Abel's Proof

An Essay on the Sources and Meaning of Mathematical Unsolvability

Peter Pesic

213 pages, parution le 19/04/2004

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Résumé

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 fiancée.

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. 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.

L'auteur - Peter Pesic

Peter Pesic is a Tutor and Musician-in-Residence at St. Johns College, Santa Fe, New Mexico. He has a Ph.D. in physics from Stanford University.

Sommaire

Introduction
The Scandal of the Irrational
Controversy and Coefficients
Impossibilities and Imaginaries
Spirals and Seashores
Premonitions and Permutations
Abel's Proof
Abel and Galois
Seeing Symmetries
The Order of Things
Solving the Unsolvable

Appendix A: Abel's 1824 Paper
Appendix B: Abel on the General Form of an Algebraic Solution
Appendix C: Cauchy's Theorem on Premutations

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Caractéristiques techniques

	PAPIER
Éditeur(s)	The MIT Press
Auteur(s)	Peter Pesic
Parution	19/04/2004
Nb. de pages	213
Format	13,5 x 20
Couverture	Broché
Poids	240g
Intérieur	Noir et Blanc
EAN13	9780262661829
ISBN13	978-0-262-66182-9