This is a charming but quirky amalgam of biography, memoir and reminiscence about the renowned mathematician Peter Lax written by Reuben Hersh, Lax’s friend and former Ph.D. student.
Lax was born into a prosperous Jewish family living in Budapest. He escaped to the U.S. with his family when he was fifteen, graduated from Stuyvesant high school in New York and enrolled in New York University at the recommendation of his mother’s cousin’s husband, Gabor Szegö. The Lax family was remarkably well-connected. They knew more than a few eminent mathematicians, including John von Neumann, at whose behest Lax, still in high school, was invited to visit the Institute for Advanced Study to be introduced to Erdös and Einstein.
To understand Lax it is important to recognize both his impressive raw ability and the amazing community that has surrounded him throughout his life. His ties to the mathematical and scientific community began in Hungary, continued in New York and at NYU, and expanded when joined the army and was soon directed to the Manhattan project. There he again saw von Neumann, worked with mathematicians like Richard Bellman and John Kemeny, and was deeply involved in the engineering aspects of the project. He has written about this time:
The time I spent in Los Alamos, especially the later exposure, shaped my mathematical thinking. First of all, it was the experience of being part of a scientific team — not just of mathematicians, but people with different outlooks — with the aim being not a theorem but a product. One cannot learn that from books; one must be a participant.
Back at NYU after the war, Lax finished his undergraduate work and started graduate work in the midst of the mathematical powerhouse that Richard Courant was building. Few places in the world had such a collection of talent in partial differential equations and applied mathematics.
Hersh argues that Lax sees no difference between pure and applied mathematics, that he “unites the pure and applied seamlessly and inseparably”. Hersh says further that Lax unites two great traditions of modern mathematics — the first a special style of functional analysis from Europe and the second an approach to machine computation and numerical analysis via Los Alamos. Even this doesn’t capture his breadth, one that ranges from shock waves, solitons and scattering theory to Lax pairs, integrable systems and the axiomatic treatment of hyperbolicity.
The book is not all about mathematics. We also learn a good deal about Lax’s personal life, his family and his interests — which include a serious interest in painting. There is a very nice collection of photographs (something that AMS has been doing very well in this and similar publications). Some of the most interesting parts of the book describe Lax’s life at NYU over the last several decades. The book is a true blend of the personal and the mathematical.
Bill Satzer (firstname.lastname@example.org) is a senior intellectual property scientist at 3M Company, having previously been a lab manager at 3M for composites and electromagnetic materials. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.