Breakthrough Prize: Frank Merle

Frank Merle received the 2026 Breakthrough Prize in Mathematics for work on equations that can suddenly spike, collapse, or spin out of control. (breakthroughprize.org) The Breakthrough Prize Foundation announced the award on April 18, 2026, and the prize carries a $3 million purse. The ceremony was held that night in Santa Monica, California. (breakthroughprize.org; gettyimages.ca) The foundation said Merle advanced the study of nonlinear evolution equations, the formulas mathematicians use to track how waves, fluids, and other changing systems behave over time. Those equations can describe cases where a solution stays smooth, scatters, or “blows up,” meaning it becomes singular in finite time. (breakthroughprize.org; scientificamerican.com) A partial differential equation is a rule that links rates of change across space and time, like a weather map that updates every second. In Merle’s area, the hard question is whether a system keeps evolving in a controlled way or hits a point where the model itself breaks down. (scientificamerican.com; breakthroughprize.org) Merle is best known for results on blow-up in nonlinear Schrödinger equations and related models, where energy can concentrate into smaller and smaller regions. His papers with Pierre Raphaël and other collaborators helped classify blow-up behavior and prove when singularities can form. (annals.math.princeton.edu; springer.com; ams.org) The American Mathematical Society awarded Merle a Bôcher Memorial Prize in 2005 and again in 2023, with the later prize citing work on blow-up solutions for defocusing nonlinear Schrödinger, Euler, and Navier-Stokes equations. That record placed him among the field’s most decorated analysts before this year’s prize. (ams.org; en.wikipedia.org) Merle holds the Analysis Chair at the Institut des Hautes Études Scientifiques in Bures-sur-Yvette, France. In an interview published April 19, he said basic research should be supported because it is a “foundation stone” for the future. (en.wikipedia.org; phys.org) The prize puts a spotlight on a corner of pure mathematics that also touches physics and fluid flow: how extreme behavior emerges from deterministic rules. Merle’s work did not make those systems simpler, but it gave mathematicians sharper ways to describe when order persists and when it fails. (breakthroughprize.org; scientificamerican.com)