Read This! The MAA Online book review column Euler and Modern Science ed. by N. N. Bogolyubov, G. K. Mikhaǐlov, and A. P. Yushkevich Reviewed by Michael Berg

What a wonderful contribution to the celebration of Euler’s 300^th birthday! Euler and Modern Science, edited by the Russian scholars N. N. Bogolyubov, G. K. Mikhailov, and A. P. Yushkevich, is a unique compendium of articles centered on the towering figure of Leonhard Euler, who resided and worked in St. Petersburg from 1727 to 1741, and then again from 1766 to 1783, the year of his death. The interval from 1741 to 1766 saw Euler in Berlin, as a member of the Berlin Academy of Sciences, so that, for most of his life, Euler lived in Russia. This chronology lends additional weight to the contributions in this volume, written by mathematicians who can boast of a special cultural connection with this giant of the mathematical art.

Euler and Modern Science appeared in its original Russian edition in 1988, as a Festschrift for the 200^th memorial of Euler’s death, celebrated five years earlier; specifically, many of the papers in the present translation first appeared as part of the proceedings of a 1983 conference held in Euler’s honor in Moscow and St. Petersburg. They are equally appropriate, however, to this year’s celebration of Euler at 300.

The articles in the book number over two dozen and include papers with a particularly technical focus, papers on things properly mathematical, some historical papers, and some lighter fare, so to speak. In the first category we find, for instance, “Euler and the development of astronomy in Russia,” by Abalakin and Grebenikov, while properly mathematical matters are represented by, e.g., “The manuscript of Euler on number theory,” by Matvievskaya and Ozhigova, “Euler’s contributions to algebra,” by Bashmakova, and “Diophantine equations in Euler’s work,” by Lavrinenko.

Among the historical contributions we encounter Grau’s “Leonhard Euler and the Berlin Academy of Sciences,” and, related to the same theme, Biermann’s irresistible “Was Leonhard Euler driven from Berlin?” Finally, in a very different vein, we have, for example, Tserlyuk-Askadskaya’s “Euler’s music-theoretical manuscripts and the formation of his conception of the theory of music.” Thus, the articles in Euler and Modern Science certainly cover a broad spectrum of topics, and this cornucopia-quality hugely contributes to the charm of the book. The articles also evince a uniformly high level of scholarship and Robert Burns’ translation is excellent.

As recent ads in our trade-journals show, Euler and Modern Science is one of a quintet of books offered by in the MAA Spectrum Series in commemoration of Euler’s 300^th birthday; if the book under review is at all representative of its four partners, the whole set should adorn every mathematical library worthy of the name, and make for nigh-on irresistible temptation for any individual mathematician.

Publication Data: Euler and Modern Science, ed. by N. N. Bogolyubov, G. K. Mikhaǐlov, and A. P. Yushkevich. Mathematical Association of America, 2007. Hardcover, 425 pages, $59.95. ISBN 9780883855645.

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

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