This got buried with the Erdos distance problem news, but GPT 5.5 Pro apparently helped to solve another decade old geometry problem this week: Talagrand's Convexity Conjecture
SUMMARYResearchers reported progress on Talagrand’s long-standing convexity conjecture, a notable geometry problem, with AI-assisted reasoning helping fill a missing proof step. The work was ultimately strengthened by a human-generated proof from Princeton mathematician Stefan Tudose and described by Michel Talagrand as extraordinary and sensational.
Unpaywalled link: https://archive.ph/mmAbD
The AI assist:
But Song couldn’t figure out the missing piece, which required manipulating a mathematical object he wasn’t familiar with. So he and his student Dongming (Merrick) Hua turned to ChatGPT. With some prodding, the large language model (LLM) was able to fill the gap in their understanding, providing a proof of the proposition they required.
Talagrand's quote on the full paper:
“This is the most extraordinary result of my entire life,” says Talagrand, who won the 2024 Abel Prize, which is often called the Nobel Prize of math. “The proper word is ‘sensational.’”
To note that there was better "human-generated" proof of this as well by Stefan Tudose, a Princeton mathematician, which was ultimately used in the paper linked below: