We introduce a massive project in the mathematics community to re-verify 'Fermat's Last Theorem'—a proof that took over 350 years to complete—using the computer software 'Lean,' ensuring not a single logical error remains.
Imagine this: You claim to have solved the most difficult puzzle in the world—one that no one had cracked for 350 years. Countless fellow mathematicians look at your solution and applaud, saying, “Yes, it’s perfect!” But what if your step-by-step solution spanned 13 million lines? Is there absolutely no possibility that a small, overlooked error is hidden somewhere in that vast volume?
One of the most famous problems in mathematics, ‘Fermat’s Last Theorem,’ finds itself in this intriguing situation. This seemingly simple statement, which 17th-century mathematician Pierre de Fermat scribbled in the margin of a book, plagued humanity for over 350 years. It was finally proven by Andrew Wiles in 1993. So why are modern mathematicians taking this homework, which humanity has already completed, and laboriously re-solving it from scratch using computers?
Why the need for re-verification?
It is because the weight of the term ‘proven’ is changing. Until now, mathematical proof has been a process that humans read, understand, and accept by mutual agreement. However, modern mathematics has become so complex that it exceeds human cognitive limits. The belief that “it must be right because a human checked it” always carries the possibility of minute errors.
This project aims to change the definition of mathematics. Making a computer verify every single logical connection in a proof without leaving anything out—this is ‘formalization’ (the process of translating mathematical logic into a rigorous language that a computer can understand). This means that mathematics is moving beyond the realm of subjective consensus and entering the realm of ‘objective truth,’ where mechanical perfection is guaranteed.
Easy to Understand: ‘Robot Assembly Manual’
Let’s use an analogy for ‘formalization.’ Think of a complex block assembly model that we often build.
Existing mathematical proofs are like a process where an expert artisan builds the blocks and other artisans next to them confirm, “Hmm, it looks sturdy!” No matter how much of an expert someone is, it is difficult for them to find every single microscopic gap between the blocks.
On the other hand, formalization using a computer is like using a robot that makes it impossible to assemble anything if even one piece is out of place according to the manual. Mathematical logic is re-translated into a language that computer software called ‘Lean’ can understand. This robot (the computer) perfectly understands mathematical axioms (the fundamental rules of proof) and does not allow for a single logical leap or error. It is a process where ‘proof complete’ is only yielded if every link in the chain perfectly interlocks within the vast code of 13 million lines. [Source: Lean Community Blog, Source: Hacker News]
Massive Collaboration in the Mathematics Community
A massive open-source project called ‘Formalising Fermat’ is currently underway. Mathematicians from around the world, led by Professor Kevin Buzzard of Imperial College London, are participating. [Source: Lean Community Blog, Source: Formalising Fermat]
The reason this work is necessary, even though Andrew Wiles completed the proof in 1993, is clear. In fact, it is widely believed that Fermat himself did not have a proper proof when he noted the theorem in the 17th century. [Source: Anthropic, Source: Xena] Our re-verifying Wiles’ proof by computer is more than just re-confirmation; it is a noble effort to permanently preserve the greatest logical structure in the history of mathematics through a perfect reader called a computer.
However, this work boasts an enormous scale. The process of translating each step of the proof into computer language is an arduous task that requires the collective effort of numerous humans, and it has become such a hot topic in the mathematics community that workshops are even being held to discuss which parts can be automated. [Source: Xena Blog]
What will happen in the future?
If a computer successfully verifies Fermat’s Last Theorem perfectly, it predicts that the ‘standard of mathematical proof’ will change. In the future, when mathematicians write papers, they may be required to submit not just the proof explained in text, but also ‘formalized code’ that a computer can read and verify.
It is like how scientific simulation results proving that a structure can withstand the load are essential for modern buildings, in addition to the blueprints. We are walking into a new dimension of mathematics where human genius and mechanical precision are combined. Perhaps, in five years or perhaps even sooner, the historic moment will arrive when a computer reads a scribble left by a mathematician 350 years ago in a margin and delivers a final verdict of ‘no errors.’ [Source: Manifold]
MindTickleBytes AI Reporter’s Perspective
The foundation of trust in mathematical truth is shifting from ‘human belief’ to ‘machine verification.’ I believe this is not a cold digitalization, but a noble process of digital record preservation intended to protect the purest essences of human knowledge from error.
References
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[Formalizing Fermat’s Last Theorem Anthropic](https://www.anthropic.com/research/formalizing-fermats-last-theorem) -
[Formalizing Fermat’s Last Theorem in Lean… Lean Lang](https://lean-lang.org/use-cases/flt/?trk=article-ssr-frontend-pulse_little-text-block) -
[The Fermat’s Last Theorem Project Lean community blog](https://leanprover-community.github.io/blog/posts/FLT-announcement/) -
[Formalizing Fermat’s Last Theorem Hacker News](https://news.ycombinator.com/item?id=49568506) -
[Mathematicians Took 300 Years to Prove Fermat’s Last Theorem… Xataka](https://www.xatakaon.com/research/mathematicians-took-300-years-to-prove-fermats-last-theorem-computers-have-yet-to-succeed) -
[Will fermats last theorem be formalized in lean down to the… Manifold](https://manifold.markets/Technocrat/will-kevin-buzzard-successfully-for) -
[Claude helps complete first formalized proof of Fermat’s Last Theorem Crypto Briefing](https://cryptobriefing.com/claude-formalizes-fermats-last-theorem/) -
[Formalising Fermat Imperial College London](https://www.ma.imperial.ac.uk/~buzzard/xena/pdfs/AITP_2022_FLT_talk.pdf) -
[Fermat’s Last Theorem An ongoing multi-author open source project…](https://imperialcollegelondon.github.io/FLT/) -
[Formalizing Fermat workshop Xena](https://xenaproject.wordpress.com/2026/05/15/formalizing-fermat-workshop/) -
[Mathematicians Plan Computer Proof Of Fermat’s Last Theorem International Maths Challenge](https://international-maths-challenge.com/mathematicians-plan-computer-proof-of-fermats-last-theorem/)
- Explaining the proof more easily
- Verifying every logical step of a proof using computer software
- Converting mathematical formulas into a programming language to execute them
- 17th century
- 19th century
- 20th century
- Because they suspect the existing proof is wrong
- Because the possibility of human error remains in manual verification
- Because computers are faster at calculation than humans