An Essay on the Sources and Meaning of Mathematical Unsolvability
By (author) Peter Pesic
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Abel's Proof by Peter Pesic
Book DescriptionIn 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 fiance. 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.
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Book DetailsISBN: 9780262661829
(203mm x 136mm x 12mm)
Imprint: MIT Press
Publisher: MIT Press Ltd
Publish Date: 2-Apr-2004
Country of Publication: United States
Books By Author Peter Pesic
Levels of Infinity, Paperback (March 2013)
Original anthology features less-technical essays discussing logic, topology, abstract algebra, relativity theory, and the works of David Hilbert. Most have been long unavailable or previously unpublished in book form. 2012 edition.
Mind and Nature, Hardback (March 2009)
A collection of the author's general writings on philosophy, mathematics, and physics. It includes the author's exposition of his synthesis of electromagnetism and gravitation.
Sky in a Bottle, Paperback (March 2007)» View all books by Peter Pesic
The age-old question "Why is the sky blue?" begins a quest through science, history, and art, from Aristotle and Newton through Goethe and Einstein.
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Author Biography - Peter Pesic
Peter Pesic is Tutor and Musician-in-Residence at St. John's College, Santa Fe. He is the author of Labyrinth: A Search for the Hidden Meaning of Science; Seeing Double: Shared Identities in Physics, Philosophy, and Literature; Abel's Proof: An Essay on the Sources and Meaning of Mathematical Unsolvability; and Sky in a Bottle, all published by the MIT Press.
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