Claude's Fermat formalization and an AI-assisted proof stir debate over math's future

In the same week that Anthropic's Claude completed a formalization of Fermat's Last Theorem in the Lean proof assistant, a separate preprint appeared proving a geometry conjecture that had stood open for roughly half a century, with acknowledged help from an AI system. Both developments are drawn together in a blog post on mbmccoy.dev, written by a trained mathematician, that reached the front page of Hacker News and argues that research mathematics has quietly crossed a threshold.

Fermat's Last Theorem, machine-checked

Fermat's Last Theorem, the claim that no three positive integers satisfy a to the n plus b to the n equals c to the n for any exponent greater than two, took humanity more than three centuries to settle, with Andrew Wiles's 1990s proof closing the case. According to the blog post, Claude has now finished formalizing that proof in Lean, meaning the argument has been rewritten so that software verifies every logical step rather than relying on human referees.

Formalizing a proof is not the same as discovering one, and the theorem was already established. But Wiles's argument rests on a deep stack of modern number theory, and converting it into a fully machine-checked form is a substantial formal-mathematics project. An AI system completing it suggests a move from models that merely suggest tactics toward systems that can carry out large verification efforts largely on their own.

A 1974 conjecture, proved with Codex

The second result lands closer to the author's own career. A preprint by Wang and Wu of Hunan University proves the Spherical Hadwiger Conjecture, which the author describes as a specialized but significant piece of integral geometry that had been open since around 1974. The author attempted it in graduate school and tried again earlier this year with AI assistance, without success.

The paper's acknowledgment states that OpenAI's Codex assisted with developing proof details, identifying gaps and points needing clarification, organizing and typesetting the manuscript, and editing the English, while the authors reviewed and verified all AI-assisted content, made every final decision, and accept full responsibility for the work. As the author points out, that division of labor leaves open the possibility that the model performed much of the reasoning, filling in arguments and repairing gaps, that until very recently required a research mathematician. The author has not fully verified the proof; an initial read-through, partly conducted with another AI model, surfaced no obvious problems, and the paper reportedly follows the AI-disclosure principles of the Leiden Declaration.

The profession with the highest exposure

The post recalls a whitepaper OpenAI published alongside GPT-4's launch that modeled how exposed various occupations were to large language models. Mathematicians topped every category examined: one hundred percent of the job was judged exposed across all three labor models in the study, ranking above writers, translators, artists, and graphic designers. The author's reading is that mathematics simply took longer to feel the effects, and suggests the delay owed as much to the field's limited training data and modest direct economic value as to its inherent difficulty.

A conservatory for mathematics

The essay's central metaphor is classical music: an art form society chose to preserve through conservatories, training a small number of practitioners and paying a handful of the best to perform professionally. Pure mathematics, the author argues, already inhabits such an institution, the academy, with few jobs outside universities and results understood by small communities.

The questions that follow are practical. AI tools can make it harder to judge whether a long argument is correct, and harder still to allocate credit, funding, and tenure when a machine contributes decisive intellectual labor. The author closes by asking whether society will keep supporting a culture of human mathematicians once their output no longer compares with what computers can produce, and expresses hope that it will.

Why it matters

Two independent signals in a single week, a completed machine-checked formalization of one of the most famous theorems in mathematics and an acknowledged AI-assisted proof of a standing research conjecture, indicate that AI systems are now operating at the level of professional mathematics rather than classroom exercises. If AI-assisted proofs become routine, the bottleneck shifts from producing mathematics to verifying and understanding it, which puts proof assistants like Lean and disclosure norms like the Leiden Declaration at the center of the discipline's future. The Wang and Wu proof still awaits full community vetting, and one essay is not a survey of an entire field, but the shift it describes is now visible in preprints and formalization repositories alike.