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This Book Is In French. ... Read more

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Chapters: Niels Henrik Abel, Ola Raknes, George Bradshaw. Source: Wikipedia. Pages: 42. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Ola Raknes (17 January 1887 28 January 1975) was a Norwegian psychologist, philologist and non-fiction writer. Born in Bergen, Norway, he was internationally known as a psychoanalyst in the Reichian tradition. He has been described as someone who spent his entire life working with the conveying of ideas through many languages and between different epistemological systems of reference, science and religion (Dannevig, 1975). For large portions of his life he was actively contributing to the public discourse in Norway. He has also been credited for his contributions to strengthening and enriching the Nynorsk language and its use in the public sphere. Raknes was known as a thorough philologist and a controversial therapist. Internationally he was known as one of Wilhelm Reich's closest students and defenders. Ola Raknes was the son of the farmer Erik Askildson (Askjellson) Raknes (1856 1926) and Magdali Olsdotter (born Raknes) (1859 96) and grew up at the family farm of Raknes in Hamre on the island Osterøy in the Osterfjorden fjord near Bergen in a strict pietist environment. He was married twice: in his first marriage in 1911 with Aslaug Vaa (1889 1965, the marriage was dissolved in 1938) they begot the children Magli (1912 1993), Anne (1914 2001), Tora (1916 1995), Erik (1919-) and Tor (1923-). The second marriage in 1941 with Gjertrud Bonde (born 1913) gave him the daughter Ada. Ola Raknes attended folkeskole (primary school) on the neighbouring farm and then worked for a while on the family's farm prior to enrolling at middelskole (the next higher level in the education system of that time) in Volda. After that he graduated from the Hambros skole in Ber...More: http://booksllc.net/?id=18634162 ... Read more

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Chapters: John Horton Conway, Évariste Galois, Niels Henrik Abel, Felix Klein, Sophus Lie, Richard Borcherds, Arthur Cayley, John R. Stallings, James W. Cannon, Brian Bowditch, Karen Vogtmann, Zlil Sela, Mladen Bestvina, Rostislav Grigorchuk, Marcus Du Sautoy, Arthur Byron Coble, John G. Thompson, Ferdinand Georg Frobenius, Mikhail Gromov, Theodor Molien, Yozo Matsushima, Jacques Tits, Joseph Gallian, James Alexander Green, Guido Zappa, Max Dehn, Richard Brauer, Charles Leedham-Green, Irving Kaplansky, Issai Schur, Bertram Huppert, Camille Jordan, William Burnside, Stephen Arthur Jennings, Jonathan Lazare Alperin, Hanna Neumann, Robert Fricke, Joseph Bernstein, Geoff Smith, Marshall Hall, László Pyber, Michael Aschbacher, George Glauberman, Otto Hölder, Graham Higman, David Harbater, Philip Hall, Daniel Gorenstein, Friedrich Wilhelm Levi, Bernhard Neumann, Hellmuth Kneser, James Wiegold, Bhama Srinivasan, Cheryl Praeger, Walter Feit, Hermann Rothe, Michio Suzuki, Richard A. Parker, Roger Evans Howe, Brian Hartley, Gilbert Baumslag, Wilhelm Magnus, Charles Sims, Mark Ronan, Robert Arnott Wilson, Sergei Adian, Hans Julius Zassenhaus, Christine Hamill, Paul Gustav Heinrich Bachmann, Dan Segal, Alfred Young, Pyotr Novikov, Émile Léonard Mathieu, Käte Fenchel, Robert Steinberg, Peter Ludwig Mejdell Sylow, Giovanni Frattini, Walther Von Dyck, Dudley E. Littlewood, Simon P. Norton, John Mckay, Hans Fitting, Zvonimir Janko, Aleksandr Gennadievich Kurosh, Edna Grossman, Roger Carter, Donald G. Higman, John Britton, Panos Papasoglu, Otto Schreier, R. L. Griess, George Abram Miller. Source: Wikipedia. Pages: 317. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Arthur Cayley (16 August 1821 26 January 1895) was a British mathematician. He helped found the modern British school of pure mathematics. As ...More: http://booksllc.net/?id=311034 ... Read more

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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 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. ... Read more

Customer Reviews (10)

Abel's Proof

This book is intelligently written and does not assume advanced mathematics. Look for it to become a classic. It includes, as an appendix, Pesic's translation of Abel's 1824 paper "Memoir on algebraic equations, in which is demonstrated the impossibility of solving the general equation of the fifth degree", along with a brief commentary. Two additional appendices further help in understanding Abel's paper. In his notes, Pesic offers a wealth of suggestions for reading beyond his book.

The story is of mathematicians' pursuit of solving polynomial equations. Pesic tells this story with concision, clarity and brilliant elegance. Technical details are boxed and separate from the main text. Not only does this allow readers to bypass such details if they choose but, in being highlighted, the details can be easily located later.

One of the best books in the history of math
I think this book is great.It provides a very readable history and talks about the high level ideas behind the proofs.It nicely provides short boxes that clarify details in the story.

For those who want to understand the mathematics in more detail, it provides additional information in appendices.It also includes an English translation of Niels Abel's 6 page paper that established his famous proof.

The discussion on Paolo Ruffini and Francois Viete are especially worthwhile.There's information here that's not generally well known.

This book is a model of how a math book should be written.I am very glad to highly recommend this book.Most of the books on this topic focus primarily on Evariste Galois so it's very nice to see Niels Abel also get his due.:-)

Henk's review on Abel's proof
The actual proof of Abel is in the appendix at the end of the book and the book outlines a history on the life of the mathematicians that worked on the problem.So the book is in fact a history book instead of a real
mathematics book.Therefore I was a little bit disappointed because there is little explanation on the actual proof.

focuses on the contributions of Abel to the unsolvability of the quintic
Abel's Proof takes an interesting approach to mathematical writing. The author places all mathematical formulas and derivations in boxes that are separate from the flow of the text so you don't have to do the math if all you want is a knowledge of the history of this era in mathematics. The author does a great job of explaining this history, covering the story of the factoring of polynomials in general but focusing on the unsolvability of the quintic. Abel's life of poverty is covered in detail. There is a lot of mathematics, if you are interested, including how to factor a cubic polynomial and Abel's proof of the unsolvability of the quintic. I found the math somewhat hard to follow but worth the effort of doing so. I found Abel's story to be very sad. The book is worth reading just for his life story alone.

a nice little gem
"Abel`s Proof" is a nice little book which tackles with the unsolvability issue in mathematics within the context of Niels Henrik Abel`s proof of the unsolvability of quintic equations with radicals. The text is an enjoyable account of a rather importantsubject in the whole history of mathematics in some 200 pages, and the quality of writing is laudable. The mathematical details and clarifications are given in boxes along the way, and the book in general is blended with numerous mathematical figures and portraits.

A firm high-school background in basic algebra should suffice to grasp the whole material, yet it has a real potential of teaching a noticeable chunk of mathematics to almost anyone along with valuable comments on its subject-matter.

I recommend this book wholeheartedly to anyone who has some genuine interest in going one step beyond the conventional popular science writing. And the price is right of course. ... Read more

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This digital document is an article from Science and Its Times, brought to you by Gale®, a part of Cengage Learning, a world leader in e-research and educational publishing for libraries, schools and businesses.The length of the article is 574 words.The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase.You can view it with any web browser.The histories of science, technology, and mathematics merge with the study of humanities and social science in this interdisciplinary reference work. Essays on people, theories, discoveries, and concepts are combined with overviews, bibliographies of primary documents, and chronological elements to offer students a fascinating way to understand the impact of science on the course of human history and how science affects everyday life. Entries represent people and developments throughout the world, from about 2000 B.C. through the end of the twentieth century. ... Read more

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This digital document is an article from Science and Its Times, brought to you by Gale®, a part of Cengage Learning, a world leader in e-research and educational publishing for libraries, schools and businesses.The length of the article is 1556 words.The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase.You can view it with any web browser.The histories of science, technology, and mathematics merge with the study of humanities and social science in this interdisciplinary reference work. Essays on people, theories, discoveries, and concepts are combined with overviews, bibliographies of primary documents, and chronological elements to offer students a fascinating way to understand the impact of science on the course of human history and how science affects everyday life. Entries represent people and developments throughout the world, from about 2000 B.C. through the end of the twentieth century. ... Read more