8 Quotes by Niels Henrik Abel

He is like the fox, who effaces his tracks in the sand with his tail.{Describing the writing style of famous mathematician Carl Friedrich Gauss}

By studying the masters and not their pupils.

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.

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.

He is like the fox, who effaces his tracks in the sand with his 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.

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils.

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.