Anyone with an interest in mathematics is likely to be drawn in by a work subtitled "Heroes, Martyrs, and the Rise of Modern Mathematics." The attraction is even greater upon learning that the book recounts the life and death of legendary mathematician and French revolutionary Evariste Galois.
The Author, Amir Alexander, is a historian and writer living in Los Angeles. He has written a previous book on the history of mathematics, Exploration Mathematics: The Rhetoric of Discovery and the Rise of Infinitesimal Methods.
Duel at Dawn has its moments. But, Alexander's constant repetition of his thesis, his constant restating of his unifying themes (just in case it wasn't properly appreciated or understood the first three times), end up making for something quite a bit less than compelling reading. If this book lost 30 pages, it would be a greatly improved.
The Tragic Lives of the Mathematicians
The author strives, quite successfully, to make two major points. The first is that some mathematicians have achieved legendary status due to their brilliant but short lives during which their efforts were not appreciated. In the same way that the stature of rock stars and actors is magnified by early death, so have the lives of the principle players in Alexander's dramatic mathematical landscape been rendered larger than life and surrounded by mystery and wonder. Throw in a good dose of the evil and entrenched establishment that failed to see their genius, and it makes for tragedy par excellence.
The biographies of Norwegian Niels Abel, Frenchman Evariste Galois, and Hungarian Janos Bolyai, along with detailed descriptions of the important aspects of their work, are the high points in this book.
Abel almost made it before dying young of tuberculosis. Galois was a truly colorful character who marched the streets of Paris dressed in the uniform of a banned revolutionary organization, and more or less invented group theory before being killed in a duel at the age of 20. Bolyai was a Hungarian military officer and the son of a mathematician, who set out to prove Euclid's 5th postulate (that pesky one dealing with parallel lines) and instead discovered an entirely new mathematical world that was entirely self-consistent, yet in which the laws of standard Euclidean geometry did not hold. Too bad no one really cared at the time.
Toward Modern Mathematics
The second point of the book is that the work of the unsung heroes Abel, Galois, and Bolyai (among others), paved the way for mathematics to break free of its linkage with the natural world and into its own realm as an abstract pursuit that was founded on internal principles alone. Thus was born the age of rigorous proofs and mathematics for mathematics' sake, without need for the art to be limited to only addressing practical problems or natural phenomenon.
Alexander does a fine job of making connections between these men, their elders and contemporaries, and the evolution of mathematical thought and philosophy as it developed in the 18th and 19 centuries Many greats of mathematics make an appearance (some cast as villains, some as heroes of truth, or both at the same time) including Lagrange, D'Alembert, Laplace, Legendre, Euler, Cauchy, Hardy, Ramanujan, Jacobi and Gauss. It is clearly a well researched endeavor.
There are some inspiring and entertaining moments in Duel at Dawn. One's knowledge of many interesting and important figures in mathematics will certainly be enhanced by reading it. It is the author's annoying habit of "reminding" the reader, over and over again, of what he has previously told us that really takes the shine off of what otherwise would be an excellent read. As it is, it is merely "acceptable."
References
Duel at Dawn; Amir Alexander, Harvard University Press; Cambridge, MA: 2010
Philip McIntosh - The author holds a B.Sc. in Botany and Chemistry and an M.A in Biology and he has thirty + years of experience in science and industry.
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