Niels Henrik Abel famous quotes

Last updated: Sep 5, 2024

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 finite; but is that permissible? I think not. Where is it demonstrated that one obtains the differential of an infinite series by taking the differential of each term? Nothing is easier than to give instances where this is not so.
-- Niels Henrik Abel

#Thinking #Giving #Infinite
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

#Purpose #Dare #Mathematician
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

#Important #Doe #Foundation
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

#Progress #Want #Study
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

#Special #Analysis #Way
By studying the masters and not their pupils.
-- Niels Henrik Abel

#Study #Masters #Pupils
He is like the fox, who effaces his tracks in the sand with his tail.
-- Niels Henrik Abel

#Track #Tails #Foxes
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

#Science #Devil #May
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

#Light #People #Effort

Promise me you'll always remember: You're braver than you believe, and stronger than you seem, and smarter than you think.
Think it over, think it under.
Well," said Pooh, "what I like best," and then he had to stop and think. Because although Eating Honey was a very good thing to do, there was a moment just before you began to eat it which was better than when you were, but he didn't know what it was called.
My goal has been to encourage jointness, to push people to think of affiliations rather than to operate as solo entrepreneurs.
I think I feel rather differently about sympathy to what seems the normal view. I like just to feel it is there, but not always expressed.
If a boxer ever went as crazy as Nijinsky all the wowsers in the world would be screaming 'punch-drunk.' Well, who hit Nijinsky? And why isn't there a campaign against ballet? It gives girls thick legs
Well, fancy giving money to the Government! Might as well have put it down the drain.
In a word, they failed to take into account man's almost infinite appetite for distractions.
Dieu est le point tangent de zeÂ ro et de l'infini. God is the tangential point of zero and the infinite.
Ritual is the passage way of the soul into the Infinite.

Niels Henrik Abel famous quotes

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