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Niels Henrik Abel: Norwegian Mathematical Genius

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Niels Henrik Abel (August 5, 1802–April 6, 1829)

The Biography of Niels Henrik Abel: His last years

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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 (August 5, 1802–April 6, 1829)

The paper was originally published in French, as a pamphlet, in Oslo. Translation by W. The insights from this paper led to the modern theory of equations.

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. From letter to his professor Christoffer Hansteen in Oeuvres , 2, Until now the theory of infinite series in general has been very badly grounded.

The Biography of Niels Henrik Abel: His last years

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. As quoted and translated in Reinhold Remmert and Robert B. Je crois que non.

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. No mathematician should ever allow him to forget that mathematics, more than any other art or science, is a young man's game.

His friends urged the Norwegian government to grant him a fellowship for study in Germany and France. In , while waiting for a royal decree to be issued, he published at his own expense his proof of the impossibility of solving algebraically the general equation of the fifth degree, which he hoped would bring him recognition.

He sent the pamphlet to Gauss , who dismissed it, failing to recognize that the famous problem had indeed been settled. Abel spent the winter of —26 with Norwegian friends in Berlin, where he met August Leopold Crelle , civil engineer and self-taught enthusiast of mathematics, who became his close friend and mentor. The first volume contains papers by Abel, including a more elaborate version of his work on the quintic equation.

Other papers dealt with equation theory, calculus, and theoretical mechanics. In Abel went to Paris, then the world centre for mathematics, where he called on the foremost mathematicians and completed a major paper on the theory of integrals of algebraic functions. Abel returned to Norway heavily in debt and suffering from tuberculosis. He subsisted by tutoring, supplemented by a small grant from the University of Christiania and, beginning in , by a temporary teaching position. His poverty and ill health did not decrease his production; he wrote a great number of papers during this period, principally on equation theory and elliptic functions.

Risum teneatis amici. However, if I am not mistaken, they have not as yet succeeded.

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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. We can continue in this way until we reach rational functions of a, b, c, d, and e.

Niels Henrik Abel was a Norwegian mathematician who made pioneering contributions in a variety of fields. His most famous single result is the first complete. Niels Henrik Abel, (born August 5, , island of Finnøy, near Stavanger, Norway—died April 6, , Froland), Norwegian mathematician, a pioneer in the development of several branches of modern mathematics. Abel’s father was a poor Lutheran minister who moved his family to the.

Now the first member has different values, while the second member has only 10; hence y can not have the form that we have found: but we have proved that y must necessarily have this form, if the proposed equation can be solved: hence we conclude that It is impossible to solve the general equation of the fifth degree in terms of radicals. It follows immediately from this theorem, that it is also impossible to solve the general equations of degrees higher than the fifth, in terms of radicals.

Everybody works for himself without concern for others. All want to instruct, and nobody wants to learn.

The most absolute egotism reigns everywhere. The only thing the French look for in strangers is the practical; no one can think except himself, he is the only one who can produce anything theoretical. This is the way he thinks and so you can understand it is really difficult to be noticed, particularly for a beginner.