La prova di Abel
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Sinossi
Nel 1824 un ventunenne norvegese di nome Niels Henrick Abel dimostrò definitivamente che le equazioni algebriche di quinto grado sono insolubili. L’importanza di questo evento nella storia del pensiero non fu tuttavia immediatamente riconosciuta, e Abel morì povero e depresso cinque anni dopo. Questa vicenda umana è ricostruita da Pesic nel quadro di una storia che inizia con i greci e continua fino a oggi. Egli mostra come la matematica trovò le sue fonti nel mondo reale (le forme delle cose, i bisogni contabili dei mercanti) e procedette poi verso qualcosa di più universale, nel senso dell’astrazione, già con i pitagorici e poi con l’algebra. Per rendere corrente e agevole la lettura, gli sviluppi matematici sono separati dal testo in appositi riquadri. In appendice una nuova traduzione annotata del testo originale della prova di Abel.
- ISBN: 8833915468
- Casa Editrice: Bollati Boringhieri
- Pagine: 194
- Data di uscita: 01-09-2005
Recensioni
The formula for the solution of the general equation of the third degree by the Italians Del Ferro, Tartaglia, and Cardano, in the 16th Century, was one of the triumphs of Renaissance mathematics, and one that was a clear improvement upon the achievements of the Ancients. Soon thereafter Cardano's s Leggi tutto
I ought to begin with the positives: Pesic clearly presents specific mathematical ideas, embeds some bits of cute narrative throughout, and is able to cite a genuine abundance of sources in his endnotes. However, Pesic's approach to historical narrative serves to obfuscate the meaningful mathematical Leggi tutto
An interesting history of the insolvability of the quintic. I was expecting a somewhat dry explanation of the proofs and instead read a pleasant history of how mathematical thought changed over time, the introduction of algebra into mathematics and more. The explanations of the proof were just acces Leggi tutto
Best book I've found on Abel-Ruffini.
Fascinating. 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 g Leggi tutto
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 Leggi tutto
Very interesting read. One might read all the math involved if interested or just skip those bits and yet not lose the thread of the essay. I am now interested in reading some of the suggested references too!
Great read, easy to follow and with good details inside.
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