Last week I did some research on Abel for my weekly mathematician post and I have found a lot of interesting things. I have to say that I knew about him from Analysis (Abel’s test) and also from Abelian functions, but the rest was kind a mystery for me.
Niels Henrik Abel, born on 5th August 1802, was a Norwegian mathematician who made pioneering contributions in a variety of fields. His most famous single result is the first complete proof demonstrating the impossibility of solving the general quintic equation in radicals. This question was one of the outstanding open problems of his day, and had been unresolved for 250 years. As expected his solution was not completely accepted at the beginning (I understand that after so many years in which mathematicians from everywhere searched a solution, when a child from a not so popular school comes with an idea it is quite shocking). He was also an innovator in the field of elliptic functions, discoverer of Abelian functions.He invented (independently of Galois) an extremely important branch of mathematics (also my favorite at this point) known as group theory.
It is quite interesting to read about his Europe (especially Germany and France) tour to meat mathematicians and publish his work in different countries. But the ones that gave him the money to go considered it a failure because he didn’t meet Gaus and didn’t publish anything in Paris. I consider it was a great adventure for him and that he did learn quite a lot, also he published a lot in a German mathematical journal, Journal für die reine und angewandte Mathematik.
Unfortunately, while in Paris, Abel contracted tuberculosis and died at the age of 26. Regarding Abel, the French mathematician Charles Hermite said: “Abel has left mathematicians enough to keep them busy for five hundred years.”
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