Two researchers, working with AI agents, resolved the 31-year-old KLS geometry conjecture
Xinzhi Zhang of Microsoft Research and a collaborator proved the Kannan–Lovász–Simonovits conjecture, proposed in 1995. It says that for a broad class of high-dimensional distributions, the best flat cut is within a fixed factor of the best cut of any shape, in any number of dimensions. These cuts govern how quickly random walks explore a distribution, which underpins sampling algorithms. AI agents explored more than 100 candidate approaches while the researchers directed the search.