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Checking that a major mathematical proof is correct can take years. Formalization—converting the mathematical reasoning into a form computer proof assistants like Lean can verify—can help. Last month, Claude completed the first formalized proof of Fermat’s Last Theorem, one of the most famous theorems of all time. This was a project experts thought would take many years. It is the largest Lean proof ever written. Fermat’s Last Theorem was first proven in 1995 by Sir Andrew Wiles, more than 350 years after it was conjectured. Our proof, which totals over 13 million lines of code, provides machine verification. More importantly, it proves over 29,000 other theorems that the proof requires, across many areas of math which had never before been formalized. We see this as a major step in the long process of firming up the core of mathematical knowledge, building on work from three centuries of mathematicians and hundreds of contributors to Lean and Mathlib. We are optimistic that AI-assisted verification of mathematical proofs will help reduce the burden of refereeing mathematics in an era where more proofs are being produced than ever before. You can read about the process on our Science Blog: https://www.anthropic.com/research/formalizing-fermats-last-theorem And see the complete proof on GitHub: https://github.com/anthropics/fermats-last-theorem

Our evaluation results for Orbis 1.0: Across automated benchmarks, Orbis scores highest on DOVER aesthetic and technical quality, and on VideoAlign visual and motion quality. It also leads three physical-plausibility protocols: VideoPhy-2, Physics-IQ, and VBench-2.0 Physics. In a randomized human Arena study of state-of-the-art real-time interactive video systems, Orbis ranked first in overall preference and first in temporal stability, the prerequisite for long-form generation. Full report: https://www.visko.ai/blog/papers/files/Visko_Orbis_1_0__A_Live_Model_for_Real_TimeInteractive_Long_Video_Generation.pdf

New OpenAI repo with a Lean formalization by GPT-6-Astra proves that there are infinitely many pairs of consecutive primes whose distance is at most 186 https://github.com/openai/PrimeGaps186

We invite you to read the full TRACES technical report Inside: the definitions, evaluation rubric, and registry of problems spanning biomedicine, clinical translation, and frontier-model engineering. Led by Apodex Lead Scientist @profshengwang, the report brings together the technical framework underpinning this effort. Behind it: 10 STEM PhDs, two months of research, and 561 industries surveyed to identify 423 problems worth solving—real, high-stakes questions that can take human experts years to work through. Bring a problem. Bring a solver. Both doors are open. *Submit a Problem: https://traces.apodex.com/submit-your-problem *Submit a Solver: https://traces.apodex.com/submit-your-solver