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A collection of interviews and occasional professional autobiographies in the 1960s-1980s focusing on mathematicians who worked in the 1920s-1970s or people closely associated with the field in other capacities (Martin Gardner, while describing himself as a journalist, impacted the field majorly through his famed Scientific American columns on recreational mathematics; another interview is with a biographer of Hilbert & Neyman, Constance Reid).Some of these mathematicians one may well be familiar (Conway, Diaconis, Erdos, Gardner, Graham, Kline, Knuth, Mandelbrot, Pólya, Smullyan, Ulam), but many just made me draw a blank (Birkhoff, Blackwell, Chern, Coxeter, Halmos, Hilton, Kemeny, Lefschetz, Pollak, Rees, Reid, Robbins, Taussky-Todd, Tucker), so theres a wide range from the famous and public intellectuals to the working mathematicians.The interest of the interviews likewise range: Smullyans autobiographical essay (extracted from his autobiography, apparently) is stuffed full of hilarious stories and jokes as any reader of his books might expect, Diaconis has an interesting life story in going from a traveling stage magician to a mathematician/statistician who continues to dabble in magic (like Smullyan), Knuths reminiscences are of interest to any programmer, while Cherns life is an unusual look into what its like to bring modern mathematics to a place like early Communist China; others are just terribly dull. Another issue is that the more pure mathematicians struggle to describe to interviewers in a short approachable fashion what, exactly, theyve accomplished and why its of interest, while the geometers can at least draw pictures of some sort and the ones who dabble in application and especially statistics have all sorts of immediately-interesting topics to discuss. I admit I got very little out of the pure mathematicians, aside from being a bit amused at the aesthetic prejudices on display as algebraists sniff at analysts who sniff at topologists who sniff at combinatorics and meanwhile I have hardly any idea what those specialties are much less any opinion on their respective merits. It is difficult to maintain an interest in topics you dont know anything about and the discussants cant explain, so a good deal of the book was wasted on me.Some topics surface repeatedly, to ones surprise: New Math, a failed American program to rewrite lower mathematical pedagogy into teaching math in a much more abstract fashion, comes up repeatedly (perhaps because of the striking failure, none of the interviewees are willing to endorse it although Kline spends much time attacking it); the Hungarian Martians seem to come up in every other interview as the interviewee either taught or worked with a Hungarian, was inspired by a Hungarian, or was a Hungarian (Von Neumann, Halmos, Pólya, Erdős, Wald, and others), although none of the interviewees seemed to have any good suggestions for why the Martian cluster seems to exist (yes, Hungary was poor and so geniuses there might turn to math preferentially, but then why dont we see similar clusters from other impoverished countries? the Hungarian per capita GDP in the early 1900s is probably equaled or exceeded by scores of countries since and present). Other tendencies in the biographies remind me of similar observations I noted in my review of Past, Present, and Future of Statistical Science - academia seems to have been infinitely less cutthroat than it is now and many of the subjects seem to almost luck into jobs and positions (Mandelbrot in particular seems to have been a beneficiary as he was able to continue his tertium quid career until fractals became a phenomenon), and in every professional life there is a clear discontinuity at WWII where it seems all of Europes intelligentsia packed up for America and get sucked into the military-industrial complex for application to complex Cold War topics (the Cold War was particularly good to statistics, as one can see how statistics & probability are mentioned only occasionally pre-WWII but then suddenly everyone is dabbling in it post-WWII; likely the Cold War/WWII influence would be even more obvious if interviewers & interviewees didnt step so gingerly around the topic out of a mix of patriotism & shame, the former exemplified by a mention of the cryptographic work in WWII which the interviewee doesnt describe but assures us has been written up in abstract form for the open literature); people married remarkably young and had children immediately which would be a bit odd in this age of prolonged PhDs & multiple postdocs & the two-body problem.Other topic dont: computers are surprisingly rarely mentioned, with the exception of one or two discussions of the four-color computer proof, and Kemeny who turn out to have been quite prophetic about computers becoming ordinary tools of scholars & to have been one of the developers of BASIC; a mathematically-inclined layman or technologist will be surprised at the general absence of topics like P=NP or Fermats last theorem, but of course those problems were only formulated or solved long after most of these interviews were conducted.And I did like some of the anecdotes related. For example, I learned that the origin of Walds celebrated frequentist sequential analysis came from an incident which for all the world sounds like Bayesian reasoning: These two men were puzzled because a Navy captain with whom they had discussed the problem of destructive sampling of munitions had said that he didn’t see why he had to destroy so much of the evidence—that there ought to be a way whereby, after a while, an experimenter, like a savvy captain, would know that this was a good batch or a bad one and stop sampling...Since they were unable to get anywhere with it because it required very special mathematical skills, they took it to an outstanding mathematical statistician who was associated with them—Abraham Wald, an émigré from Hitler’s He was intrigued by the problem and solved it by developing a new technique in statistics that is now one of great importance: sequential analysis.Active mathematicians may find these old interviews of great interest, but I think most people would be better off reading just a few of them: Diaconis, Knuth, Smullyan, Pólya, the 2 Gardner articles, Conway, Chern, Kemeny, Kline, and Mandelbrot (in no particular order).

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