Jeremy Avigad asks what mathematics should become as AI turns into a research participant
Posted to arXiv on August 24, 2026, a new essay by Jeremy Avigad argues that recent theorem-proving milestones should widen, not narrow, the conversation about how AI can serve mathematical practice.
A recent AI-math essay asks a better question than "can the model solve it?"
Jeremy Avigad's essay What is mathematics now, and what should it be?, posted to arXiv on August 24, 2026, is notable because it does not treat AI and mathematics as a race for one more headline result. Instead, it starts from the observation that recent neural theorem-proving advances are real, then asks what a healthier mathematical culture should do with them.
Why this matters for AI in mathematics
That shift is important for MathsAI readers. Once AI systems can formalize statements, search proof paths, and contribute to research workflows, the central question is no longer only whether they can produce mathematical artifacts. It is also how mathematicians, teachers, and tool builders should organize explanation, verification, authorship, and training around those capabilities.
What the source reports
According to the arXiv abstract, Avigad argues that impressive neural theorem-prover results can obscure a broader vision of what AI can do for mathematics and how mathematicians can engage with it. The abstract frames the paper as an essay offering a more expansive and optimistic point of view, rather than a narrow scorecard about benchmark wins.
The practical lesson
This is a useful reminder that AI applications in mathematics should be judged by more than problem-solving demos. A strong system might help a learner compare two definitions, help a researcher inspect where a formal proof diverges from an informal sketch, or help a department rethink what students should still memorize versus what they should learn to verify, explain, and question. Those uses are less theatrical than a single solved conjecture, but they may matter more in everyday mathematical life.
What MathsAI readers should watch next
Expect more of the conversation to move from raw capability toward mathematical governance and design: which parts of mathematical work should be delegated, which should stay human-centered, and how tools should expose uncertainty, provenance, and the difference between a checkable result and genuine understanding. That makes this essay timely even though it is reflective rather than experimental.