https://arxiv.org/abs/2303.09521

Timothy Gowers: «I was at an amazing seminar yesterday in Cambridge, where Julian Sahasrabudhe announced that he, Marcelo Campos, Simon Griffiths and Rob Morris have obtained an exponential improvement for the bound for diagonal Ramsey numbers.

The preprint came out on arXiv today. It is 57 pages but written in a relaxed expansive way (he tells me). I imagine there will now be a flurry of developments as people digest the argument, which is surprisingly elementary (e.g. it doesn't make use of quasirandomness). It was one of my favourite problems, but I would never have found this argument, so am very happy to see it solved. Huge congratulations to all involved.»