mlsanityData to 7 Oct 2026

Artificial Intelligence and the Structure of Mathematics

arXiv 2604.06107 ↗First posted 7 Apr 2026cs.AI math.HO math.LOcited by 2

Not on the map. Why?

Abstract (arXiv)

Recent progress in artificial intelligence (AI) is unlocking transformative capabilities for mathematics. There is great hope that AI will help solve major open problems and autonomously discover new mathematical concepts. In this essay, we further consider how AI may open a grand perspective on mathematics by forging a new route, complementary to mathematical logic, to understanding the global structure of formal proofs. We begin by providing a sketch of the formal structure of mathematics in terms of universal proof and structural hypergraphs and discuss questions this raises about the foundational structure of mathematics. We then outline the main ingredients and provide a set of criteria to be satisfied for AI models capable of automated mathematical discovery. As we send AI agents to traverse Platonic mathematical worlds, we expect they will teach us about the nature of mathematics: both as a whole, and the small ribbons conducive to human understanding. Perhaps they will shed light on the old question: "Is mathematics discovered or invented?" Can we grok the terrain of these Platonic worlds?

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 25 of its 86 references that are in the map. First posted on arXiv 7 Apr 2026.

Builds on

25 of 86 references.

References · 25

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13 more
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Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026A Theoretical Framework for Self-Play Theorem Proving Algorithmscited by 1
  2. 2026Learning to Discover Interesting Mathematicscited by 0