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."

A younger me would have been very interested in learning about advanced topics in math, but nobody around me knew those topics or had time to share them with me. If I had AI to chat with, I very likely would have asked it to teach me things. Similarly, for many people in the world, even buying math books and other resources is challenging. Also, people who love to teach math now have new resources to do a better job at it. Lastly, AI will be discovering new and beautiful things. Which both increases the quantity of fun, fascinating things to study, and also produces a lot of new things which in some ways is more exciting than studying very old math

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