## Our Mathematical Debt to Europe

**March 1, 2010**

**Book ReviewPhilip J. Davis**

**Mathematicians Fleeing from Nazi Germany: Individual Fates and Global Impact**.

*By Reinhard Siegmund-Schultze, Princeton University Press, Princeton, New Jersey, 2009, 504 pages, $49.50.*

Let me say right up front that by one of those paradoxes or absurdities of this absurd world, I have to thank Adolf Hitler for a not insubstantial portion of my mathematical education. Mathematicians who fled from Germany, beginning in the mid-1930s, would teach several important courses I took in the '40s: I learned projective geometry from Oscar Zariski, relativity theory and the philosophy of mathematics from Philipp Frank. And Stefan Bergman taught me about kernel functions and the theory of several complex variables.

Concerned as a student primarily with grades and with the possibility that I would be drafted as America drifted slowly into war, I did not realize during those undergraduate years that Oscar Zariski was constantly listening to the radio for news of the war, trying to infer the fate of relatives back home, or that Stefan Bergman was putting together in his mind a technical book that he would dedicate to his two sisters who were swallowed up by the terrible events in Poland. Philipp Frank was talking to Richard von Mises, his friend, co-author, and fellow refugee at Harvard, about the demise of the Vienna Circle of logical positivists, scattered to the winds by the incursion of Nazi power.

All these people were, of course, older than I was; all had, after struggles whose details they rarely aired in public, achieved some academic stability and status. And all, in addition to lecturing on mathematics, gave me grades, helped me find jobs, wrote recommendations, and encouraged me when I wanted to do my own thing, independent of their own specialties.

Along with these three men at whose feet I sat were many other mathematical refugees who, in the years that followed, augmented my understanding and appreciation of the mathematical world, life, character, and content. To name just a few: Olga Taussky-Todd, Otto Neugebauer, Max Schiffer, Franz Alt, Arthur Erdélyi, Kurt Mahler, Bernhard Neumann, Stan Ulam, William Prager.

And then there were the books, written by some of those named above and by other war refugees, that I pored over and that infused my own work and helped shape my philosophy: Hilbert and Cohn-Vossen, Frank and von Mises, Hermann Weyl, Gabor Szegö, Georg Pólya, Richard Courant, Salomon Bochner, Stefan Bergman---books so well known in our business that I need not provide titles for them.

If I personally owe so much to these brilliant mathematicians, then it is clear that their presence in the United States elevated a thousand times more the international status of American mathematics, lending it new directions, problems, points of view, philosophies, and leading it to new achievements.

***

*Mathematicians Fleeing from Nazi Germany*, a book that I cannot praise too highly, tells the sad, often terrifying, comprehensive story of one of the most irrational and hardly understandable chapters of world intellectual history. On every page of the book, which includes biography, letters, diaries, photographs, necrologies, detailed references, one can hear the bells tolling, now of inhuman behavior, now of chance, now of despair. But occasionally, one also hears bells that celebrate heroism, the struggle to live, and the will to achieve.

A brutal---but, alas, partly true---saying ascribed to Joseph Stalin is that while one death is a tragedy, a million deaths are only a statistic. If one were so minded, one could cull from this book mere statistics: 140 mathematicians exiled, such a number expelled, so many persecuted or murdered, so many driven to suicide, and so on. But the book also records that, as time marched on, many mathematicians were successfully re-established in countries whose languages were not spoken at their cradles and whose ways of life seemed a bit strange. Status, lost at first, was often slowly regained. Reinhard Siegmund-Schultze, displaying or referring to archival material, has provided enough references or leads for a reader who wishes to follow more deeply the fate of any particular individual.

To provide one example: Of the three refugee mathematicians mentioned in the

first paragraph of this review, I came to know Stefan Bergman the most intimately. I knew, impressionistically, a bit of his life story---from his boyhood in Czestochowa, Poland, to his career in the USA.

*Mathematicians Fleeing*filled me in as to exact dates and places, exact reasons for his wanderings, and his relationships with mathematical acquaintances, American scientific bigwigs, and relief institutions.

Siegmund-Schultze is a professor of the history of mathematics at the University of Agder, in Kristiansand, Norway. He has published easily twenty articles describing the impact of 20th-century European social and political history on mathematics. Having met him some years ago, I felt free to ask how it came about that he was attracted to this aspect of the history of mathematics. Here is his answer:

"The main point which aroused my interest was the dearth of literature on mathematics in the Third Reich until the 1980s and 1990s, which was caused by political shortsightedness and partisanship both in West Germany and in East Germany, although for different reasons. Raised in the German Democratic Republic, my interest in the fate of Jewish mathematicians, in emigration, and the international aspects of mathematics was certainly stimulated by the lack of our possibilities for communication and by the inability of Marxist (or rather self-declared Marxist) theories to account for anti-Semitism which did not nicely fit into a simple scheme of class struggles."

In the post-World War II years, with large parts of England and Europe devastated and only slowly recovering physically, financially, educationally, and emotionally, large numbers of remaining or newly graduated mathematicians were invited to visit, work, and lecture in American universities and other institutions. Many, to the advantage of America, stayed on permanently.

If the USA (among other countries) was the beneficiary of all this talent, the countries from which it was driven were soon bereft, and one may ask how long it will take for them to recoup their lost pre-eminence. The recorded history of mathematics is long---easily four thousand years---and mathematics has flourished here and there over the surface of the earth, at different times and often with different concerns, methods, symbolisms, interpretations. It has even withered in places in which it once throve with ample support and brilliant éclat. While the future is hidden, the question asked is not beyond conjecture.

*Philip J. Davis, professor emeritus of applied mathematics at Brown University, is an independent writer, scholar, and lecturer. He lives in Providence, Rhode Island, and can be reached at philip_davis@brown.edu.*