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Niels Henrik Abel

Niels Henrik Abel Books

Mathematician

Niels Henrik Abel was a Norwegian mathematician who made significant contributions to the field of mathematics, particularly in elliptic functions and integral equations. His work had a profound impact on later mathematicians, especially his proof that algebraic equations cannot be solved by radicals, known as the Abel-Ruffini theorem.

Abel on analysis: papers of N.H. Abel o...

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The Legacy of Niels Henrik Abel: The Ab...

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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.”

People Stills Light Today Effort Plans Logic Certainty Uncertainty Analysis Reasoning Immense Reign Obscurity Ontology Rigor

Author: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 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.”

Ifs Has Beens Purpose Theory Prove Findings Solutions Dare Memoir Gaps Mathematician Mistaken Equations Impossibility Good Will

Author:Niels Henrik Abel

“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.”

Ifs Thinking Giving Has Beens Term Theory Easier Infinite Series Instance Operations Grounded Finite Abel

Author: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 rigorously determined. In other words, the things which are the most important in mathematics are also those which have the least foundation.”

Doe Has Beens Important Infinite Mathematics Foundation Series Determined Exception

Author: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.”

Ifs Want Should Study Progress Masters Mathematics Pupils

Book:Abel on analysis: papers of N.H. Abel on Abelian and elliptic functions and the theory of series

Source: Abel on analysis: papers of N.H. Abel on Abelian and elliptic functions and the theory of series

“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.”

Way Has Beens Science Special Logic Miserable Analysis Paradox Peculiar Procedures Theorems Abel Concluding

Author:Niels Henrik Abel

“By studying the masters and not their pupils.”

Science Study Masters Mathematics Math Mathematical Pupils Abel

Book:The Legacy of Niels Henrik Abel: The Abel Bicentennial, Oslo, June 3-8, 2002

Source: The Legacy of Niels Henrik Abel: The Abel Bicentennial, Oslo, June 3-8, 2002

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

Mathematics Track Math Mathematical Sand Tails Foxes Abel

Author: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 conclusion he pleases and that is why these series have produced so many fallacies and so many paradoxes.”

May Science Please Draws Devil Shame Series Invention Conclusion Paradox Demonstration Fallacy Divergent Divergent Series Abel

Author:Niels Henrik Abel

About the Author

Born: August 5, 1802
Died: April 6, 1829
Known for: Mathematician
Quotes: 9

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Abel Has Beens Mathematics Ifs Science Series Analysis Infinite Logic Masters

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Books & Sources

Abel on analysis: papers of N.H. Abel on Abelian and elliptic functions and the theory of seriesRelated source material

The Legacy of Niels Henrik Abel: The Abel Bicentennial, Oslo, June 3-8, 2002Related source material

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