The German mathematician Friedrich (Fritz) Hirzebruch passed away a couple days ago, at the age of 84. Hirzebruch was perhaps the most important mathematician in the Germany of the postwar period, responsible for the founding of the Max Planck Institute in Bonn, as well as the yearly Bonn Arbeitstagung conference. The Mathematics Genealogy Project lists him as having 52 Ph.D. students and 368 descendants. There’s a wonderful interview and article about him at the Simons Foundation web-site.
Hirzebruch’s first great mathematical achievement was the proof in 1954 of the generalization of the classical Riemann-Roch theorem to higher dimensional complex manifolds, now known as the Hirzebruch-Riemann-Roch theorem. This used the new techniques of sheaf cohomology and was one of the centerpieces of the explosion of new results in geometry and topology during the 1950s. Further generalization of this led to the Grothendieck-Riemann-Roch theorem, and the Atiyah-Singer index theorem. Hirzebruch’s monograph on the subject Topological Methods in Algebraic Geometry was the essential textbook in this area for many years.
The last time I heard Hirzebruch talk was at the celebration of Atiyah’s 80th birthday in Edinburgh, where Hirzebruch gave a talk about his interactions with Atiyah. He displayed some of their correspondence from this period, which makes fascinating reading and is now available here.
With the loss of Raoul Bott a few years ago, and now Fritz Hirzebruch, the math and physics communities are deprived of two of the great figures who built parts of modern mathematics that appear crucially in the structure of the Standard Model. Much of this connection between math and physics remains a mystery, and it’s too bad they won’t be around to help make progress unraveling it.
Update: The New York Times has a very good obituary of Hirzebruch here.