Euler and Modern Science; Euler at 300

Euler and Modern Science, N.N. Bogolyubov, G.K. Mikhailov and A.P. Yushkevich (eds): 2007, 425 pp. hardcover, $59.95 (member price $47.95) ISBN:  978-0-88385-564-5

Euler at 300: An Appreciation, Robert Bradley, Lawrence D’Antonio and C. Edward Sandifer (eds): 2007, 298 pp. hardcover, $51.95 (member price $41.95)  ISBN: 978-0-88385-565-2;  Mathematical Association of America, Washington, D.C. 1-800-331-1622 or www.maa.org

These two volumes complete and round out the MAA’s published tribute to the genius and accomplishments of Leonard Euler (1707-1783).  As with the other three books in this series, they are well done.  The selection of material complements and expands that given in the previous volumes.  Articles are appealing and illustrated by photos and diagrams and well documented, allowing for further research on the topics considered.

Euler and Modern Science is a translation and reprinting of the 1988 Russian edition, which in turn resulted from a 1983 symposium of the Soviet Academy of Sciences on the “Modern Developments of Euler’s Ideas.”  Its 25 essays focus on Euler’s varied work in applied mathematics and his association with the St. Petersburg Academy of Sciences.  Several of his accomplishments in mechanics, hydrodynamics, astronomy, ballistics and the theory of vibrations and music are presented and discussed.  A reader of this book also obtains some appreciation  of Euler’s personal traits:  his exceptional administrative ability; his involvement with the publications of the Berlin Academy and his deep religious nature.  Insights from his personal correspondence with Clairaut, d’Alembert and Lagrange are revealed.  We also learn of his difficulties with Frederick the Great.  The reader comes away with a deeper appreciation of Euler the scientist and Euler the man. 

In the years leading up to Euler’s tercentenary, many academic meetings and presentations were given in his honor.  The contents of these talks and discussions resulted in a substantial body of work on the life and accomplishments of Leonhard Euler.  The editors of Euler at 300: An Appreciation have selected 20 of the more informative and revealing contributions from this prologue of activity to present in this book.  As a whole, the collection provides an excellent survey of the scope and depth of Euler’s mathematical achievements.  It further supplies insights into some of the motives driving Euler’s research and promotes an understanding of 18th century mathematical processes.  It is both good mathematics history and good reading.

Each of these books are highly recommended for library acquisition.  Perhaps of the pair, Euler at 300 is a better survey of Euler’s life and work for the general reader and personal acquisition.  However, the whole series of five volumes in this Euler tercentenary tribute is a fine collection of scholarship illuminating one of the greatest mathematical careers of all time.  The complete series can be purchased for $235.50 or at a MAA members price of $189.00 – a worthwhile investment!

Frank Swetz, Professor Emeritus, The Pennsylvania State University

See also the MAA Reviews by Michael Berg and David P. Roberts.