by Yuri I. Manin
Friedrich Hirzebruch was eighteen years old in December 1945 when he started his study at Münster University. Reminiscing about this time in 2009 he wrote:
Wenn ich damals einen kurzen Lebenslauf abgeben musste, dann enthielt er immer den Satz “Von Mitte Januar 1945 bis zum 1. Juli 1945 durchlief ich Arbeitsdienst, Militär und Kriegsgefangenschaft.” (In those days, whenever I had to supply a short CV, it always contained the sentence: “Between mid-January 1945 and July 1, 1945, I served fatigue duty, military duty, and was detained as prisoner of war.”)
This statement puts a double distance between the present day and painful youth of war years, defies any attempt to express this pain more eloquently, and does so by silence.
After settling in Bonn in 1956, Hirzebruch put great effort into the restoration of the European mathematical community, destroyed, like so many other institutions and lives, by the war. The brilliant idea of annual Arbeitstagungen and later the founding of the Max Planck Institute for Mathematics (MPIM) bore rich fruit. Hirzebruch struggled for the new Europe, like Henri Cartan in France, using all the influence that he possessed as an internationally renowned researcher.
My first close contact with Fritz and Inge Hirzebruch came in 1967. I spent six weeks at the Institut des Hautes Études Scientifiques in Bures-sur-Yvette, where Grothendieck taught me the “fresh-from-the-oven” project of motivic cohomology. After that I got permission and a German entry visa, which enabled me to visit Bonn and to participate in the Arbeitstagung on my way back to Moscow.
The blissful stress of study with Grothendieck and of Paris magic did something to my body, but in Bonn, Inge and Fritz treated me as their son and helped my healing. Their kindness and generosity forever remain in my memory.
In 1968 an abrupt end came to these budding direct contacts between mathematicians of Western Europe and their colleagues in the Soviet Union and Eastern Europe. The next generation, coming after Hirzebruch’s and then mine, had different concerns. As one of those young men recalled recently, “We thought it highly likely we would be blown off the planet, and that, somehow, it was up to us — children after all — to prevent it.”1 We were not blown off the planet. The existing order of things again started to seem stable — or stagnating. I had not the slightest premonition that this epoch would also pass during my life and that almost a quarter of a century afterwards I would meet Fritz again and become a colleague of his in the MPIM. After 1990 and the fall of the Berlin Wall, Friedrich Hirzebruch, through an immense effort, helped many mathematicians from East Germany find jobs and continue their scientific lives in a new environment.
Mathematics is a travail de longue haleine. Leonard Euler (born in Basel and working in St. Petersburg), inspired perhaps by the seven bridges of Königsberg (mostly destroyed by bombings in 1944 and 1945), discovered the notion of Euler characteristic of a graph. This notion had evolved during two centuries and by the time Friedrich Hirzebruch was maturing as a mathematician, found reincarnation as an alternating sum of dimensions of cohomology groups of (invertible) sheaves on an algebraic manifold. The celebrated Riemann–Roch–Hirzebruch formula of 1954 (described by Atiyah) expressed this number through geometric invariants of the base, crucially using the Todd genus, discovered by J. A. Todd from Liverpool. At the first Arbeitstagung in 1957, Alexander Grothendieck, son of a Russian anarchist and an eternal exile in France and everywhere else, presented its great generalization.
Perhaps the Riemann–Roch–Hirzebruch–Grothendieck Theorem, which fused and crowned efforts of a dozen great spirits from all corners of Europe, deserves to be put on the flag of the united Europe more than any other symbol.
