The second of these explanations dose seem the more likely, especialy since Gaus had written in his thesis of 1801 that the algebraic solution of an equation was no better than devising a symbol for the root of the equation and then saying that equation had a root equal to the symbol.
Crelle was detained in Berlin nd could not travel with Abel to Paris. Abel therefore did not go directly to Paris, but chose to travel again with his Norwegian friends to northem Italy before crossing the Alps to France. In Paris Abel was disappointed to find there was little interest in his work. He wrote back to Holmboe:-
…The Frence are much more reserved with strangers than the Germans. It is extremely difficult to gain their intimacy, and I do not dare to urge my pretensions as that; finally every beginner had a great deal of difficultty getting noticed here. I have just finished an extensive treatise on a certain class of transcendental functions to present it to the Institute which will be done next Monday. I showed it to Mr Cauchy, but he scarcely designed to glance at it.
The contents and importance of this treatise by Abel is described in :-
It dealt with the sum of intergrals of a given algebraic function. Abel’s theorem states that any such sum can be expressed as a fixed number p of these integrals, with intergration arguments that are algebraic functions of the original arguments. The minimal number p is the genus of the algebraic function, and this is the first occurrence of this fundamental quantity. Abel’s theorem is a vast generalisation of Euler’s relation for elliptic integrals.
Two refferees, Cauchy and Legendre, were appointed to referee the paper and Abel remained in Paris for a few months:-
…emaciated, gloomy, weary and constantly worried. He …..could only afford to eat one meal a day
He published some articles, mainly on the results he had already written for Crelle’s Journal, then with no money left and his health in a very poor state, he returned to Berlin at the end of 1826. In Berlin, Abel borrowed some money and continued working on elliptic functions. He wrote a paper in which:-
…he radically transformed the theory of elliptic integrals to the theory of elliptic functions by using their inverse functions…
Crelle tried to persuade Abel to remain in Berlin until be could find an academic post for him and he even offered Abel the editorship of Crelle’s Journal. Howver, Abel wanted to get home and by this time he was heavily in debt. He reached Christainia in May 1827 and was awarded a small amount of money by the university although they made sure they had the right to deduct a corrresponding amount from any future salary he earned. To make a little more money Abel tutored schoolchildren and his fiancee was employed as a goveness to friends of Abel’s family in Froland.
Hansteen received a major grant to investigate the Earth’s magnetic field in Siberia and replacement was needed to teach for him at the University and also at the Military Academy. Abel was appointed to this post which improved his position a little.
In 1828 Abel was shown a paper by Jacobi on transformations of elliptic integrals. Abel quickly showedthat Jacobi’s results were consequences of his own and added a note to this effect to the second part of his major work on elliptic functions. He had been working again on the algebraic solution of equations, with the aim of solving the problem of which equations were soluble by radicals (the problem which Galois soved a few years later). He put this to one side to compete with Jacobi in the theory of elliptic functions, quickly writing serveral papers on the topic.
Legendre saw the new ideas in the papers which Abel and Jacobi were writing and said :-
Through these works you two will be placed in the class of the foremost analysis of our times.
Abel continued to pour out high quality mathematics as his health continued to deteriorate. He spent the summer vacation of 1828 with his fiancee in Froland. The masterpiece which he had submitted to the Paris Academy seemed to have been lost and so wrote the main result down gain:-
The paper was only two brief pages, but of all his many works perhaps the most poignant. He called it only “A theorem” : it had no introduction, contained no superfluous remarks, no applications. It was a monument resplendent, in its simple lines- the main theorem from his Pris memoir, formulated in few words.
The second of these explanations dose seem the more likely, especialy since Gaus had written in his thesis of 1801 that the algebraic solution of an equation was no better than devising a symbol for the root of the equation and then saying that equation had a root equal to the symbol.
Crelle was detained in Berlin nd could not travel with Abel to Paris. Abel therefore did not go directly to Paris, but chose to travel again with his Norwegian friends to northem Italy before crossing the Alps to France. In Paris Abel was disappointed to find there was little interest in his work. He wrote back to Holmboe:-
…The Frence are much more reserved with strangers than the Germans. It is extremely difficult to gain their intimacy, and I do not dare to urge my pretensions as that; finally every beginner had a great deal of difficultty getting noticed here. I have just finished an extensive treatise on a certain class of transcendental functions to present it to the Institute which will be done next Monday. I showed it to Mr Cauchy, but he scarcely designed to glance at it.
The contents and importance of this treatise by Abel is described in :-
It dealt with the sum of intergrals of a given algebraic function. Abel’s theorem states that any such sum can be expressed as a fixed number p of these integrals, with intergration arguments that are algebraic functions of the original arguments. The minimal number p is the genus of the algebraic function, and this is the first occurrence of this fundamental quantity. Abel’s theorem is a vast generalisation of Euler’s relation for elliptic integrals.
Two refferees, Cauchy and Legendre, were appointed to referee the paper and Abel remained in Paris for a few months:-
…emaciated, gloomy, weary and constantly worried. He …..could only afford to eat one meal a day
He published some articles, mainly on the results he had already written for Crelle’s Journal, then with no money left and his health in a very poor state, he returned to Berlin at the end of 1826. In Berlin, Abel borrowed some money and continued working on elliptic functions. He wrote a paper in which:-
…he radically transformed the theory of elliptic integrals to the theory of elliptic functions by using their inverse functions…
Crelle tried to persuade Abel to remain in Berlin until be could find an academic post for him and he even offered Abel the editorship of Crelle’s Journal. Howver, Abel wanted to get home and by this time he was heavily in debt. He reached Christainia in May 1827 and was awarded a small amount of money by the university although they made sure they had the right to deduct a corrresponding amount from any future salary he earned. To make a little more money Abel tutored schoolchildren and his fiancee was employed as a goveness to friends of Abel’s family in Froland.
Hansteen received a major grant to investigate the Earth’s magnetic field in Siberia and replacement was needed to teach for him at the University and also at the Military Academy. Abel was appointed to this post which improved his position a little.
In 1828 Abel was shown a paper by Jacobi on transformations of elliptic integrals. Abel quickly showedthat Jacobi’s results were consequences of his own and added a note to this effect to the second part of his major work on elliptic functions. He had been working again on the algebraic solution of equations, with the aim of solving the problem of which equations were soluble by radicals (the problem which Galois soved a few years later). He put this to one side to compete with Jacobi in the theory of elliptic functions, quickly writing serveral papers on the topic.
Legendre saw the new ideas in the papers which Abel and Jacobi were writing and said :-
Through these works you two will be placed in the class of the foremost analysis of our times.
Abel continued to pour out high quality mathematics as his health continued to deteriorate. He spent the summer vacation of 1828 with his fiancee in Froland. The masterpiece which he had submitted to the Paris Academy seemed to have been lost and so wrote the main result down gain:-
The paper was only two brief pages, but of all his many works perhaps the most poignant. He called it only “A theorem” : it had no introduction, contained no superfluous remarks, no applications. It was a monument resplendent, in its simple lines- the main theorem from his Pris memoir, formulated in few words.
การแปล กรุณารอสักครู่..
![](//thimg.ilovetranslation.com/pic/loading_3.gif?v=b9814dd30c1d7c59_8619)