Andrew Wiles worked on Fermat's Last Theorem alone in his attic for 7 years and told nobody except his wife. The problem was 358 years old. Fermat scribbled in a margin in 1637 that he had a proof and no room to write it, and every mathematician since had failed. Wiles saw the statement in a library book at 10 years old. He never let it go. He was a Princeton professor when he started in 1986. He stopped publishing new work and released old results in pieces to hide the silence. He announced it in Cambridge in June 1993, over 3 lectures, revealing the target only at the end. Newspapers ran it worldwide. Then a referee found a gap. One step in the proof did not hold, and the error was fundamental. He spent 14 months trying to close it in public view, with the whole field watching. He was ready to quit. The fix arrived in September 1994. He has said he stared at it in disbelief for 20 minutes. The BBC filmed him describing that moment. He gets a few words out, then turns away from the camera in tears. He kept the greatest result of the century secret so nobody could take it.

My son asked me what infinity plus ten equals. I’ve been training for this moment my whole life.

Some fascinating developments following OpenAI's shock breakthrough proof of the Quasi-Riemann Hypothesis, which was released publicly on October 6: 1. Building on OpenAI's proof, a recent Hexagon preprint (released on October 12) by Cureton and Thorner establishes that ALL finite-order Hecke L-functions are zero-free to the right of 1 - 1/6000. 2. And now, today, an arXiv preprint by Frei, Somos and Widmer uses this result to prove unconditionally the 2007 Ellenberg–Venkatesh bounds on ℓ-torsion in class groups of number fields. I was amused to see the AI declaration in the second paper: "No artificial intelligence tools were used in this work."

I love this theorem. And I hope many people work to improve AI’s proof of it. The Book Proof is still out there! :-)

“okay, so what? it’s just math.” no, you don't get it. here’s what OpenAI’s math breakthroughs could eventually help make possible in the real world: Vlasov–Maxwell → stronger foundations for fusion research, whose ultimate prize is virtually limitless clean energy to power civilization Calderón’s Problem → portable body scanners using electrical signals, making medical imaging cheaper and easier to access Maximum-Cardinality Matching → faster searches for compatible kidney swaps across large donor pools, helping hospitals coordinate lifesaving transplants Inverse Elasticity Problem → scans that map tissue stiffness, helping doctors locate suspicious growths inside the body Mumford–Shah Conjecture → better tools for spotting tissue changes in brain scans, helping doctors identify signs of disease Bose–Einstein Condensation → stronger foundations for quantum sensors that could help vehicles navigate without GPS Simple Stochastic Games → better safety checks for self-driving cars and robots before dangerous mistakes reach the real world Matrix Multiplication → cheaper AI and bigger scientific simulations using the same computers Edit Distance → faster DNA comparisons, helping researchers study genetic changes linked to disease The k-Server Problem → robots that waste less movement and energy, making warehouses more efficient and goods cheaper to move a reminder that math is the foundation of science. so accelerating mathematical discovery could compress centuries of scientific progress into years. insane timeline to be alive for!

so we all agree the color for math is blue right

We created gyms because modern day work no longer required physical activity. Without exercise, our muscles atrophy. I predict we’ll need gyms for our brains too, once AI starts doing our knowledge work.

The most important briefings of the day. Karl Deisseroth, professor of bioengineering and of psychiatry and behavioral sciences, shares the news of his Nobel Prize with his kids.