# Oscar E. Lanford III

## Professor of Mathematics

Oscar Erasmus Lanford III was born in New York on January 6, 1940, and passed away in Switzerland in November 16, 2013, at the age of 74. Lanford received a B.A. in mathematics from Wesleyan University in 1960, and his Ph.D. in quantum field theory from Princeton University in 1966. His advisor at Princeton was Arthur Wightman and, according to the Mathematics Genealogy Project, his lineage included towering figures in physics and mathematics such as Arnold Sommerfeld and Felix Klein. Lanford spent only part of his impressive academic career at the University of California, Berkeley. He joined the faculty in 1966 and left in 1983 to take a position at the Institut des Hautes Études Scientifiques (IHES) outside of Paris, followed by positions at the Swiss Federal Institute of Technology Zurich (ETH) in Switzerland (1987–2005) and the Courant Institute of Mathematical Sciences at New York University (2005-2012).

Oscar was the one member of the Department of Mathematics at Berkeley whom I knew best before I joined it in 1974. I was a graduate student at Rockefeller University in New York City, and every year there was a two-day workshop in statistical mechanics organized by Joel Lebowitz at Yeshiva University. It was there that I first met Oscar, as well as other “West coast people” such as Donald Ornstein from Stanford University. After Oscar left Berkeley, we continued our brief encounters. I remember having dinner with him during some of my visits to Paris. He was always interested in knowing what was happening in the mathematics department here. His devotion to the department was truly remarkable. He undertook any department duty with utmost seriousness. For several years he was in charge of scheduling classes both for our undergraduate as well as graduate offerings. He did an amazing job and everything ran very smoothly. On one occasion, somebody suggested that I may consider taking up that job if Oscar were to move to a different department committee. I had a short chat with Oscar inquiring how many hours a week he spent on this task. His answer was precise and scary: 14 hours each week! I decided that it was not a job for me. Many years later, after I served one term as department chair, I took on his old scheduling job, and (probably) did it reasonably well, but I never came close to spending as much time as Oscar had mentioned.

Shortly after I arrived in Berkeley, Lanford undertook the extremely difficult committee assignment of heading the mathematics department’s computer committee. I was not directly involved in any of the many discussions as to what operating system we should use, since most of my numerical and symbolic computing was done either at the Lawrence Berkeley National Laboratory or (remotely) at the Massachusetts Institute of Technology. Maybe this was the reason why Lanford would talk freely with me about all the opposing sides in the “operating system” debate. I still remember vividly some heated arguments between those that preferred VMS versus those that went for Unix. In spite of these agitated arguments, Lanford managed to keep the peace at a difficult time. Before Oscar actually resigned from Berkeley to join IHES he was on leave for a few years. Rumor had it that he was granted these leaves on the assumption on the part of the dean that he would come back and serve as chair of the department. I prefer to think that he did not leave Berkeley to escape from this job.

Lanford’s research in the broad areas of mathematical physics and dynamical systems involved a few extremely deep problems. I will talk briefly about only two of these areas that have been permanently shaped by the work of Lanford. Lanford did very fundamental work proving in a rigorous way the existence of solutions (at least for short times) of the Boltzmann equation of statistical mechanics in a certain appropriate limit (the Grad limit). This equation had been proposed more than a hundred years earlier by Ludwig Boltzmann (who visited Berkeley at one point) but it had resisted a complete mathematical treatment until the work of Lanford. His contribution can be found in the set of lecture notes, “Time Evolution of Large Classical Systems,” in *Dynamical Systems, Theory and Applications, Lecture Notes* in *Physics*, ed. Jurgen Moser 38, Springer-Verlag, 1975. Lanford is also known as one of the very first mathematicians to produce rigorous proofs that were “computer-assisted”. His best known work in this area is a “Computer-Assisted Proof of the Feigenbaum Conjectures,” *Bulletin of the American Mathematical Society, vol. 6, issue 3,* published in 1982. This topic plays a very important role in chaos theory, a subject that was being created at that time. Conceptual proofs that did not make use of computers appeared about 10 years later, but they were very long and difficult, whereas his groundbreaking work relied on detailed numerical estimates proved with the help of a computer.

By today’s standards the number of works published by Lanford is not large. His style consisted in writing up extremely polished “unpublished notes” or “drafts,” which in many cases were only seen by his closest friends. He would lecture to students at all levels using these notes and improve them every single time that he was in front of the chalkboard. Oscar had a total of 11 Ph.D. students, five of them while he was on the faculty at Berkeley and six at ETH in Zurich. He received the 1986 U.S. National Academy of Sciences Award in Applied Mathematics and Numerical Analysis, and an honorary doctorate from Wesleyan University. He became a Fellow of the American Mathematical Society in 2012. When Lanford left Berkeley, I remember well congratulating him on his new, very prestigious position and at the same time lamenting the loss that this meant for Berkeley. Looking back now only reaffirms my view that he was an extremely valuable colleague at Berkeley and a first-rate mathematician on the world scene.

He and his wife Regina had one daughter.

F. Alberto Grünbaum

2018