Irving MA

openai says its ai just solved three famous open problems at once: one in math, one in computer science and one in physics. the math one has been open since 1991. the computer science one is an assumption hundreds of papers were built on, and openai says it's wrong. the physics one touches a millennium prize problem. outside experts are now checking all three, so none of it is settled until they're done. 1. math: waves can't stay focused for long picture ripples in a pond all rushing toward one spot. for a split second they pile up into a tall spike, then spread out again. in 1991 a mathematician named sogge guessed that this extreme focusing is always brief, and that at a random moment a wave is much calmer than at its worst. it was proved in 2 dimensions in 2019. openai says its model proved it in every dimension, which also settles two other famous problems, the kakeya and restriction conjectures. the next day it was checked in lean, a program that only accepts a proof if every single step is correct. 2. computer science: a shortcut that "shouldn't exist" some puzzles seem to force you to try nearly every combination, like a lock where the only way in is testing code after code. the exponential time hypothesis (eth) is the widely believed idea that for puzzles like this there's no big shortcut. hundreds of papers in graph theory, biology, databases and more lean on it to say "this can't be done much faster." openai says its model proved eth is false, also checked in lean. that reopens how much faster a lot of those tasks could get. the researchers who first proposed eth, impagliazzo and paturi, are leading the group checking it, with ryan williams. the proof is public for anyone to look at. 3. physics: putting the strong force on solid math the strong force is what holds tiny particles called quarks together inside every atom, using carrier particles called gluons as the glue. physicists describe it with a theory called qcd and use it constantly, but nobody had proved it holds up as rigorous math. openai says its model proved it does, and did the same for a unified version of the standard model, physics' main theory of particles. one piece of the work, proving that yang-mills theory exists, is part of one of the clay institute's millennium prize problems. the physics group is led by david gross, who shared a nobel prize for work that helped establish qcd. they're holding the ai's work for now and writing it up themselves. openai says it wants no academic credit for any of this. the experts checking it are unpaid, signed no ndas, and are free to publish whatever they find.