Until now the theory of infinite series in general has been very badly grounded. One applies all the operations to infinite series as if they were fi…

- Niels Henrik Abel

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 …

- Niels Henrik Abel

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

- Niels Henrik Abel

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 re…

- 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 …

- Niels Henrik Abel

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

- Niels Henrik Abel

By studying the masters and not their pupils.

- Niels Henrik Abel

The mathematicians have been very much absorbed with finding the general solution of algebraic equations, and several of them have tried to prove the…

- Niels Henrik Abel

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 rigorousl…

- Niels Henrik Abel