Just now, another shocking piece of news emerged in the mathematics community.
A team led by a prodigy from Tsinghua University's Yao Class has completely conquered Fermat's Last Theorem using Claude.
With this, AI has completed the largest proof in the history of mathematics.
Once upon a time, Fermat's Last Theorem tormented humanity for over 350 years, requiring mathematicians to dedicate years of effort and write a 129-page esoteric paper to prove it.
Today, however, Anthropic announced that Claude completed the first end-to-end machine-verified proof of Fermat's Last Theorem in just 11 days!
To achieve this, Claude frenziedly wrote 13 million lines of code, produced 30,300 verifiable theorems, of which 29,500 were adopted directly into the final proof.
This volume is more than 5 times that of the world's largest mathematical theorem library, Mathlib! Moreover, the entire process consumed a whopping 6 billion tokens.
This is the largest Lean proof written to date.
The news sent shockwaves across the internet. Some exclaimed: 'They formalized Fermat's Last Theorem in just a month? This muscle-flexing makes the math world look like it's crawling like snails.'
Yao Class prodigy Peng Tianyi
A 350-Year Century Puzzle, Solved by Claude in 11 Days
In 1637, the French mathematician Pierre de Fermat was reading a book when he casually scribbled in the margin:
Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et generaliter nullam in infinitum ultra quadratum potestatem in duos eiusdem nominis fas est dividere cuius rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caperet.
He added a dig: 'I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.'
That single sentence tormented mathematicians for over three hundred years.
It wasn't until 1995 that British mathematician Andrew Wiles, using profound modern mathematical tools, produced a 129-page proof, finally putting an end to this 350-year-old mystery.
But here's the problem: Wiles' proof is incredibly complex.
Modern mathematics has advanced to a point where ordinary people can't even understand the problem statement. Proving a theorem is like building an ultra-complex logical chain; if one link breaks, the whole thing collapses.
When Wiles first announced it in 1993, a fatal flaw was found. He spent another agonizing year in seclusion to fix it. Verifying the correctness of such a top-tier mathematical proof often requires top experts to spend months or even years.
Is there a way to make a computer check its correctness like verifying a calculator result, running through it once to know if it's right or wrong?
Yes! This is 'formalization.'
Simply put, it translates human-written mathematical proofs into programming languages that computers can execute (like Lean), then lets the machine deduce step by step. If it runs through, it proves the proof is absolutely correct.
However, formalizing Fermat's Last Theorem is universally recognized in the mathematics community as a mega-project measured in 'years.'
Just the initial blueprint for the project led by Imperial College London Professor Kevin Buzzard was 86 pages long!
Then, Claude came along.
Work that humans estimated would take several years, it completed in just 11 days, and did so 'largely autonomously.'
13 Million Lines of Code, 6 Billion Tokens
'11 days, 13 million lines of code' – behind this lies a double whammy of AI's brute-force aesthetics and precise system design.
Let's look at what Claude actually did:
It didn't just prove Fermat's Last Theorem itself.
Because formal proofs must be built from the most fundamental axioms upwards, layer by layer, Claude also proved over 29,000 other mathematical theorems needed along the way.
This involved algebra, geometry, number theory, harmonic analysis... many branches that hadn't been formalized before. Claude directly 'pioneered' them.
The entire process required minimal human intervention.
Researchers gave only high-level instructions, like 'the Jacobian variety as a scheme has high priority' or 'advance the Mazur theorem quickly.'
For the rest, dozens of Claude agents were frantically talking to each other, defining concepts, proving intermediate theorems, and building up layer by layer.
In the end, the Lean compiler checked everything and passed, relying on only three fundamental standard axioms.
When the program finished running and the console displayed that sacred word 'PROVED,' even Claude's internal logs seemed excited:
'!!! Fermat's Last Theorem root node read as PROVED...... This was the goal of this campaign...... A historic moment.'
See, even the AI itself knew how amazing this was.
The Mastermind Behind the Scenes: A Super Scholar from Tsinghua's 'Yao Class'
The person capable of directing Claude to pull off such a miracle is certainly no ordinary individual.
The leader is Columbia Business School Assistant Professor and Anthropic researcher – Peng Tianyi.
This guy's resume is essentially a cheat sheet:
Undergraduate (2013-2017): Tsinghua University's 'Yao Class,' recipient of the Best Thesis Award, and a member of the National Training Team for the International Olympiad in Informatics.
PhD at MIT in Operations Research, graduated with a perfect 5.0 GPA.
Currently serves as an Assistant Professor at Columbia University while working on AI agents and formal tools at Anthropic.
Interestingly, Peng Tianyi's obsession with 'AI automated verification of mathematical proofs' stems from a 'painful experience' during his undergraduate years.
Back then, his advisor wanted to include his thesis results in *Nature*, but asked him: 'Are you 100% sure the proof is correct?'
He answered honestly: 'About 99% confident, but with something this long, I can't be 100% certain.'
Because of that 1% uncertainty, he missed the chance to be published in *Nature*.
Now, he has used AI to plug that '1%' gap himself.
From Failure to Deification: How Prove2Me Saved the AI
Do you think getting an AI to prove theorems is as simple as typing 'Please prove Fermat's Last Theorem' and having it spit out 13 million lines of code?
Absolutely wrong.
At the beginning, the experiment nearly failed.
Anthropic revealed that early on, collaboration between dozens of Claude agents quickly descended into chaos. They were like headless flies, couldn't keep up with each other's progress, and the collaboration efficiency was abysmal. The code from early failed attempts ultimately constituted only 7% of the final proof.
The 'amnesia' and 'hallucinations' of large language models are fatal flaws in the face of rigorous mathematics – one wrong line, and millions of subsequent lines are wasted.
At the critical moment, Peng Tianyi's team created the Prove2Me platform.
This thing is like equipping the AIs with a 'super project manager,' specialized in dealing with all sorts of issues:
Theorem DAG (Task Tree): Gives each AI a clear roadmap, telling it which intermediate node to prove next, greatly alleviating memory decay and allowing dozens of agents to work efficiently in parallel.
Separation of Statement and Proof: Speeds up compilation and saves resources.
Natural Language Indexing: Each theorem retains a human-language description, making it much easier for AIs to retrieve and reuse results.
Paired with the multi-agent framework of Claude Code, the AIs were like engineers with GPS, racing through the mathematical maze and clearing all levels in 11 days.
The Mathematics Community is Convinced
As soon as the results were published, X and major tech forums were flooded.
The Imperial College professor who originally planned to spend years on formalization, after seeing it, was impressed, giving high praise: 'This is a major step forward in the automated formalization of modern mathematical literature! It can be used in the future to check for errors in human mathematical libraries and verify mathematical conclusions generated by large models.'
But netizens had even more novel ideas.
One witty comment: 'The way AI solves mathematics is – giving you an extremely complex answer (13 million lines of code). Proving it wrong is harder than solving it yourself. So you can only give up resisting and accept that it's correct. Isn't that just math-world PUA?'
Another said: 'Writing 13 million lines of code just to make a 350-year-old theorem sit still before a machine... Humanity's desk isn't ready for something of this scale.'
Even more impressive, to show off, Anthropic also ran a small experiment.
Using 3 ordinary accounts on Prove2Me, they spent 3 days and also formalized the famous 'Vinogradov's theorem' (on sums of three primes) in number theory!
In other words, with the right tools, amateur scientists in the future could just buy a few consumer-grade AI accounts and verify humanity's most advanced mathematical theorems!
AI Won't Replace Mathematicians, But It Will Completely Change Mathematics
So, are mathematicians going to lose their jobs?
Anthropic officials gave the answer: No replacement, but it will completely change the game.
Historically, there have been many 'tragedies' in mathematical verification.
For example, in 1998, someone proved the Kepler conjecture. The review panel took 4 years and could only say they were '99% certain.' Perelman's proof of the Poincaré conjecture took the entire mathematics community 4 years and three 300+ page books just to barely understand it. Some theorems were accepted as truth for years, others built upon them, only to later discover the foundation was flawed.
The technology Claude brings aims to end this 'uncertainty.'
In the future, AI won't just be a mathematician's calculator; it will be the strictest referee.
When AI can rapidly generate thousands of new conjectures and proofs, and humans can't keep up, then making 'including formal verification code' a standard for papers might become the norm.
In the era of large models, large-scale automated formalization is unfolding new possibilities in a way that is close to engineering implementation.
References:
https://www.anthropic.com/research/formalizing-fermats-last-theorem
Editor: Aeneas
This article is from the WeChat public account "New Zhiyuan" (ID: AI_era), Author: ASI Apocalypse
