Home Business Tech Markets Entrepreneurs Leadership Personal Finance ForbesLife Lists Opinions Video Blogs E-mail Newsletters Portfolio Tracker Special Reports Commerce Energy Health Care Logistics Manufacturing Media Services Technology Wall Street Washington CIO Network Enterprise Tech Infoimaging Internet Infrastructure Internet Personal Tech Sciences Security Wireless Bonds Commodities Currencies Economy Emerging Markets Equities Options Finance Human Resources Law & Taxation Sales & Marketing Management Technology Careers Compensation Corporate Citizenship Corporate Governance Managing Innovation CEO Network Reference ETFs Guru Insights Investing Ideas Investor Education Mutual Funds Philanthropy Retirement & College Taxes & Estates Collecting Health Real Estate Sports Style Travel Vehicles Wine & Food 100 Top Celebrities 400 Richest Americans Largest Private Cos World's Richest People All Forbes Lists Business Opinions Investing Technology Opinions Washington & The World Companies People Reference Technology Companies Events People Reference Companies People Companies Events People Reference Companies Events People Reference

Book Review

The Rise Of Modern Mathematics

Michael Patrick Brady, 04.13.10, 01:09 PM EDT

Amir Alexander's ''Duel at Dawn.''

Although Dr. Grigori Perelman's refusal of the prestigious Millennium Prize for mathematics--and its million-dollar purse--was met with shock in the media this past March, it was not without precedent. Though Perelman's hermetic lifestyle, eccentric behavior and bitter denunciations of the academic establishment may seem to indicate a troubled mind, he is actually fulfilling an archetype that can be traced back nearly two centuries, to the very birth of modern mathematics.

In Duel at Dawn: Heroes, Martyrs and the Rise of Modern Mathematics, author Amir Alexander argues that the popular image of mathematicians as strange, reclusive figures springs from the early 19th century. It was then that mathematics began to evolve from a science based in the empirical realities of the Enlightenment to an art form informed by the ideals of Romanticism, concerned only with its own internal truths. 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.

Article Controls







At the end of the 18th century mathematics was concerned primarily with explaining the concrete, observable realities of the world. The grand mathematicians of the time were men like Jean le Rond d'Alembert, whom Alexander describes as a "natural man" in the model of Jean Jacques Rousseau's Emile. Alexander says that "mathematics was a science of the material world and could never be understood separately from it." To suggest otherwise was heresy.

That was not a problem for the new generation of early-19th-century mathematicians, least of all Evariste Galois. Though he lived for only 20 years, his forward-thinking theories and violent demise in a Parisian duel made him a legend whose story has been passed down to aspiring mathematicians ever since. For Alexander, Galois is a Byronic figure who represents the confluence of mathematics and Romanticism that he believes profoundly changed the field. At the provocation of brash young men like Galois, mathematics would slip its worldly bonds and venture into realms of greater abstraction.

Duel at Dawn is not merely about transformative mathematical achievements, but also about how these men's stories more often reflect the ideals of their eras than reality. Galois, for example, has long been heralded as an innocent martyr whose groundbreaking work was ignored by a jealous and hard-hearted academy. Through extensive research, Alexander shows that he was in fact a boorish, arrogant troublemaker who, despite the encouragement of his elders, thumbed his nose at those who would seek to lend him aid. He was a rabble-rousing French radical republican, utterly convinced of his own genius and not afraid to make powerful enemies. His penchant for self-destruction was matched only by his belief that all the forces of the world were set against him.

"This is the fate of the pure man of genius in Galois' eyes," Alexander writes, "to be cast out and marginalized by a cold and ruthless establishment and despised by the general public. His only refuge is his own purity and the beauty of disembodied mathematics itself."

Alexander deftly dismantles the Galois myth and reveals a tradition of hagiography in mathematics in which friends and allies gloss over unsavory or inconvenient facts in order to employ their subjects as unassailable weapons against critics and detractors. He provides concise yet compelling biographical sketches of the mathematical luminaries of the period. They are portrayed warts and all, with all their petty jealousies, personal foibles and professional rivalries exposed.

In his introduction Alexander suggests that readers may skip the sections of the book that delve deeply into the equations and formulas of Galois, Abel and Bolyai, but it's an unnecessary disclaimer. These are among the most engrossing and informative parts of the narrative, thanks to Alexander's crisp, comprehensible prose. 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.

Next >