Niels Henrik Abel Quotes

Norway, Mathematician
August 5, 1802 – April, 6, 1829.

Niels Henrik Abel (/ˈɑːbəl/; Norwegian: [ˈɑːbl̩]) 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 over 350 years. He was also an innovator in the field of elliptic functions, discoverer of Abelian functions. He made his discoveries while living in poverty and died at the age of 26 from tuberculosis.

The divergent series are the invention of the devil, and it is a shame to base on them any demonstration whatsoever. By using them, one may draw any conclusion he pleases and that is why these series have produced so many fallacies and so many paradoxes.

Niels Henrik Abel
By studying the masters and not their pupils.

Niels Henrik Abel
- Study
- Masters
- Pupils

The mathematicians have been very much absorbed with finding the general solution of algebraic equations, and several of them have tried to prove the impossibility of it. However, if I am not mistaken, they have not as yet succeeded. I therefore dare hope that the mathematicians will receive this memoir with good will, for its purpose is to fill this gap in the theory of algebraic equations.

Niels Henrik Abel
- Theory
- Gap
- Equations
I shall devote all my efforts to bring light into the immense obscurity that today reigns in Analysis. It so lacks any plan or system, that one is really astonished that there are so many people who devote themselves to it - and, still worse, it is absolutely devoid of any rigor.

Niels Henrik Abel
He is like the fox, who effaces his tracks in the sand with his tail.

Niels Henrik Abel
- Tracks
- Fox
- Tail
With the exception of the geometrical series, there does not exist in all of mathematics a single infinite series the sum of which has been rigorously determined. In other words, the things which are the most important in mathematics are also those which have the least foundation.

Niels Henrik Abel
There are very few theorems in advanced analysis which have been demonstrated in a logically tenable manner. Everywhere one finds this miserable way of concluding from the special to the general and it is extremely peculiar that such a procedure has led to so few of the so-called paradoxes.

Niels Henrik Abel
- Way
- Special
- General