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Mathematical Apocrypha

Steven G. Krantz
Mathematical Association of America
Publication Date: 
Number of Pages: 
[Reviewed by
Michael Berg
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Perhaps it is because our profession is so outré that we mathematicians derive such perverse enjoyment from telling tales. Gossip is almost never considered a vice among our ranks, unless it’s particularly malicious, and eccentricity, which appears to be so rampant a trait with us, is generally ranked as both a virtue and a genetic inheritance (pace Keith Devlin and his “math gene”). In any case, mathematicians are very often story-tellers, and, like all accomplished raconteurs, generally prefer a good tale to a true one. Nonetheless, truth is stranger than fiction and the tales in Steve Krantz’ Mathematical Apocrypha have been checked and double-checked: says Krantz in his Preface, “Most of the stories here are in fact verifiable, and have been checked (in the fashion of investigative reporters) with other witnesses.” So much the better, then: the real scoop!

When I knew Steve Krantz in my student days (he was a young rookie assistant professor at the time) he already evinced a host of symptoms of raconteurism, as well as a concomitant off-beat sense of humor, making him a favorite with students and colleagues alike. He admits in the aforementioned Preface: “I have spent my entire adult life hanging around academics, and have certainly never encountered a group that is so hell-bent on telling stories about each other as are mathematicians. With this book I plant my flag as a story-teller.” Manifestly Steve has spectacularly lived up to his early promise (in both senses of the phrase: he is of course also a very accomplished complex analyst!): the Apocrypha is a terrifically entertaining compendium of tales about mathematicians of all sorts, of different eras, of different places. Some stories are necessarily n-th hand, n large, others are first or second-hand. They’re uniformly entertaining and some are down-right hilarious. Here are a few samples:

  • [p. 89] “It is said that, late in life, Hilbert was reading a paper and got stuck at one point. He went to his colleague in the office next door and queried, ‘What is a Hilbert space?’”
  • [p. 93] “…Weil was preparing a lecture in which he had to use some Fourier analysis. One particular point kept confusing him and he consulted [Mitchell] Taibleson [also of the Institute for Advanced Study] several times for help. In fact he went to Taibleson repeatedly on the same point. He eventually declared that he had it straight. But, during the lecture, Weil once again became confused. Looking at the audience in exasperation, he finally declared, ’If you don’t understand this, consult your analyst.’”
  • [p. 118] “On his 36-th birthday [Besicovitch] convinced himself that his best and most intensive years of research were over. He said to some friends, ‘I have 4/5 of my life.’ Twenty-three years later … when he was awarded the Rouse Ball Chair … at Cambridge , someone reminded him of his frivolous remark, pointing out that he had written more than half of his papers in the intervening time —many of them among his best. Besicovitch’s reply was, ‘Well, numerator was correct.’”
  • [p. 168] “When Stone was chairman of the University of Chicago Mathematics Department in the 1940’s, he used to come to work early each day so he could go from room to room in Eckhart Hall and wash the blackboards. Such was life in the Stone age.”
  • And possibly my single favorite: [p. 31] “On one occasion, Gödel attended one of the Institute’s twice-yearly formal dinners. He was seated across from John Bahcall … the famous young astrophysicist. The two introduced themselves, and Bahcall related that he was a physicist. Gödel replied scornfully, ‘I don’t believe in natural science.’” This anecdote is of course particularly interesting in light of Gödel’s famous close friendship with Einstein.

Speaking of Einstein, I found one tale in the Apocrypha which must be false, and, upon my pointing this out to Krantz, learned from him that others had also noted this particular story had serious problems. It’s a good tale, of course: [p. 67] “One of the Einstein legends concerns an event just after his arrival at the Institute for Advanced Study in Princeton . He went for a walk on the idyllic grounds, and he met J Robert Oppenheimer … on a footbridge. At that time Einstein knew no English and Oppie knew no German. Of course they each knew who the other was, and they wanted to be friendly. After a bit Oppie pointed down at the water and said, ‘Fish.’ ‘Ja,’ said Einstein, ‘Fisch.’” The difficulties lie in the facts that Oppenheimer’s PhD was from Max Born in Göttingen in 1926: Oppie spoke wonderful German already early in his life; Einstein came to the IAS in 1933, Oppie assumed the Directorship in 1947, so when they met in this setting, Einstein presumably spoke English at least well enough. In any case the tale is compromised. But it’s evidently an isolated singularity and Krantz’ veracity and accuracy batting-average is phenomenal.

Mathematical Apocryphais a book that is impossible to put down, and succeeds spectacularly in its light-hearted objectives. Its 200 or so pages are subdivided into six parts, carrying such titles as “Great Foolishness” and “Great Pranks” — irresistible stuff right from the frontispiece. There are a large number of pictures, too, including a marvelously feline shot of Kovalevskaya herself on p. 125. Just get it and have fun!

Michael Berg is Professor of Mathematics at Loyola Marymount University in Los Angeles

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