Abel's Proof: An Essay on the Sources and Meaning of Mathematical Unsolvability

(Paperback)

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In 1824 a young Norwegian named Niels Henrik Abel proved conclusively that algebraic equations of the fifth order are not solvable in radicals. In this book Peter Pesic shows what an important event this was in the history of thought. He also presents it as a remarkable human story. Abel was twenty-one when he self-published his proof, and he died five years later, poor and depressed, just before the proof started to receive wide acclaim. Abel's attempts to reach out to the mathematical elite of the day had been spurned, and he was unable to find a position that would allow him to work in peace and marry his fiancee. But Pesic's story begins long before Abel and continues to the present day, for Abel's proof changed how we think about mathematics and its relation to the "real" world. Starting with the Greeks, who invented the idea of mathematical proof, Pesic shows how mathematics found its sources in the real world (the shapes of things, the accounting needs of merchants) and then reached beyond those sources toward something more universal. The Pythagoreans' attempts to deal with irrational numbers foreshadowed the slow emergence of abstract mathematics.

Reviews

"Readers of Pesic's fascinating little book will be led to an inescapable verdict: Niels Abel was guilty of ingenuity in the fifth degree." - William Dunham, Muhlenberg College, and author of Journey through Genius: The Great Theorems of Mathematics"

Author Bio

Peter Pesic, writer, pianist, and scholar, is Director of the Science Institute and Musician-in-Residence at St. John's College, Santa Fe. He is the author of Abel's Proof- An Essay on the Sources and Meaning of Mathematical Unsolvability; Seeing Double- Shared Identities in Physics, Philosophy, and Literature; Sky in a Bottle; and Music and the Making of Modern Science, all published by the MIT Press.