Quotes by Niels Henrik Abel - Page 1

By studying the masters and not their pupils.
Niels Henrik Abel / Mathematician
Science
Abel
Math
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He is like the fox, who effaces his tracks in the sand with his tail.
Niels Henrik Abel / Mathematician
Math
Tails
Track
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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 / Mathematician
Progress
Study
Want
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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 / Mathematician
Science
Devil
Divergent
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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 / Mathematician
Effort
Light
People
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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 / Mathematician
Doe
Foundation
Important
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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 / Mathematician
Science
Peculiar
Special
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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 / Mathematician
Abel
Giving
Thinking
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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 / Mathematician
Gaps
Purpose
Theory
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Niels Henrik Abel Quotes - Page 1

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