Gauss, Titan of Science

We mathematicians seem to be, without exception, gossips. Put two of us in a room together and, before long, typically after mathematics proper has been exhausted as a topic, the conversation turns to other mathematicians. And sooner or later ratings are conceived, comparisons are made, and prodigious achievements are multiplied and hyperbolized. But there are untouchables: almost every one agrees that Archimedes, Newton, and Gauss stand alone atop Mount Olympus, essentially unchallenged. So Gauss' life is, or should be, a subject of unmatched interest in the mathematical community.

Bizarrely, however, there are rather few "popular" biographical sources to be had, given the incomparable importance of their subject. E. T. Bell's famous article, "The Prince of Mathematicians," comes to mind right away, the fourteenth chapter in his famous (or notorious) Men of Mathematics, which is also reprinted in James R. Newman's gargantuan four-volume work, The World of Mathematics. Howard Eves has written eloquently on Gauss in his Mathematical Circles series (see Quadrant IV of In Mathematical Circles, Mathematicall Circles Squared, and Mathematical Circles Adieu, for example), and Eves is a marvelous story-teller, of course. Then there's W. K. Bühler's 1981 scholarly monograph, Gauss, A Biographical Study, which, although a very serious contribution to the history of mathematics, is probably not what one would call "light reading." And, at least according to the Springer-Verlag web site, Bühler's book is currently out of print, to boot.

The same used to be true about the book under review, whose original publication date is 1955 and has heretofore been rather hard to find, even in the second-hand bookstore world. Over the years I have only come across a few copies altogether (in university libraries), and have had to rely primarily on the tales told by Bell for my own store of Gauss-trivia. No more, however! Dunnington is back — and how! This brand-new edition, published by the MAA, comes equipped with an introduction by Jeremy Gray, a sketch of the author by Fritz-Egbert Dohse, supplementary articles on Gauss' famous diary (with Gray playing a huge part), and lots of pictures. All of it is great fun, even if, like me, the reader is merely a huge fan of Gauss rather than a real historian of mathematics (or science: after all, Gauss was a major figure in 19^th century astronomy as well as physics).

Gauss, Titan of Science comes equipped with no fewer than nine appendices, including genealogical material. Twenty years ago Bühler himself "called Dunnington's book 'by far the most important' of the major biographies of Gauss" (which are, of course, unknown to guys like me). Indeed, Dunnington's book is a true labor of love by a true academic. Dunnington, a professor of German, was taught as a boy in grade school by none other than Gauss' own granddaughter, who inspired in her student a life-long interest in the great man. Eventually Dunnington became a premier expert on the life of Gauss with a real devotion to his subject; he even arranged to live for a whole year in Gauss' apartments at the Göttingen observatory!

And the amount of detail available in the book under review is, well, astronomical. Dunnington's discussions of, for example, Gauss' travels in connection with his work in geodesy (surveying, etc.) are simply amazing by virtue of the minutiae offered. On the other hand, since to mathematicians it is really Gauss the mathematician who matters most, these descriptions can safely be glossed over without doing major damage to the continuity of the story. But they do possess a charm all their own.

The professional (i.e. mathematical) aspects of Gauss' life are magnificently dealt with in the book, notwithstanding the fact that Dunnington was not a mathematician himself. The nice discussion of Disquitiones Arithmeticae is a good example, and so is the discussion of Gauss' treatment of quadratic reciprocity. And so on. It's all there, from the fundamental theorem of algebra, through the method of least squares (so useful in Gauss' astronomical work), to differential as well as non-Euclidean geometry. Moreover, the supplementary discussions (by Jeremy Gray) of Gauss' mathematical diary are delectable, if terse; and Gauss' entries are given verbatim!

There is also plenty of discussion of Gauss' interactions with, e.g., Sophie Germain, both Bolyais, Bessel, Helmholtz, Eisenstein, Möbius, Dedekind (whose reminiscences of Gauss are quoted at length), and, of course, Riemann. All of these accounts are fascinating on two fronts in that they deal not just with Gauss as a sublime mathematician, to whom others would come for advice, help and guidance, but also with his humanity. What was Gauss' capacity for friendship? (Consider, for example, Bolyai.) What was he like as a maven in the presence of gifted fledglings? (Consider Sophie Germain. Or consider Eisenstein. Indeed, consider his Ph.D. students, including the incomparable Riemann.) Was Gauss a cold fish or was he warm-blooded? (I vote for the latter option.)

What comes through most clearly in this wonderful and well-written book is G. Waldo Dunnington's deep interest in (and profound respect for) Gauss as a Mensch, a human being. In the pages of the book Gauss takes on a genuine human personality, not caricatured, but eminently believable. Dunnington treats Gauss' love for his wives (he was twice a widower) with great sensitivity and very often lets Gauss speak for himself: there are numerous quotations from Gauss' remarkably touching love-letters, first to Johanna (who died in 1809) and later to Minna (who died in 1831). Gauss lost his first wife when he was in his early thirties, his second when he was in his fifties. Johanna bore him three children; Minna bore him three children, the youngest of whom, Therese, took care of Gauss in his old age.

Finally, as regards the matter of Gaussian arcana and trivia, so crucial to mathematicians' chats, Dunnington sets a very high standard. To wit: From early boyhood on, Gauss was very nearsighted and this played something of a (minor) role in his early days as a surveyor. As a young student at the Collegium Carolineum, Gauss studied the writings of Newton, Lagrange and Euler — on his own. Laplace urged the bellicose Napoleon Bonaparte to spare Göttingen entirely because of Gauss' presence there. Later Laplace paid Gauss' share of Göttingen's war bounty to Napoleon; Gauss paid it back, with interest. And there are scores and scores more of these bits of cool data.

Just get the book!

Michael Berg (mberg@lmu.edu) is professor of mathematics at Loyola Marymount University.