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Niels Henrik Abel Quotes

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

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
Niels Henrik Abel, Philip Horowitz (2007). “Abel on analysis: papers of N.H. Abel on Abelian and elliptic functions and the theory of series”

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

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, Divergent

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

Niels Henrik Abel
Math, Track, Tails

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
Science, Special, Peculiar
Letter to Professor Christoffer Hansteen (1826) "Oeuvres Complètes de N. H. Abel", mathematician, Nouvelle edition (1881) ed., Peter Ludwig Mejdell Sylow & Sophus Lie, Vol. 2, pp. 263-265, as quoted by Øystein Ore, "Niels Henrik Abel: Mathematician Extraordinary", p. 113, 1957.

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, Gaps, Theory
"A Source Book in Mathematics". Book edited by David Eugene Smith, "A Memoir on Algebraic Equations, Proving the Impossibility of a Solution of the General Equation of the Fifth Degree" (1824), 1929.

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, Foundation, Doe

By studying the masters and not their pupils.

Niels Henrik Abel
Math, Science, Abel
Niels Henrik Abel, Olav Arnfinn Laudal, Ragni Piene (2004). “The Legacy of Niels Henrik Abel: The Abel Bicentennial, Oslo, June 3-8, 2002”, p.353, Springer Science & Business Media

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, Abel

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