When I was a teenager I discovered — and devoured — Bell’s Men of Mathematics, and I soon resolved to keep the titans populating the pages of that wonderful old book as major players in my pantheon of mathematical heroes. Very little has changed over the years: there are other figures in the pantheon, of course, but none of the old heroes have been displaced. Indeed, the experience of teaching a large number of courses in the history of mathematics has significantly deepened a sense of almost personal acquaintance with these great men. Undoubtedly, this experience, deeply rooted in the experience of reading Bell’s book, is shared by a huge number of mathematicians of my generation, and many readers of these reviews.
But Men of Mathematics seems to have fallen out of favor with the younger generation, or even the last couple of generations (tempus fugit!). Or perhaps it’s just that the wave that has swept the beach clean of coelacanths like me, bringing with it a very different way of serving a mathematical apprenticeship, leaves less and less room for the old masters. The current vogue of doing mathematics seems geared toward building community at all levels, with study and work groups dominating the scene from high school mathematics contests through graduate programs, and support groups available for every one at every level, and this may provide an explanation for the lamentable ignorance that mathematical rookies so often display regarding the history of their discipline: there’s no psychological need for solitary day-dreams about the heroic life of Riemann if one’s formation is an unbroken sequence of group activities. In my cynical moments I wonder whether the ubiquity of these new trends isn’t to blame for what looks to be the passing of an age: as far as pantheons of idols from the past are concerned, today’s young mathematical Turks look to be more disposed to a Götterdämmerung than to paying homage to Archimedes, Newton, and Gauss. Well, maybe I am just out of step.
But it would truly be a tragedy, a threat both to mathematical culture properly so-called and to scholarship itself, if the study of the history of mathematics, by the rank and file, were to wane, and surely steps should be taken to reintroduce aspiring mathematicians to the lives of the titans from past ages. More recent players might even be added to the list; after all, in many ways ours is a very young art.
This having been said, Simon Gindikin’s Tales of Mathematicians and Physicists is absolutely on target. Covering the last five centuries, this eminently readable book consists of fifteen essays on mathematicians and mathematics of particular historical importance and gravity, factoring Gindikin’s perspective into the equation (Newton receives essentially only one page of coverage (p. 157): clearly Leibniz and the Bernoulli’s have won the author over completely), and also his taste: geometry and analysis receive a great deal of coverage, algebra and arithmetic less so, a full chapter on Ramanujan notwithstanding. The book begins with a consideration of Cardano’s 16th century Ars Magna, replete with a nice treatment of the cubic, and ends with an interesting essay titled, “The complex world of Roger Penrose.” In between, there are, among other things, wonderful chapters on Euler, Gauss, and Poincaré, as well as a long essay on Galileo, which certainly conveys the sweep of Gindikin’s pedagogical vision.
Tales of Mathematicians and Physicists is a worthwhile book to read, especially for novices, which is consonant with the fact that the indicated essays first appeared in Kvant . But it’s fun for every one, and enlightening. Additionally, for me and those of my mathematical generation it’s especially pleasant to encounter old heroes again and, indeed, learn more about them — much more, in fact: this is serious scholarship and the mathematics is very good. And it would be an easy task to adapt Tales of Mathematicians and Physicists for use as a supplementary text in a course on the history of mathematics; in fact, I may do so the next time I’m up at bat. It’s a pleasure to recommend this book.
Michael Berg (firstname.lastname@example.org) is professor of mathematics at Loyola Marymount University.