Jürgen Kurt Moser (July 4, 1928 – December 17, 1999) was a German-American mathematician, honored for work spanning over four decades, including Hamiltonian dynamical systems and partial differential equations.

Jürgen Moser's parents lived in Königsberg, German empire and resettled in Stralsund, East Germany as a result of the Second World War.

Moser attended the Wilhelmsgymnasium (Königsberg) in his hometown, a high school specializing in mathematics and natural sciences education, from which David Hilbert had graduated in 1880.

His older brother Friedrich Robert Ernst (Friedel) Moser (August 31, 1925 – January 14, 1945) served in the German Army and died in Schloßberg during the East Prussian offensive.

He was survived by his younger brother, the photographic printer and processor Klaus T. Moser-Maync from Northport, New York, his wife, Gertrude Moser from Seattle, their daughters, the theater designer Nina Moser from Seattle and the mathematician Lucy I. Moser-Jauslin from Dijon, and his stepson, the lawyer Richard D. Emery from New York City.

After his thesis, he came under the influence of Carl Ludwig Siegel, with whom he coauthored the second and considerably expanded English language edition of a monography on celestial mechanics.

Having spent the year 1953 at the Courant Institute of New York University as a Fulbright scholar, he emigrated to the United States in 1955 becoming a citizen in 1959.

He was director (sharing office with Armand Borel in the first two years) of the Forschungsinstitut für Mathematik at ETH Zürich in 1984–1995, where he succeeded Beno Eckmann.

He developed it for both elliptic and parabolic problems, and beyond recovering De Giorgi and Nash's results, he was able to use it to prove a new Harnack inequality.

Research of Henri Poincaré and Élie Cartan in the early twentieth century had clarified the two-dimensional CR geometry, dealing with three-dimensional hypersurfaces of smooth four-dimensional manifolds which are also equipped with a complex structure.