Mathematicians in the age of AI

Jeremy Avigad

math.HOMar 4, 2026

Mathematicians in the age of AI

Authors: Jeremy Avigad

Abstract

Recent developments show that AI can prove research-level theorems in mathematics, both formally and informally. This essay urges mathematicians to stay up-to-date with the technology, to consider the ways it will disrupt mathematical practice, and to respond appropriately to the challenges and opportunities we now face.

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Artificial Intelligence and the Structure of Mathematics

Maissam Barkeshli, Michael R. Douglas, Michael H. Freedman

Meta Superintelligence Labs, Fundamental AI Research · Department of Physics and Joint Quantum Institute, University of Maryland, College Park · Center for Mathematical Sciences and Applications, Harvard University+1

AI Agents for Scientific Discovery Mathematical Reasoning

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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 mathematicallogic, to understanding the global structure of formal proof****s. 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?

Abstract

Explore similar work

Artificial Intelligence and the Structure of Mathematics

What is mathematics now, and what should it be?

Machine learning and information theory concepts towards an AI Mathematician