steered in a new direction, as well as shaping modern analysis in a significant way. Based on this example, Louis Nirenberg, Lars Hörmander and others have outlined some important changes to the theory and structure of the field. This was adopted by many analysts and mathematicians as a major development. He also worked on several complex variables in relation to nonlinear hyperbolic equations and elliptic equations, well-posedness for initial value problems of wave fronts (now commonly called Sobolev spaces) in the early 1930s, solutions of the classical problems of Hermann Weyl and Hermann Minkowski for analytical data (the original problem was solved by Louis Nirenberg in 1949 as part of his PhD thesis), the extendibility of minimal surfaces on and analytical nature of its boundaries which is fully free or in part, free boundary problems of water wave fronts in hydrodynamics, and the proof of quadratic reciprocity theorem in number theory from 'hydrodynamical' perspective. Awards and honors Lewy was elected to the National Academy of Sciences in 1964, and was also a member of the American Academy of Arts and Sciences. He became a foreign member of the Accademia dei Lincei in 1972. He was awarded a Leroy P. Steele Prize in 1979, and a Wolf Prize in Mathematics in 1986 for his work on partial differential equations. In 1986, the University of Bonn gave him an honorary doctorate. Publications A selection of his work, edited by David Kinderlehrer and including his most important works, was published as the two volume work and . With biographical essays by Helen Lewy and Constance Reid, and commentaries on Lewy's work by Erhard Heinz, Peter D. Lax, Jean Leray, Richard MacCamy, Louis Nirenberg and François Treves. . The following works are included in his "Selecta" in their original language or translated form. . There are also two English translations of the 1928 German original paper: the first one is a translation from the German by Phyllis Fox, circulated as a research report: . The second one is a typographical improvement of the first, published by IBM as: . A freely downloadable version of this one can be found here . . See also Lewy's example Courant–Friedrichs–Lewy condition References External links . . An audio interview, available at eCommons@Cornell from the [Eugene B. Dynkin Collection of Mathematics Interviews Eugene B. Dynkin Collection of Mathematics Interviews ]. . The biographical entry about Hans Lewy at