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Terence Tao published a blog post detailing his reasons for not adding his name to a letter signed by fellow Fields Medal winners. The post opens with an extended personal anecdote about his childhood fascination with Fermat's Last Theorem before turning to his actual rationale for abstaining from the collective statement.
OpenAI announced its AI agents helped solve a 90-year-old math problem carrying a $1 million prize, building on work by mathematicians Diego Córdoba and Luis Martínez-Zoroa, though the solution still requires independent verification. Mathematician Tristan Buckmaster alleges OpenAI rushed to publish after learning of his own unpublished work with Anthropic researcher Levent Alpöge, and tried to shape who received credit. The dispute follows Anthropic's recent claim that its Claude model proved thousands of small theorems while formalizing a proof of Fermat's Last Theorem.
Two children died in separate gene-editing clinical trials in China, prompting scrutiny from researchers, ethicists and legal scholars over how such studies are approved and monitored. Investigators say the trials involved ethical breaches that could carry lasting consequences for China's biomedical research sector.
Anthropic announced that an advanced prototype of its Claude AI model converted Andrew Wiles' famous proof of Fermat's Last Theorem into a fully computer-verified formal proof, spanning roughly 13 million lines of code. The task, expected to take human mathematicians about a decade, was completed by the AI in just 11 days. Researchers including Alex Kontorovich and Kevin Buzzard called the achievement astonishing given how quickly AI's formalization skills have advanced.
Mathematicians Wang and Wu of Hunan University released a preprint proving the Spherical Hadwiger Conjecture, an integral-geometry problem unsolved since 1974, using OpenAI Codex to help develop proof details, spot gaps, and draft the manuscript. The authors say they verified all AI-generated mathematical content themselves and take full responsibility for the final result, following disclosure practices similar to the Leiden Declaration guidelines for AI use in research.
A complete formalization of Fermat's Last Theorem has been written and verified in the Lean 4 proof assistant, built atop the Mathlib library and following the Frey-Serre-Ribet-Wiles-Taylor-Wiles argument. The repository builds all 60,475 modules from scratch, with every declaration checked by the Lean kernel, and the final theorem relies solely on Lean's three standard axioms rather than any sorry or added axiom. An independent tool, leanprover/comparator, confirmed the proved statement matches a separately stated Mathlib-only challenge and that the entire proof chain replays correctly.