'Stunning' percolation proof solves decades-old puzzle about phase transitions

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?

> 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.

Refreshing to read about a proof where the critical part is not how they cheered Claude to solve it.