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 (opens a new tab) and Philip Easo (opens a new tab), graduate student Ritvik Ramanan Radhakrishnan, Benny Sudakov (opens a new tab), and Vincent Tassion (opens a new tab) — was perfecting a solution to one of the biggest open problems in percolation theory, the study of flow in a network.
Percolation captures a vast array of phenomena, but the prototypical examples involve fluids, like hot water seeping through a bed of coffee grounds. Diskin, Easo, Radhakrishnan, Sudakov, and Tassion were trying to work out something fundamental about how graphs — networks of points connected by lines, or edges — can be taken over by large connected areas, the equivalent of pools of fluid. The group had glimpsed a simple argument that could deal with a huge variety of graphs at once.
“We almost didn’t believe it at first,” Radhakrishnan said.
They raced to confirm each detail, eager to get their idea down before it shimmered away — and heedless of the holiday. “I’m not sure the girlfriends and the families were as happy as we were. But we were all very happy at that moment,” Diskin said. “It’s really rare that you’re able to hit something that feels so big and so meaningful.”
They worked through the night. By the morning of December 17, exhilarated from the effort, they were convinced their idea was correct. By Christmas, they’d nailed down a proof.
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