Louis Nirenberg, Abel Prize, 2015

Louis Nirenberg (28 February 1925 – 26 January 2020) was a Canadian-American mathematician, considered one of the most outstanding mathematicians of the 20th century.

He made fundamental contributions to linear and nonlinear partial differential equations (PDEs) and their application to complex analysis and geometry. His contributions include the Gagliardo–Nirenberg interpolation inequality, which is important in the solution of the elliptic partial differential equations that arise in many areas of mathematics, and the formalization of the bounded mean oscillation known as John–Nirenberg space, which is used to study the behavior of both elastic materials and games of chance known as martingales. His other achievements include the solution to long-standing problems of Weyl and Minkowski, relating to the embedding of a 2-sphere and curvature, respectively; the theory of pseudo-differential operators initiated along with Joseph J. Kohn, the Newlander-Nirenberg theorem of complex structures, Vanishing Mean Oscillation (VMO), the symmetries of solutions of PDEs along with Gidas and Ni, among many others.

Nirenberg's work on PDEs has been described as "about the best that's been done" (as of 2002) towards solving the Navier–Stokes existence and smoothness problem of fluid mechanics, which is a Millennium Prize Problem.