‘Stunning’ Percolation Proof Solves Decades-Old Puzzle About Phase Transitions
Mathematicians found that a broad class of networks will abruptly shift behavior past a critical point. The post ‘Stunning’ Percolation Proof Solves Decades-Old Puzzle About Phase Transitions first appeared on Quanta Magazine
In December 2025, a team of five mathematicians at ETH Zurich worked tirelessly to solve a decades-old problem in percolation theory. The group, comprising Sahar Diskin, Philip Easo, Ritvik Ramanan Radhakrishnan, Benny Sudakov, and Vincent Tassion, aimed to understand how fluid flows through a network of points connected by lines.
They believed they had found a simple argument that could apply to a wide variety of graphs. After working through the night and into the following morning, the mathematicians were convinced their proof was correct. Percolation theory, which studies flow in networks, has applications in various phenomena, including fluid flow, virus spread, gas passage, and wildfire propagation.
The concept originated from Rosalind Franklin's studies of coal in the 1940s, who used it to understand the properties of coal. The mathematicians' proof confirmed the sharpness conjecture, which predicts that fluid pools grow very quickly once a certain probability threshold is reached. This discovery has significant implications for understanding phase transitions in various systems.
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