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

Abel's Proof

An Essay on the Sources and Meaning of Mathematical Unsolvability

Paperback Published: 27th February 2004
ISBN: 9780262661829
Number Of Pages: 222
For Ages: 18+ years old

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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 fianc‚�rBut 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. Pesic focuses on the contested development of algebra--which even Newton resisted--and the gradual acceptance of the usefulness and perhaps even beauty of abstractions that seem to invoke realities with dimensions outside human experience. Pesic tells this story as a history of ideas, with mathematical details incorporated in boxes. The book also includes a new annotated translation of Abel's original proof.

"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"

Introductionp. 1
The Scandal of the Irrationalp. 5
Controversy and Coefficientsp. 23
Impossibilities and Imaginariesp. 47
Spirals and Seashoresp. 59
Premonitions and Permutationsp. 73
Abel's Proofp. 85
Abel and Galoisp. 95
Seeing Symmetriesp. 111
The Order of Thingsp. 131
Solving the Unsolvablep. 145
Abel's 1824 Paperp. 155
Abel on the General Form of an Algebraic Solutionp. 171
Cauchy's Theorem on Permutationsp. 175
Notesp. 181
Acknowledgmentsp. 203
Indexp. 205
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9780262661829
ISBN-10: 0262661829
Series: The MIT Press
Audience: Professional
For Ages: 18+ years old
Format: Paperback
Language: English
Number Of Pages: 222
Published: 27th February 2004
Publisher: MIT Press Ltd
Country of Publication: US
Dimensions (cm): 20.1 x 13.7  x 1.4
Weight (kg): 0.24