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

3.76 of 5 stars 3.76  ·  rating details  ·  37 ratings  ·  4 reviews
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 work, 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 21 when he self-published his proof, and he died five years later, poor and depre ...more
Hardcover, 213 pages
Published May 1st 2003 by MIT Press (MA)
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An interesting history of the proof that there is no general solution of a fifth degree polynomial equation. The story extends from the discovery of irrational numbers by the Greeks, through the work of Lagrange, Ruffini, Abel and Galois.

Galois discovered the same proof but in complete generality. Consequently most algebra textbooks present Galois theory but not Abel’s proof. After studying Galois theory elsewhere, I was curious about Abel’s proof and found a good resource here.

James Swenson
It was always going to be a difficult project to write a short book about the non-existence of a quintic formula for a general audience. Peter Pesic has probably done as well as anyone could. The appendices offer the primary sources, and the notes include a lot of helpful references.

As far as I can see, the text is accurate, though translation from MathSpeak to English necessarily introduces some imprecision. The author introduces not only Abel's ideas but a fair amount of the history of algebra
Rishiyur Nikhil
Interesting book for anyone who likes the history of science.

Abel was a Norwegian mathematician who, in 1824, published the first comprehensive proof of an old problem involving certain algebraic equations. The book traces the history of attempts starting from the Greeks.

A secondary theme is the lack of respect for Abel from mathematicians at the "center of the universe", namely France, Germany etc., because he was from that distant backwater, Norway. I love this quote from one of Abel's letters
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