Anthropic 'formalizes' Fermat's Last Theorem like never before using Claude — but it still took 11 days to write out

Claude turned a famous mathematical proof into millions of checkable code lines Anthropic says Claude completed years of expected work in 11 days The massive proof contains 13 million lines of Lean code Anthropic has used its Claude artificial intelligence system to produce a fully computer-checked

<![CDATA[ <article> <ul><li><strong>Claude turned a famous mathematical proof into millions of checkable code lines</strong></li><li><strong>Anthropic says Claude completed years of expected work in 11 days</strong></li><li><strong>The massive proof contains 13 million lines of Lean code</strong></li></ul><p>Anthropic has used its Claude artificial intelligence system to produce a fully computer-checked version of a famous, centuries-old mathematical proof.</p><p>The proof addresses Fermat's Last Theorem, a hypothesis first proposed by the mathematician Pierre de Fermat back in the year 1637.</p><p>Mathematician Andrew Wiles produced the very first full mathematical proof of the theorem back in 1995, spanning 129 pages total in length.</p><h2 id="a-proof-rebuilt-for-machines">A proof rebuilt for machines</h2><p>Formalizing a proof simply means converting its mathematical reasoning into code that computers can check automatically without any human assistance.</p><p><a href="https://www.anthropic.com/research/formalizing-fermats-last-theorem" target="_blank" rel="nofollow">Anthropic</a> says it expected the entire task to take several years, based on how mathematicians first described the project.</p><p>Instead, the company says its internal research model finished the entire proof in only 11 days of continuous, largely unsupervised work.</p><p>The finished proof runs to 13 million lines of specialized code written in a programming language called Lean, used by mathematicians.</p><p>Along the way, Claude's agents reportedly proved roughly 30,300 separate theorems, ultimately using 29,500 of them in the final version.</p><p>Human input was reportedly limited to occasional high-level guidance, rather than any direct hands-on coding throughout the entire eleven-day process.</p><p>At 13 million lines, the resulting proof is over five times larger than Mathlib, the community's own main proof library.</p><p>"This extraordinary autoformalization achievement…proves Fermat's Last Theorem with no assumptions other than the axioms of mathematics," said Kevin Buzzard, a mathematician at Imperial College London.</p><p>“Along the way we see autoformalization of algebra, harmonic analysis, geometry and number theory, and we learn that AI autoformalization artefacts are now robust enough to be built upon; the proof is multi-layered.”</p><p>Anthropic attempted the formalization several times before succeeding, with those efforts contributing roughly 7% of the final proof’s non-boilerplate lines.</p><h2 id="not-anthropic-39-s-first-math-breakthrough">Not Anthropic's first math breakthrough</h2><p>The formalization arrives just one month after Anthropic detailed a separate breakthrough involving the Riemann zeta function, a well-studied mathematical object.</p><p>That function sits at the very center of the Riemann hypothesis, considered one of mathematics' hardest unsolved problems worldwide.</p><p>Rival lab OpenAI is also pursuing similar work, using its newest Astra model to solve several classic Erdős problems.</p><p>That same OpenAI effort also reportedly narrowed several long-standing open questions within the field of theoretical computer science.</p><p>Anthropic says its breakthrough came only after giving Claude access to an open-source software tool named Prove2Me, built by outside collaborators.</p><p>The software helps AI agents pick the most useful next step during a long, multi-stage research workflow, while also cutting inference costs.</p><p>Anthropic has also expanded free access and research credits for mathematicians working specifically on formalization projects, alongside dedicated larger grants.</p><p>Despite the record pace set here, an eleven-day timeline still shows how labor-intensive full formalization remains, even with today's most capable systems.</p><figure class="van-image-figure inline-layout" data-bordeaux-image-check ><div class='image-full-width-wrapper'><div class='image-widthsetter' style="max-width:676px;"><p class="vanilla-image-block" style="padding-top:31.51%;"><img id="diM9tpwF2Lz85R8q85CT78" name="tr-g_news" alt="Google logo on a black background next to text reading 'Click to follow TechRadar'" src="https://cdn.mos.cms.futurecdn.net/diM9tpwF2Lz85R8q85CT78.jpg" mos="" align="middle" fullscreen="" width="676" height="213" attribution="" endorsement="" class="inline"></p></div></div></figure> </article> ]]>