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Sunday, 15 February 2009 08:02

Introducing Niels Henrik Abel (1802-29)

 

Niels Henrik Abel (1802-29) was one of the greatest mathematicians of the beginning of the last century. He works on the borders of Mathematics solving the most important problems of him epoch, like to proof that the quintic is not generally soluble.

He also works extensively with series, like Divergent Series. He also comment about the interchanging limit process was called into question by him, in 1826. Cauchy had included in his Cours d'Analyse the proposition that if a serie of functions converges in the neighborhood of a point a, and if its terms are continuous at a, then the serie converges to a function that is likewise continuous at a. Abel in 1826, used the example Σ (-1)n+1(sin nx)/n to illustrate the incorrectness of Cauchy's proposition. He also showed, however, that for certain types of infinite series continuity of the sum can be deduced from continuity of the terms; it is precisely the uniform convergence of these serie to which he appeals.

Abel life were complicated. He travel across all Europe and meet personally, Gauss and Cauchy as well others. He was a contemporary of Évariste Galois, which method is used today in Mathematics, because more powerful. But while Galois method solve the problem completely, him approach is really extensive and complicated. Abel approach is clear and simple, and at the same time complete.

We at FTHumanEvolutionCourse will consider the Abel works in full, specially him Oeuvres available in two volumes.  

 

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Last Updated on Sunday, 15 February 2009 08:41