Niels Abel writes to August Crelle

The following letter, which was handwritten in German, was written by Niels Abel and sent to August Crelle about six months before Abel's death:


Christiania, 25 September 1828.
I received your kind letter dated 10 September some days ago and I thank you greatly for it. It made me extra glad since I had not expected such a quick answer. I would have written to you sooner, but I wanted to take the opportunity to also send you a short manuscript.

It pleases me greatly, of course, that the hope of an appointment in Berlin is good and I thank you in advance for your efforts. But I implore you, let me know as soon as possible when anything has been decided, be it favorable or not, for if it does not work out as I hope I must be prepared to improve on my conditions here. I can take no steps until I know what will happen. This request you will certainly grant me.

Thank you very much for taking the trouble to copy and send me excerpts from the letters you received from Jacobi and Legendre. You can just imagine with what pleasure I have read these. Indeed, Herr Jacobi says too much. I see from his remarks that he has arrived at the transformation theory for elliptic functions by taking a different path than I did, but if he has throughout found something general then I can not comprehend how he has arrived at this, and I am very curious to learn about his method. Please encourage him to reveal something, for it is clear that he is in possession of excellent things.

If you do not mind I would appreciate if you would publish in the journal the remarks on elliptic functions that are enclosed. Perhaps you have a few pages to spare in the upcoming fourth issue. It pleases me greatly that you will print my "Précis d'une théorie des fonctions elliptiques". I shall exert myself to make it as clear and good as possible, and hope I shall succeed. But do you not think that it would be better to commence with this paper instead of the one on the equations? I ask you urgently.

Firstly, I believe that the elliptic functions will be of greater interest; secondly, my health will hardly permit me to occupy myself with the equations for a while. I have been ill for a considerable period of time, and compelled to stay in bed. Even if I am now recovered, the physician has warned me that any strong exertion can be very harmful.

Now the situation is this: the equations will require a disproportionately greater effort on my part than the elliptic functions. Therefore, I should prefer, if you do not absolutely insist on the article on equations - in that case you shall have it - to begin with the elliptic functions. The equations will follow soon afterward. If you have nothing against it, I would prefer to divide it into short sections, so that something about elliptic functions and something about equations could appear in each issue; for the first issue I should like to send only elliptic functions.

Please let me hear your opinion on this.

Yours sincerely,
N Abel


JOC/EFR April 2016

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