Mathematicians Crack the Sharpness Conjecture for Percolation
'Stunning' percolation proof solves decades-old puzzle about phase transitions
A team of five mathematicians at ETH Zurich has solved a decades-old problem in percolation theory, proving the sharpness conjecture for all infinite transitive graphs. Their simple proof, completed in December 2025, shows that above the critical probability, a single infinite cluster dominates, resolving a question that had stumped researchers since the 1990s. The result, described as 'stunning' by experts, opens new avenues for understanding phase transitions.
“We almost didn’t believe it at first,” Radhakrishnan said.
- plaidfuji
> The week before Christmas 2025, five mathematicians were holed up in a classroom at ETH Zurich.
So happy this didn’t end with, “tweaking their prompt for ChatGPT Sol” or whatever.
> He, Diskin, and Radhakrishnan made some progress and brought their results to Sudakov and Tassion. As Tassion took in their work, an idea — perhaps an outrageous one — formed in his mind. … Over those weeks, the collaboration became frenzied. The mathematicians traded ideas constantly, often texting late at night.
It will be a truly sad world if we automate this away.
- karmakurtisaani
Refreshing to read about a proof where the critical part is not how they cheered Claude to solve it.
- catapart
I feel like I can almost see the shape of this, but that it's still very blurry for me. Seems like it could be used for some cool stuff, but I can't quite make out what. Procedural generation? Shader effects? Beyond the more important physical stuff they describe in the article, seems like there's some potential for fun with this?