'Stunning' percolation proof solves decades-old puzzle about phase transitions
A team of five mathematicians at ETH Zurich successfully proved a long-standing puzzle in percolation theory regarding phase transitions in networks. The breakthrough provides a fundamental understanding of how connected areas form within complex graphs.
Why it matters
This mathematical advancement provides new insights into network flow and connectivity, which has broad implications for physics, biology, and computer science.
Home ‘Stunning’ Percolation Proof Solves Decades-Old Puzzle About Phase Transitions Comment Save Article Read Later Share Facebook Copied! Copy link Email Pocket Reddit Ycombinator Comment Comments Save Article Read Later Read Later graph theory ‘Stunning’ Percolation Proof Solves Decades-Old Puzzle About Phase Transitions By Leila Sloman August 31, 2026
Save Article Read Later DVDP for Quanta Magazine
graph theory mathematics probability proofs randomness All topics The week before Christmas 2025, five mathematicians were holed up in a classroom at ETH Zurich. The mood was electric: They were this close to a career-defining breakthrough.
The group — consisting of then-postdocs Sahar Diskin and Philip Easo , graduate student Ritvik Ramanan Radhakrishnan, Benny Sudakov , and Vincent Tassion — was perfecting a solution to one of the biggest open problems in percolation theory, the study of flow in a network.
Get smarter about the news
Sign up free for a feed built around what you actually care about, Dive Deeper research on any story, and the full text of every article.
Create free accountAlready have an account? Sign in