On october 30, 1826, Niels Henrik Abel presented the Paris Academy of Sciences with a epoch-making work entitled Mémoire sur une propriété générale d’une classe très étendue de fonctions transcendantes. This memoir contains the extension of Euler’s addition theorem for elliptic integrals, to the case of integrals of functions R(x,y(x)), where R is a rational function of the variable x and of any algebraic fonction y(x). Abel enounced his theorem as follows:
Si l’on a plusieurs fonctions dont les dérivées peuvent être racines d’une même équation algébrique, dont tous les coefficients sont des fontions rationnelles d’une même variable, on peut toujour exprimer la somme d’un nombre quelconque de semblables fonctions par une fonction algébrique et logarithmique, pourvu qu’on établisse entre les variables des fonctions en question un certain nombre de relations algébriques.
(see: Oeuvres Complètes, I, p.146). Abel had arrived in Paris on July 10, and after a while he begun to working on what was to became his most famous memoir. “I showed it to Cauchy, but scarscely gave it a glance. And I dare say with all modesty, it is good. I am curios to hear Institute’s verdict” he wrote to his friend Holmboe. To return to Norway with his memoir having been praised by the Academy would be important for his career, so for the rest of his saty in Paris Abel was just waiting for an answer but, as long as he lived, he never got it. Legendre and Cauchy were designed referees for Abel’s paper. Legendre, that for forty years had worked on elliptic integrals, was certainly in a good position to appreciate Abel’s work but he was very old and left the manuscript to Cauchy. The latter was the leading active mathematician in Paris, but too busy with is own research to pay attention to that of others. Thus Abel’s manuscript remained forgotten somewhere at the Academy. Only after a formal request from the Norwegian Government to the French autorities, was Abel’s manuscript found among Cauchy’s documents and finally published in 1841: twelve years after Abel’s death.
Guglielmo Libri, professor of mathematics at both Collège de France and the Sorbonne had the responsability supervising the printing in Mémoires présentés par divers savants à l’Académie Royale des Sciences de l’Institut de France. But Abel’s manuscript disappeared again a short time after it was printed. While S. Lie e L. Sylow were preparing a new edition of Abel’s Collected Works, they attempted in vain to get the Parisian manuscript from the Academy, and in fact in the introduction they wrote:
Il nous a paru très désirable de pouvoir collationner le mémoire imprimé avec l’original, et M. Sophus Lie obtint en 1874 de l’Académie des Sciences de Paris la permission de consulter le manuscrit d’Abel; mais il fut constaté dans les archives de l’Academie que le manuscrit ne s’y est pas trouvé après l’impression du mémoire.
The search for the manuscript of the Parisian memoir continued. In 1942 Paul Heegaard from Oslo thought to have found the lost manuscript at the Biblioteca Nazionale of Rome, but a later expertise showed that it was only an old handwritten copy of the printed article. Finally on October 1952, Viggo Brun, Professor at the University of Oslo, found part of it in Florence. In one of his notes announcing his discovery we read:
En octobre 1952, au cours d’un voyage a Florence, j’ai demandé au Pr Sansone s’il existait quelques écrits manuscrits de Libri. Le Pr Sansone me signala un chapitre d’un livre publié par Giacomo Candido en 1942: Sulla mancata pubblicazione della celebre Memoria di Abel où il était mentionné qu’il existait à la bibliothèque Moreniana de Florence un manuscrit intitulé: A. Legendre - Nota autografa, ritrovata nel Fondo Palagi-Libri, attaccata alla copia, fatta dal Libri, della Memoria di Abel… Aussi, est-ce avec beaucoup d’émotion qu’aidé par M. Pr Procissi, j’ai ouvert le vieux manuscrit jauni de la bibliothèque Moreniana proche l’église de Lorenzo. [lettera]
What Brun found was not the complete manuscript but the first 16 pages and the last one numbered 61. A microfilm of this manuscript was sent to Oslo and an exper declared that it was written by Abel himself. [pag. 1] [pag 61]
Other pages (all except 8) of the manuscript were later found by A. Procissi, after a closer and patient scrutiny of all documents kept at the deposition Palagi-Libri. Unfortunately Procissi did not leave any reference to this second part of Abel’s original manuscript and I have rediscovered those pages only after another meticulous inspection like that made by Procissi. After examining the two parts I saw that the pages 21-24 and 31-34 were those still missing.
In 1959 the Moreniana Library of Florence enriched with a new deposition. This stock of letters, scientific manuscripts and other documents, was acquired by the Province of Florence from a Florentine antiques dealer. Only in 1983 was a first inventory given of the about twenty thousand sheets, for its content the new deposition was called Nuovo Fondo Libri. Among these papers, I discovered documents that convinced me it was material coming from Count Giacomo Manzoni’s archives, one of the three executors that Libri named in his testament.
In the Nuovo Fondo Libri I hoped to discover the still missing pages of Abel’s manuscript and after a patient scrutiny, sheet by sheet, of the content of several boxes constituting the Nuovo Fondo Libri, on July 6, 2000, I thought to have found all the missing pages. In fact I discovered 8 pages numbered 21-24 and 31-34 that, like a puzzle, fit in perfectly (and not only for numbering) with those already known of Abel’s manuscript. Unfortunately this was not the case and I realized it only in February 2002 when, by mere chance, I found another set of pages numbered 31-34 at the Labronica Library in Livorno [pag31]. These latter are undoubtedly due to Abel’s hand and were showed, together with Abel’s autograph preserved at the Moreniana, during the exibition held in Oslo on June 2002, in the occasion of Abel’s Bicentennial Conference. The manuscript has been completely reproduced in facsimile in a volume devote to it [2].
Comparing the two handwritten version of pages 31-34 and the corresponding pages of the printed article I noticed some differences that suggest that the copy was made by G. Libri befor the manuscript was sent to print. The reason Libri made copy of the 8 pages is not clear to me.
What about the still missing pages of Abel’s parisian manuscript? Once Libri wrote: “Cependant, lorsqu’il s’agit de manuscrits, on ne doit jamais déspérer de rien”, so the search will continue!
_____________
For details on the history of the Parisian memori, of other Abel’s manuscripts and other informations on their fate, see the following papers and the references therein:
1. A. Del Centina, The manuscript of Abel’s Parisian memoir found in its entirety, Hist. Math. 29 (2002) 65-69, Corrigenda, Hist. Math. 30 (2003) 94-95.
2. A. Del Centina, Abel’s manuscripts in the Libri collection: their history and their fate; in Il manoscritto parigino di Abel preservato nella Biblioteca Moreniana di Firenze/ Abel’s Parisian manuscript preserved in the Moreniana Library of Florence, A. Del Centina ed., L. S. Olschki, Firenze 2003, 87-103
3. A. Del Centina, La memoria parigina di Abel e la sua importanza per la geometria, Lettera matematica, 47 (2003) 45-55 (italian).
