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Indiscrete thoughts. With forewords by Reuben Hersh and Robert Sokolowski. Edited, with notes and an epilogue by Fabrizio Palombi. (English) Zbl 0862.00005

Boston: Birkhäuser. xxii, 280 p. (1997).
Here, one will not find, e.g., the Hahn-Banach Extension Theorem or some new exotic proof of a combinatorial result. Instead one will find deep discussions of the inner workings of the culture and phenomenology of mathematical activity embedded in its historical context. One might almost say: Life imitates mathematics!
The author, defender of the combinatoric faith, brings out strong connections between beauty and mathematics, but leaves alone the nearly as strong link between ethics and mathematics. He believes that the deepest truths offend and, usually in the deepest ways. His sharp opinions would most likely, exclude him from any popular position, say, of a political kind. For Rota, it is impossible to find a beautiful proof of an ugly theorem. However, the reviewer believes it is more interesting to discover why and how there are so many beautiful theorems with ugly proofs!
The book is neither an autobiography nor a Collected Works. Rather, a great part of it deals with amusing and enraging incidents amongst mathematicians, some dead. E.g., N. Wiener and P. Cohen discussing Hilbert’s non-mathematical term “nostrification”. There is a broad range of topics: Fine Hall (at Princeton); Alonzo Church (but not Hilbert’s comments); William Feller; Emil Artin; Solomon Lefschetz; Stan Ulam; The Second Scottish Café; Edward Teller; P. Erdös (briefly); Husserl; Ten Lessons I Wish I Had Been Taught; and A. Mathematician’s Gossip. Also included are several book reviews already published by Rota over the last three decades; e.g., one of P. R. Halmos’ books.
One may not agree with many of Rota’s remarks, but none of them is wrongheaded as far as I can determine from my own experiences. Anyone seriously interested in the history or sociology of mathematics must read this book. But be prepared to digest many aphorisms!

MSC:

00A30 Philosophy of mathematics
00-02 Research exposition (monographs, survey articles) pertaining to mathematics in general
01A60 History of mathematics in the 20th century
01A70 Biographies, obituaries, personalia, bibliographies
01A73 History of mathematics at specific universities
01A80 Sociology (and profession) of mathematics
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