The October proof removes dimension dependence from a 1995 bound, after a human-directed AI search helped identify the key mathematical criterion.
By [Ryan Merket](https://runtimewire.com/author/ryan-merket)
· Published
· Updated
Primary source: [Microsoft Research](https://www.microsoft.com/en-us/research/blog/solving-a-31-year-old-grand-challenge-in-mathematics-the-kls-conjecture/)
Why it matters #
The proof turns a widely used assumption about high-dimensional sampling into a theorem. Its AI contribution is also specific: guided exploration helped researchers find a useful criterion, while human mathematical judgment shaped and completed the proof.
A proof posted on October 4th resolves the Kannan-Lovász-Simonovits conjecture, a 1995 problem about how efficiently random walks can explore high-dimensional probability distributions. Microsoft Research announced the result on October 21st, crediting Microsoft researcher Xinzhi Zhang and collaborator Zhao Song. Their paper establishes a bound that does not grow with the number of dimensions, the defining claim of the conjecture.…
When you purchase through links in our articles, we may earn a small commission. This doesn’t affect our editorial independence.