AI solving PhD-level problems in mathematics

An update for the current 21-st edition of “Kourovka Notebook (Unsolved Problems in Group Theory)” is  posted. A few new solutions and new references appear, both for problems from the latest section and from the previous ones. (But of course many problems remain very much open:-).)

Remarkably, for the first time in history, some of the solutions (for example, 20.125, 21.150) had been obtained by Artificial Intelligence! A few more solutions by AI will appear in the next update. In some cases, human contribution was still needed, as, for example in the solution of 21.10 in https://arxiv.org/abs/2605.10402 , and humans had to verify the solutions proposed by AI experts and discard some of the incorrect attempts by AI.

Recall that “Kourovka Notebook” is a famous collection of open problems in group theory proposed by hundreds of mathematicians from all over the world, published every 2-4 years since 1965.