# Book:Article/Niels Henrik Abel/Mémoire sur une Propriété Générale d'une Classe Très-Étendue de Fonctions Transcendantes

## Journal Article

**$\text {1841}$: Mémoire sur une Propriété Générale d'une Classe Très-Étendue de Fonctions Transcendantes**

## Description

This contains the discovery about integrals of functions now known as Abel's Theorem.

It is the foundation for the later theory of Abelian integrals, Abelian functions and much of algebraic geometry.

## Historical Note

Niels Henrik Abel completed his paper *Mémoire sur une Propriété Générale d'une Classe Très-Étendue de Fonctions Transcendantes* soon after arriving in Paris in $1826$(?).

It was submitted to the French Academy, but was mislaid (possibly by Augustin Louis Cauchy).

Abel ran out of funds while waiting to hear about it, and had to return to Berlin, and then home, deep in debt.

The manuscript was found again in $1830$, after Abel had died, but was still not published until $1841$.

Then the manuscript was once again lost, and not found again till it reappeared in Florence in $1952$.

## Critical View

*Abel has left mathematicians enough to keep them busy for $500$ years.*