Duel at Dawn: Heroes, Martyrs, and the Rise of Modern Mathematics (review)

Everyone is unhappy after his or her own fashion, but the font of possible stories is limited. Hence stories tend to flatten the many particular sorrows into a few single types of narrative misery. Amir Alexander is interested in one such type: the misery of the Outsider Mathematical Genius. That story emerges in the early nineteenth century, its most prominent exponent being Évariste Galois, whose tale (youth, rebellion, eureka, duel) is perhaps the most famous of all mathematical narratives. As Alexander is right to point out, the story is since retold, by every mathematical generation, of its very prominent mathematicians—all the way down to Grothendieck and beyond. A version of the same story was told, of course, of the very prominent Romantic poets. It was not told—an essential observation made by Alexander (and perhaps the most important in this book)—of natural scientists. This observation makes Alexander's central thesis more probable: that the rise of a new "abstract" mathematics in the nineteenth century was correlated with the rise of the Outsider Mathematical Genius story. A new image of the mathematician went hand in hand with a new set of goals for mathematical practice. We should be grateful to Alexander for providing us with an original, compelling, and well-written story. One comes away energized with many new questions. For instance, the Galois story really came into its own at around the middle of the twentieth century—could it be not merely a "Romantic" story, then, but also a reflection of a newly emerging youth culture? I am interested in such questions as a historian, but they really ought to be shared, above all, with our friends the mathematicians. This side of rock music, no other field of human endeavor is as much obsessed with youth as mathematics is. So tell this to middle-aged mathematicians: stop agonizing about your lost Galois youth; anticipate with pleasure your Euler old age.