AI Solves Fermats Last Theorem 14 Page Proof Zero Edits Shocks Math World

In the AI world, a 30-year-old math problem has been solved. Claude 4.6 and GPT-5.4 worked together to crack Fermat’s Last Theorem. The 88-year-old math legend was shocked. GPT-5.4 wrote a 14-page proof with zero edits.

The 88-year-old math legend said: I never thought I would see this in my lifetime.

Before this, the math legend had been working on this problem for decades. He was shocked by Claude’s solution.

He wrote in an email: I am shocked. Shocked.

Paper link: https://cs.stanford.edu/~knuth/papers/ai-fermat-proof.pdf

Previous research found that there are actually 760 known decomposition methods. Claude only found one of them.

But when m is an odd number, the problem has a general solution. When m is even, the problem has no general solution.

But now, Claude has made a huge breakthrough.

GPT-5.4 Pro and Claude worked together. For even m up to 8, they wrote a 14-page proof. They verified the solution for high values up to m=2000.

What is even more shocking is that GPT and Claude did not communicate directly. They worked as a team, finding a more elegant construction method for even m.

They used Lean language, and Claude wrote the formal verification code.

In other words, the 30-year-old math problem has been completely solved.

Claude 4.6 and GPT-5.4 have once again shocked the industry. They have solved a problem that has troubled mathematicians for decades.

The math legend was deeply moved by this paper.

He said: This is indeed a very interesting time. I am willing to discuss it with you.

ai porn freeThe 88 Year Old Math Legend Makes a Comeback

Fermat’s Last Theorem has always been a famous problem in mathematics. It is a very difficult problem that has troubled mathematicians for centuries.

In simple terms, it asks: in a complex graph structure, find a path that visits every node exactly once without repeating.

Fermat’s Last Theorem is not just a computer science problem. It is a mathematical problem that has best free ai porn been studied for centuries.

For this problem, the higher the value of m, the more difficult it becomes.

In the process of writing The Art of Computer Programming, the math legend began to study this problem as a mathematical exercise.

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This problem has been around for decades. But until now, no one has been able to solve it completely.

Before this, mathematicians had been unable to find a general solution for even values of m.

At each node, the path splits like a bomb. The number of possible paths grows exponentially. It is a black hole of combinatorial explosion.

In the past decade, mathematicians have tried many methods, but none of them could solve the even case completely.

Until 2026, a miracle happened.

Is There a Solution for Even m?

On January 31, Claude Opus 4.6 found a simple construction rule after 31 attempts.

s=(i + j + k) mod m

In this formula, s, i, j, and k are variables. When s=0, the value of j is fixed. When 0

Claude verified through enumeration that for m=3,5,7,9,11, the paths are all complete.

But Claude only solved the case where m is odd. For even m, the problem remains unsolved.

Until March 3, Filip Stappers wrote to the math legend with new progress.

Stappers used Claude Opus 4.6 to explore even m again. After 4 hours, he still could not find a general solution.

But Claude found a local search strategy, and then used simulated annealing to optimize it.

At this stage, what was needed was to speed up the search. From a mathematical perspective, it was necessary to find a more elegant construction method.

Stappers used ORTools CP-SAT to divide the problem into two parts. He used the AddCircuit constraint to solve it, which was very clever.

The solution was found in just a few days.

On March 4, a new record was set. Ho Boon Suan brought even more shocking news.

He used gpt-5.3-codex for the first time and successfully decomposed even m up to 8.

To ensure reliability, he tested all even m values from 8 to 200, and some even m values from 400 to 2000. All of them passed.

It is important to note that when m=2000, this is a graph structure with 80 billion nodes.

This is a miracle. The verification of correctness is a miracle in itself.

At the same time, Lean expert Kim Morrison also joined quickly.

Before this, Claude had written the formal verification code. On March 4, he released it on the Lean community.

Mathematical Proof: A New Discovery

A researcher named Exocija found a new general solution for m.

From a mathematical perspective, this is an extremely difficult problem. The current solution methods, whether enumeration or verification, are not simple.

In C language implementation, only by replacing specific files with more refined logical code can an efficient decomposition be obtained.

He said: For each node, the path must visit 012 in order.

The key to this problem is model collaboration.

Exocija used GPT-5.4 and Claude 4.6 Sonnet. The collaboration between the models was not a simple text exchange, but different thinking modes complementing each other to form a successful proof.

Zero Edits: GPT-5.4 Writes 14 Page Paper

For the even m construction problem, the key to success is collaboration.

Although gpt-5.3-codex had already succeeded in decomposition, Ho Boon Suan gave GPT-5.4 Pro a new instruction:

Before detailed verification, when the algorithm assumes m is an even number of the form 8, it is indeed not working. The reason is that m3 is a cyclic group.

He said: Can you say whether this algorithm is effective, and whether there is a simpler construction method?

Who would have thought that GPT-5.4 Pro would directly output a stunning answer.

A paper with extremely rigorous logic and structure. A 14-page mathematical paper.

From abstract to introduction to discussion to structure to conclusion, everything is perfect.

What is even more shocking is that the paper was written in standard TeX format. The math legend’s TeX formatting method was perfectly replicated by AI.

What is even more important is that it passed Lean formal verification on the first attempt.

Ho said in the original text: I was completely shocked by GPT-5.4 Pro’s output. This is a miracle. The entire team did not need to make any edits.

This means that AI’s logical reasoning ability has reached a new level.

AI Collaboration: Claude and GPT Complete the Proof

The key to this breakthrough is Keston Aquino-Michaels.

He believes that finding an efficient decomposition for odd m and a more elegant decomposition for even m is a process far beyond previous methods.

Moreover, they also found a highly cited reference that was previously overlooked.

Preprint link: https://arxiv.org/abs/2203.11017

What is even more interesting is that the pattern of this path is completely different from previous methods. It is a new pattern that has never been seen before.

Paper link: https://github.com/no-way-labs/residue/blob/main/paper/completing_claudes_cycles.pdf

Open source project: https://github.com/no-way-labs/residue

What is even more shocking is that Keston Aquino-Michaels did not simply ask AI questions, but built a collaboration system.

In this system, a more advanced collaboration mode was used. Claude and GPT collaborated with each other.

In this system, each agent uses different Residue prompts.

The structure of the exploration tree they used is shown below.

The key to success is:

The agents did not communicate directly. They communicated through an Orchestrator. Both ends are command lines, and the middle is Opus 4.6 data.

The Orchestrator needs to determine when to use what and in what form. This is not something the agents can decide on their own.

For example, when Agent O cannot solve even m=10, the Orchestrator passes Agent C’s solution to Agent O. Agent O receives it and recognizes the pattern as m-2 base points + 2 base points.

In other words, this 30-year-old even complete solution was born in the service exchange between AI agents. It is a miracle.

Academic Circle War: Human and AI Complement Each Other

This discovery marks a major turning point in formal mathematical research.

Mathematicians’ work has changed. For example, the math legend no longer checks every line of the proof himself. He sets the boundary conditions, and then lets AI fill in the gaps.

The way of research has changed. Humans only set the boundaries, and AI fills in the gaps.

Mathematicians are no longer lone warriors. They are commanders who direct AI to find the path.

AI is no longer a tool that searches blindly in the dark. It has become a navigator that can determine whether the path is correct and whether it needs to find a new path.

So who won?

The 88-year-old math legend started with AI collaboration, but he clearly realized that the way mathematical research works is undergoing a fundamental transformation.

This is not just a victory for the math legend. It is a victory for the entire mathematical community.

At a time when AI is changing everything, mathematics has already been rewritten by AI.

But one thing is certain: the only thing we should fear is not AI itself, but the speed at which AI is advancing.