Master of chaos wins $3M math prize for ‘blowing up’ equations

Key Points:

• Frank Merle has been awarded the 2024 Breakthrough Prize in Mathematics, recognizing his pioneering work on highly nonlinear systems and their singularities or "blowups" in equations describing lasers, fluids, and quantum mechanics.
• Merle's novel approach focuses directly on the nonlinear structures of equations rather than treating them as perturbations of linear systems, allowing him to uncover persistent structures called solitons that maintain their form and energy amid chaotic behavior.
• He proved that blowups can occur in laser equations, explaining intense focusing phenomena, and demonstrated that friction in compressible fluid equations does not prevent singularity formation, contributing to understanding turbulence and fluid dynamics.
• Merle's work also challenged previous assumptions in quantum mechanics by showing that solutions to the nonlinear Schrödinger equation can exhibit blowup, overturning the belief that singularities would always disperse over time.
• His research advances the "soliton resolution conjecture," which posits that complex nonlinear systems ultimately simplify into finite, computable soliton interactions, revealing hidden simplicity within chaotic mathematical phenomena.