page_title: Louis Nirenberg
hierarchical_section_title: Louis Nirenberg
caption_attribution_description: English: Louis Nirenberg, Canadian-American mathematician, in Jerusalem.
context_page_description: Louis Nirenberg was a Canadian-American mathematician, considered one of the most outstanding mathematicians of the 20th century.
  Nearly all of his work was in the field of partial differential equations. Many of his contributions are now regarded as fundamental to the field, such as his proof of the strong maximum principle for second-order parabolic partial differential equations. He is regarded as a foundational figure in the field of geometric analysis, with many of his works being closely related to the study of complex analysis and differential geometry.
  He is especially known for his collaboration with Shmuel Agmon and Avron Douglis in which they extended the Schauder theory, as previously understood for second-order elliptic partial differential equations, to the general setting of elliptic systems. With Basilis Gidas and Wei-Ming Ni he made innovative uses of the maximum principle to prove symmetry of many solutions of differential equations. The study of the BMO function space was initiated by Nirenberg and Fritz John in 1961; while it was originally introduced by John in the study of elastic materials, it has also been applied to games of chance known as martingales.
context_section_description: Louis Nirenberg (28 February 1925 – 26 January 2020) was a Canadian-American mathematician, considered one of the most outstanding mathematicians of the 20th century.
  Nearly all of his work was in the field of partial differential equations. Many of his contributions are now regarded as fundamental to the field, such as his proof of the strong maximum principle for second-order parabolic partial differential equations. He is regarded as a foundational figure in the field of geometric analysis, with many of his works being closely related to the study of complex analysis and differential geometry.
  He is especially known for his collaboration with Shmuel Agmon and Avron Douglis in which they extended the Schauder theory, as previously understood for second-order elliptic partial differential equations, to the general setting of elliptic systems. With Basilis Gidas and Wei-Ming Ni he made innovative uses of the maximum principle to prove symmetry of many solutions of differential equations. The study of the BMO function space was initiated by Nirenberg and Fritz John in 1961; while it was originally introduced by John in the study of elastic materials, it has also been applied to games of chance known as martingales. His 1982 work with Luis Caffarelli and Robert Kohn was described by Charles Fefferman in 2002 as "about the best that's been done" on the Millennium Prize problem of Navier–Stokes existence and smoothness, in the field of mathematical fluid mechanics.
  Other achievements include the resolution of the Minkowski problem in two-dimensions, the Gagliardo–Nirenberg interpolation inequality, the Newlander-Nirenberg theorem in complex geometry, and the development of pseudo-differential operators with Joseph Kohn.
caption: Louis Nirenberg in 1975
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