In the fog of a Paris dawn in 1832, Évariste Galois, the 20-year-old founder of modern algebra, was shot and killed in a duel. That gunshot, suggests , marked the end of one era in mathematics and the beginning of another.
Arguing that not even the purest mathematics can be separated from its cultural background, Alexander shows how popular stories about mathematicians are really morality tales about their craft as it relates to the world. In the eighteenth century, Alexander says, mathematicians were idealized as child-like, eternally curious, and uniquely suited to reveal the hidden harmonies of the world. But in the nineteenth century, brilliant mathematicians like Galois became Romantic heroes like poets, artists, and musicians. The ideal mathematician was now an alienated loner, driven to despondency by an uncomprehending world. A field that had been focused on the natural world now sought to create its own reality. Higher mathematics became a world unto itself—pure and governed solely by the laws of reason.
In this strikingly original book that takes us from Paris to St. Petersburg, Norway to Transylvania, Alexander introduces us to national heroes and outcasts, innocents, swindlers, and martyrs–all uncommonly gifted creators of modern mathematics.
Duel at Dawn is a delightful examination of the ways in which certain mathematicians have been made into mythical figures, and how the tropes of those canonical treatments have changed over the years. It's a fascinating and original book.
Does romantic mathematics exist? Romantic mathematicians do. Duel at Dawn reveals how the great mathematicians of the Enlightenment used geometry to study the earth and heavens, while their 19th century counterparts cherished internal beauty rather than practicality. Amir Alexander's original and convincing book opens a new path in the history of mathematics.
Through the life stories of three of the period's most controversial figures, Evariste Galois, Niels Henrik Abel and Janos Bolyai, Alexander reveals how their transgressive work changed mathematics and led to their lionization as Romantic heroes...Duel at Dawn neither talks over the head of its readers nor condescends, but instead ensures that the work of these Romantic mathematicians is not cloaked in obscurity. Of particular note is his breakdown of Hungarian mathematician Janos Bolyai's discovery of non-Euclidian geometry. Alexander does not shy away from the intricacies of the theory, nor the drawn out, convoluted history that underlies it. He takes readers through the process step by step, using plain language and clear diagrams to chart a course through the unknown. The larger narrative remains coherent without these more technical chapters, thanks to Alexander's ability to weave much of the mathematics into the fascinating lives of his subjects, but these in-depth studies of the math behind the men is very enriching. Mathematics need not be a scary, daunting subject, and Alexander does much to prove it.
Duel at Dawn suggests how preconceptions about the trappings of genius have radiated from art to maths. But its greater value lies in peeling back the layers of hagiography from figures such as Galois to reveal gloriously complicated men.
With tremendous attention to detail, historian Alexander examines the lives of 18th and 19th century mathematicians, finding much evidence to support his theory that the earlier geniuses of math (like Évariste Galois and Neils Henrik Abel) cultivated an artistic temperament, living short but fiery lives with little recognition, while the next generation (Jean le Rond d'Alembert, Leonhard Euler) pursued mathematics (and life) with purity and rigor, becoming "successful men of affairs who were the bright stars of their era and lived to a ripe old age."...Alexander's personable history of mathematics over two centuries (rounded out by a brief look at the present and future of the field) is filled with biographical details that will interest devoted mathematicians and historians of math or science.
This is a fascinating and provocative book. It is also extremely readable: the accounts of Galois, Abel, Cauchy and Bolyai and their posthumous reputations are engaging and entertaining, and along the way we meet many other fascinating personalities, including Guglielmo Libri, the aristocratic revolutionary, mathematician and stealer of rare books. Alexander's arguments are illuminating.
Alexander sees Galois's death as a turning point in the history of modern mathematics, a point at which math became less a study of nature than a purely abstract realm of its own, uncontaminated by the external world. He skillfully tells the story of this change, weaving it around the often tragic lives of the mathematicians most responsible for the change...[A] marvelous history.
Because it is such an engrossing story, it's easy to forget that the book's purpose also is to educate. Alexander conveys a general sense of who mathematicians were and how they fit in with society.
Though the Romantic ethos has persisted for a surprisingly long time among mathematicians, Alexander suspects that a cultural change is even now underway: reliance upon computers is replacing the mathematician-as-tragic-hero with the mathematician-as-skillful-nerd. Fascinating human faces peer out at the reader from behind seemingly sterile formulas.
[Alexander's] sensitive and thoughtful presentation illuminates the inner geometry of mathematical experience, leaving us to ponder whether its creators' parallel lives and works finally meet.
- 320 pages
- 6-1/8 x 9-1/4 inches
- Harvard University Press
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