AI math proof breakthrough #GPT #ErdosProblem #NumberTheory

Added: 2026-04-29

[00:00:00]A GPT just helped crack a math problem open since the 1960s in about 80 minutes. And the problem sounds weirdly simple. Imagine building a list of numbers where no number is allowed to divide another. So, two and four cannot both be there because four is a multiple of two. Prime numbers are the cleanest example. Two, three, five, seven, 11.

[00:00:19]None of them divide each other. But Paul Erdos asked the harder question. Are primes the best possible version of this list? In other words, if you measure these lists with a special number theory sum, can any clever set beat the primes?

[00:00:31]For decades, mathematicians usually translated the problem into probability.

[00:00:35]Elegant, [music] but still a detour.

[00:00:37]Then GPT found a more direct proof path.

[00:00:40]It attacked the divisibility structure of the numbers themselves and helped prove the refined version. What happens when the numbers get infinitely large?

[00:00:48]Jared Duker-Lichtman compared it to AI finding a strange new chess opening.

[00:00:53]Always possible, but ignored because it looked wrong. And Terence Tao said the method may simplify more than one problem, possibly an entire part of number theory. The scary part is not that AI solved one old puzzle. It found a route humans trained themselves not to see. Follow for more AI breakthroughs before they become obvious.