# Learning Algebraic Structures: Preliminary Investigations

arXiv: https://arxiv.org/abs/1905.02263 · HTML: https://mlsanity.com/paper/1905.02263/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 May 2019.

## Built on by (most cited first, 15 of 15)

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- [From the String Landscape to the Mathematical Landscape: a Machine-Learning Outlook](https://mlsanity.com/paper/2202.06086/) (2022)
- [Transport of Algebraic Structure to Latent Embeddings](https://mlsanity.com/paper/2405.16763/) (2024)
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- [Learning to be Simple](https://mlsanity.com/paper/2312.05299/) (2023)
- [Murmurations: a case study in AI-assisted mathematics](https://mlsanity.com/paper/2603.09680/) (2026)

## Abstract (arXiv)

We employ techniques of machine-learning, exemplified by support vector machines and neural classifiers, to initiate the study of whether AI can "learn" algebraic structures. Using finite groups and finite rings as a concrete playground, we find that questions such as identification of simple groups by "looking" at the Cayley table or correctly matching addition and multiplication tables for finite rings can, at least for structures of small size, be performed by the AI, even after having been trained only on small number of cases. These results are in tandem with recent investigations on whether AI can solve certain classes of problems in algebraic geometry.