Mathematicians solve decades-old percolation theory problem on phase transitions

Percolation Theory Breakthrough

A team of five mathematicians, Sahar Diskin, Philip Easo, Ritvik Ramanan Radhakrishnan, Benny Sudakov, and Vincent Tassion, at ETH Zurich, successfully developed a proof for a significant open problem in percolation theory. This theory studies the flow within a network, such as fluids seeping through materials or the spread of phenomena through interconnected systems.

Addressing a Decades-Old Question

The proof specifically addresses a decades-old question concerning the rate at which a percolation network becomes flooded when fluid flow is introduced. Their work provides a fundamental understanding of how large connected areas can take over graphs, which are networks of points connected by lines.

Significance of the Discovery

The mathematicians worked through December 2025 to finalize their argument, which they found to be simple yet capable of dealing with a wide variety of graphs. Experts in the field, such as Asaf Nachmias of Tel Aviv University, have described the proof as "stunning" due to its elegance and impact on the understanding of phase transitions in networks.

Historical Context of Percolation

Percolation theory has broad applications, including modeling virus spread, gas filtration, and wildfire propagation. Its origins trace back to Rosalind Franklin's work in the 1940s at the British Coal Utilization Research Association (BCURA), where she investigated why certain types of coal allowed fluids to pass through while others were impermeable, studying the intricate properties of coal, charcoals, and graphite.