Introduction
Imagine writing down a math problem, hastily scribbling down an answer, and leaving the entire world stumped for more than three centuries.
That is exactly what happened in 1637. A French mathematician named Pierre de Fermat wrote a simple-looking equation in the margin of a textbook. He claimed he had a “marvelous proof” for it, but teased that the margin was just too small to fit it.
For 358 years, the smartest, the best, the greatest minds tried to prove he was right. However, nobody could, until Sir Andrew Wiles finally did it in 1995 writing 129 pages of math.
Fast forward to today. Anthropic released research showing that their AI model, Claude, completed an entire computer verified proof of Fermat’s Last Theorem in just 11 days.
Here is what happened, why it matters, and why this is a huge deal for the future of science.
First Off: What Is Fermat’s Last Theorem?
You already know the Pythagorean Theorem from middle school geometry:
$$a^2 + b^2 = c^2$$
There are countless numbers that make this work, such as 3, 4, and 5
$$3^2 + 4^2 = 5^2$$
Fermat’s Last Theorem asks: What happens if you change the exponent from \(2\) to anything bigger?
Fermat claimed that no positive whole numbers exist that can make this equation work for any power higher than 2. If you try it with \(n = 3\) or \(n = 4\), you’ll be searching forever.
How Claude Did It:
When Andrew Wiles proved the theorem in 1995 human experts spent months checking Andrew Wiles work to make sure there were no hidden flaws. In mathematics if a single step in a one hundred page proof is wrong the whole proof collapses like a house of cards.
To eliminate error computer scientists use a programming language called Lean. When you give Lean a proof, Lean checks every logical step automatically.
Translating math into computer code is called formalization. Humans expected formalizing Fermat’s Theorem to take years.
Instead, Anthropic set up multiple Claude AI agents working together on a collaborative platform called Prove2Me.
Why Is This Big?
Andrew Wiles solved it in 1995, so why do we need to reprove it?
Claude proving Fermat’s Last Theorem shows three things
1. Zero Room for Error
When humans solve a math problem, we make assumptions. AI does not. By writing 13 million lines of code, AI created a step by step proof with zero assumptions.
2. Partner for Future Scientists
Checking complex math proofs can take peer reviewers years. With AI being able to automatically formalize research into verified code, scientists can instantly test whether a new idea or theory is true.
3. Proof of the capabilities of AI
AI isn’t just summarizing essays or writing basic code, it is navigating multi-layered, abstract logical structures across algebra, geometry, and number theory. That’s why this is big.
The Takeaway
Fermat hastily scribbling down notes created a 350 year old mystery. Andrew Wiles solved it through human ingenuity, and now Claude efficiently formalized it in less than 2 weeks. Whether or not you’re learning algebra or writing your Ph.D dissertation, this is an era where tools are consistently evolving and changing. Tools that you will use throughout life, ones that help expand the frontiers of human knowledge. They just got an upgrade.
Sounds interesting
The amount of knowledge and years of experience it must take to solve something like that never ceases to amaze me