The paper finds the content MathML 3.0 and OpenMath definitions too vague, for instance on csymbol and on nested identifiers such as α_i. It contrasts three tokenization routes: the POM tagger on TeX, SLT trees from presentation MathML, and content MathML.
- In the proposed MOI structure, every node is itself an MOI. For example, α_i becomes a parent node whose two children are α and i.
- Planned future work covers the frequency statistics of mathematical objects, which preliminary results suggest follow Zipf's law, and tf-idf analysis of formulas. The research was funded by DFG grant GI-1259-1.

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

## Institutions

- [University of Michigan](https://md.research.elamur.ai/free/en/universities/university-of-michigan/) — University, Ann Arbor, United States · 94 works · 18,548 citations
- [National Institute of Informatics](https://md.research.elamur.ai/free/en/labs/national-institute-of-informatics/) — Research institute, Tokyo, Japan · 40 works · 3,317 citations
- [University of Konstanz](https://md.research.elamur.ai/free/en/universities/university-of-konstanz/) — University, Konstanz, Germany · 19 works · 274 citations
- [University of Wuppertal](https://md.research.elamur.ai/free/en/universities/university-of-wuppertal/) — University, Wuppertal, Germany · 2 works · 29 citations
- [University of Michigan–Dearborn](https://md.research.elamur.ai/free/en/universities/university-of-michigan-dearborn/) — University, Dearborn, United States · 3 works · 42 citations

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

## Cite

Cite as: André Greiner-Petter, Terry Ruas, Moritz Schubotz, Akiko Aizawa, William Grosky and Bela Gipp. 2019. Why Machines Cannot Learn Mathematics, Yet. arXiv:1905.08359 (2019 http://ceur-ws.org/Vol-2414/paper14.pdf).

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

```bibtex
@misc{greinerpetter2019why,
  title = {{Why Machines Cannot Learn Mathematics, Yet}},
  author = {André Greiner-Petter, Terry Ruas, Moritz Schubotz, Akiko Aizawa, William Grosky and Bela Gipp},
  year = {2019},
  doi = {10.48550/arxiv.1905.08359},
  eprint = {1905.08359},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.1905.08359}
}
```

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## References

36 references, 13 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet.

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*Updated 3 November 2026*