Klein, Hurwitz, and the “Jewish Question” in German Academia

Abstract

Mathematicians love to tell stories about people they once knew or perhaps only heard about. If the story happens to sound believable, others are apt to repeat it, possibly embellishing on the original tale. Such mathematical folklore occasionally finds its way into print, and once it does, readers are apt to take such stories at face value, lending them additional credibility. Occasionally, though, alleged facts come under scrutiny, and established stories are exposed as fiction. Yet even when someone comes along with decisive evidence refuting an earlier account it can easily happen that the original story just refuses to die.

Appendix: Two Tributes to Adolf Hurwitz

Max Born Recalling Hurwitz as a Teacher

At the end of the winter semester [1902–03] I again decided to spend the summer [studying] at another university in order to widen my views on science and life. It was only natural that I should consider Zurich, where, in addition to the Cantonal University, there was the Eidegnössische Technische Hochschule, an important school of science and engineering. My friend [Otto] Toeplitz approved my choice of Zurich as a mathematician of great renown, Hurwitz, lived there.. .. I have to confess that I went only to two mathematical courses, one (4 h a week) by Hurwitz on elliptic functions, the other (2 h) by [Heinrich] Burkhardt on Fourier analysis.

Hurwitz was a tiny man with the emaciated face of an ascetic in which burned two unnaturally large eyes. He was ailing and very frail. But his lectures were brilliant, perhaps the most perfect I have ever heard. The course was the continuation of another, on analytic functions, which I had not attended; I therefore had some difficulty in following and had to work hard, reading many books. Once when I missed a point in a lecture I went to Hurwitz afterwards and asked for a private explanation. He invited me and another student from Breslau, Kynast,. .. to his house and gave us a series of private lectures on some chapters of the theory of functions of complex variables, in particular on Mittag-Leffler’s theorem, which I still consider as one of the most impressive experiences of my student life. I carefully worked out the whole course, including these private appendices, and my notebook was used by Courant when he, many years later and after Hurwitz’ death, published his well—known book. .. the so-called Courant-Hurwitz (Born 1978, 72).

George Pólya on Hurwitz as a Colleague

Hurwitz had great mathematical breadth, as much as was possible in his time. He had learned algebra and number theory from Kummer and Kronecker, complex variable from Klein and Weierstrass. It was Hurwitz who arranged for me my first appointment at the ETH (The Swiss Federal Institute of Technology). From the time of my appointment there in 1914 until his death in 1919, I was in constant touch with him. We had a special way we worked. I would visit him and we would sit in his study and talk mathematics—seldom anything else—until he finished his cigar. Then we would go for a walk continuing the mathematical discussion. His health was not too good so when we walked it had to be on level ground, not always easy in the hilly part of Zürich, and if we went uphill, we walked very slowly. I wrote a joint paper with Hurwitz. In fact, it is a paper of mine and a paper of his, linked in a poetic form of correspondence. My connection with Hurwitz was deeper and my debt to him greater than to any other colleague. I played a large role in editing his collected works (Pólya 1987, 25).