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Friday, April 10, 2020

Niels Henrik Abel and mathematics


Photo source: Wikimedia Commons, Johan Gorbitz


Neils Henrik Abel (1802-1829) was a Norwegian mathematician best known for solving the general quintic equation, his contributions to elliptic functions and Abelian functions. Mathematician Florian Cajori said,


"During the few years of work allotted to the young Norwegian, he penetrated new fields of research, the development of which has kept mathematicians busy for over half a century." (A History of Mathematics, 1893)


Mathematician Oystein Ore said,


"Niels Henrik Abel... wrote a series of mathematical papers that secures him a position among the greatest mathematicians of all time. In his Memorire sur les equations algebriques... Abel proves the impossibility of solving general equations of the fifth and higher degrees by means of radicals." (Quotes in A Source Book in Mathematics by David Eugene Smith)


The rest of this post is some quotes from Abel.




"I shall apply all my strength to bring more light into the tremendous obscurity which one unquestionably finds in analysis. It lacks so completely all all plan and system that it is peculiar that so many have studied it." (Letter to Christoffer Hansteen, 1826)


"I have had to be extremely cautious, for the presumed theorems without strict proof... had take such a stronghold in me, that I was continually in danger of using them without detailed verification." (Letter to Christoffer Hansteen, 1826)


"On the whole, divergent series are the work of the Devil and it's a shame that one dares base any demonstration on them. You can get whatever result you want when you use them, and they have given rise to so many disasters and so many paradoxes." (Letter to Bernt Michael Holmboe, 1826)


"It is readily seen that any theory written by Laplace will be superior to all produced of lower standing. It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils." (Quoted in Niels Henrik Able by Oystein Ore)