As most readers have presumably heard by now, Paul Erdös’s Unit Distance Problem from 1946—one of the central open problems from the field of discrete geometry—has been solved by GPT5.5Pro. … The entire process seems have been one-shot: my former student Lijie Chen simply gave GPT the problem, then GPT thought for a while and output a several-page argument that, on analysis by human experts, turned out to be correct. … I heard the news maybe an hour after it broke, when some UT grad students came to my office to tell me. For what it’s worth: these students were morose, musing about how everything might soon be over for young scientists and mathematicians like themselves. I don’t know whether they’re right, but I feel like I should tell the truth about what their reaction was.
Then, a few days later, a team at DeepMind, including my UT Austin colleague Swarat Chaudhuri, announced that they were able to use a system called AlphaProof Nexus to settle nine more (!) Erdös problems, many of them in additive combinatorics, along with miscellaneous other open math problems. Notably, in this case the AI also fully formalized its proofs in Lean.
And then, just today, Jelani Nelson alerted me to a new CS theory paper, which solves a longstanding open problem about electrical flows on graphs using a proof from GPT5.5Pro.
Scott Aaronson was affected by this: