Pierre-Louis Lions is a preeminent French mathematician celebrated for his transformative contributions to the theory of partial differential equations. Born on August 11, 1956, in Grasse, he demonstrated exceptional mathematical talent from an early stage in his academic journey. After completing preparatory classes at Lycée Louis-le-Grand, he entered the École Normale Supérieure in 1975, ranking second in the entrance examination. He pursued his doctoral studies under Haïm Brezis at Université Pierre-et-Marie-Curie, defending his thesis titled 'Sur quelques classes d'équations aux dérivées partielles non linéaires et leur résolution numérique' in 1979. Following his doctoral work, he conducted research at the CNRS from 1979 to 1981 before becoming a professor at Paris-Dauphine University.
Professor Lions has made groundbreaking contributions to nonlinear partial differential equations, particularly through developing the theory of viscosity solutions for Hamilton-Jacobi equations which revolutionized the field of mathematical analysis. His seminal collaboration with Ronald DiPerna on renormalized solutions for the Boltzmann equation established fundamental frameworks for understanding transport theory and fluid dynamics. His research has profoundly impacted multiple disciplines including mathematical physics, quantum mechanics, and economics through practical applications of abstract mathematical concepts. These exceptional contributions were recognized with the Fields Medal in 1994, mathematics' highest honor, specifically awarded for his innovative work on viscosity solutions and nonlinear PDEs that resolved longstanding theoretical challenges.
As Chair of Partial Differential Equations and Applications at the Collège de France since 2001, Lions has shaped generations of mathematicians through his mentorship and scholarly leadership. He has supervised numerous doctoral students, including Cédric Villani who himself received the Fields Medal in 2010, establishing a distinguished academic lineage. His pioneering development of mean field game theory with Jean-Michel Lasry has created an entire research field with applications spanning economics, crowd dynamics, and social sciences. Through his continued scholarly output and leadership at one of France's most prestigious academic institutions, Lions exemplifies how deep theoretical insights can illuminate complex phenomena across scientific disciplines while maintaining relevance to contemporary real-world challenges.
