Leila Sloman writes about five mathematicians at ETH Zurich who, while pursuing a different problem in late 2025, stumbled upon a simple proof of the supercritical sharpness conjecture for all infinite transitive graphs—a decades-old question in percolation theory about how quickly networks flood past a critical threshold. The proof confirms that above the critical probability, fluid covers nearly the entire graph, resolving what researchers had called "the one remaining fortress" in the field.
- Percolation theory originated from Rosalind Franklin's 1940s work on coal porosity at the British Coal Utilization Research Association
- Oded Schramm, who co-initiated the study of percolation on transitive graphs with Itai Benjamini, died in a hiking fall in 2008 at age 46
- The key insight was reordering a standard "sprinkling" technique—analyzing the sprinkled edges first rather than last—which both simplified the proof and made it general enough for all transitive graphs
- The subcritical half of the sharpness conjecture had already been proved in 2007 by Antunović and Veselić
- A major open question remains: what happens exactly at the critical probability on three-dimensional lattices
- Percolation theory originated from Rosalind Franklin's 1940s work on coal porosity at the British Coal Utilization Research Association
- Oded Schramm, who co-initiated the study of percolation on transitive graphs with Itai Benjamini, died in a hiking fall in 2008 at age 46
- The key insight was reordering a standard "sprinkling" technique—analyzing the sprinkled edges first rather than last—which both simplified the proof and made it general enough for all transitive graphs
- The subcritical half of the sharpness conjecture had already been proved in 2007 by Antunović and Veselić
- A major open question remains: what happens exactly at the critical probability on three-dimensional lattices
