# Handwritten manuscripts by Niels Henrik Abel

In 2007 the handwritten manuscripts were acquired from Institut Mittag-Leffler and Kungliga Svenska Vetenskapsakademien in Sweden by the Norwegian company Scatec by its owner Alf Bjørseth, who donated the manuscripts to Det Norske Videnskaps-Akademiet. The originals are kept at Nasjonalbiblioteket.

## The history of the three manuscripts

by Arild Stubhaug

Almost all the mathematics that Abel managed to write in his brief life was published in Berlin, in *Journal für die reine und angewandte Mathematik* (also called Crelle's journal, see the biography). The fate of all Abel's original manuscripts after they had been printed appears random; at any rate they were never returned to their author.

It is likely that the journal editor, A. L. Crelle, retained the manuscript. We know that Crelle gave away or sold some of Abel's manuscripts to the Italian mathematician and manuscript collector G. Libri. He operated in Paris or London, selling old books, letters and manuscripts on a large scale. In his old age Libri returned to his native Florence, but never got around to organising his extensive collection of manuscripts. After his death much of the material was scattered to the four winds, some was even used as wrapping paper. A portion ended up in the possession of the bibliophile count G. Manzoni, who in turn sold parts of his collection to Prince B. Boncompagni, one of the greatest manuscript collectors of the age, and one with a particular interest in mathematics. Bonconpagni put his collections up for sale in 1898, and the Swedish mathematician Gösta Mittag-Leffler bought that part of the collection that included offprints and manuscripts with a mathematical content from the Middle Ages to the modern age. In addition to what was listed in Boncompagni's extensive sales catalogues, Mittag-Leffler bought three Abel manuscripts.^{1}

Two of these manuscripts contained mathematical material that had previously been printed in Crelle's journal in Berlin; in addition one contained letters to editor Crelle in which Abel told him about his illness and explained why he had to lay aside parts of his pioneering mathematical work. The third Abel manuscript that Mittag-Leffler acquired, however, was a hitherto unknown mathematical dissertation. This was now printed in the journal Acta Mathematica, which was in honour of the centenary of Abel's birth in 1902, in three volumes totalling almost 1,200 pages, devoted to Abel and his mathematics.

The publication of this unknown work provoked much attention. This was first and foremost because it was discovered that previous editions of Abel's collected works were not complete. Elaborate collector's editions had been published twice before, in 1839 and 1881: the first, edited by Bernt Michael Holmboe (Abel's teacher), the other more complete and with a commentary by the mathematicians Sophus Lie and Ludvig Sylow. Both editions had been financed by the public purse and were perceived as a kind of homage to the country's most famous scientist. Ludvig Sylow, who had put a lot of work into the editing of the 1881 edition, now dealt with the new Abel material as well. At the third Scandinavian mathematical congress, held in Kristiania (now Oslo) in 1913, Sylow commented on the material.

After publication in 1902 Mittag-Leffler put the Abel manuscripts back in his strongbox at his villa on Djursholm outside Stockholm, and here they lay for a hundred years. The villa, with its great mathematical library, was donated to the Royal Swedish Academy of Sciences in 1916 and became the Mittag-Leffler Institute, currently one of the world's leading mathematical research centres. When, in 2001, I started work on a biography of Mittag-Leffler and spent some time at the Djursholm institute, I noticed these manuscripts; and after the Abel Prize was created and first awarded in 2003 by the Norwegian Academy of Science and Letters in Oslo, I suggested to the general secretary of the Academy, Reidun Sirevåg, that Oslo would be a suitable storage site for these manuscripts – the place where, thanks to the awarding of the prize, Abel's name at least once a year comes under the scrutiny of the entire mathematical world. Another argument was that none of Abel's original manuscripts was to be found in Norway; only sketches, notebooks and letters in the National Library of Norway's Manuscript Collection.

General secretary Sirevåg took the idea to the Academy's president, Ole Didrik Lærum, who opened negotiations with Director Anders Björner of the Mittag-Leffler Institute. The Norwegian Embassy in Stockholm also participated in the subsequent discussions on takeover and purchase of the manuscripts, in the persons of Ambassador Odd Fosseidbråten and cultural attaché Bjørn Berge. The fly in the soup of the plans was the financing of any purchase.

There was universal rejoicing when in the summer of 2007 Lærum could announce that in Scatec and Alf Bjørseth they had found a private donor who would finance the purchase. A bill of sale between the Norwegian Academy of Science and Letters on the one side and the Mittag-Leffler Institute and the Royal Swedish Academy of Sciences on the other was signed on 31 October 2007, and on 6 December the manuscripts arrived by courier from Djursholm and were installed in the National Library of Norway in Oslo. During a solemn ceremony in the presence of Minister of Research and Higher Education Tora Aasland and a number of luminaries of the library and scientific communities, Alf Bjørseth donated the manuscripts to the Norwegian Academy of Science and Letters as a gift for its 150th anniversary. The manuscripts were received by National Librarian of Norway Vigdis Moe Skarstein, and will be entrusted for the foreseeable future to the National Library of Norway's Manuscript Collection.

#### The three manuscripts are as follows:

1. *Recherches sur les fonctions elliptiques (continuation)*. (8:o) 37 numbered pages, undated. This is the last portion of the Recherches, Abel's most extensive dissertation, printed for the first time in the second and third volumes of Crelle's journal, September 1827 and May 1828. The dissertation is included in both editions of Abel's collected works.

2. *Note sur quelques formules elliptiques, plus letters*. (4:o) 8 numbered pages, dated 25/9 1828 by Abel on page 7. Page 8 contains a letter from Abel to Crelle. The dissertation was printed for the first time in Crelle's journal in 1829, and is included in both editions of Abel's collected works.

*Recherches sur les fonctions elliptiques (Second Mémoire)*. (8:o). 28 numbered pages, dated August 27, 1828 by Abel. This manuscript was printed for the first time in Acta Mathematica in 1902. The paper was discussed by Sylow in *On Abel's works and plans in his last years, illustrated by documents that came to light after the second edition of his works*, reprint of the proceedings of the third Scandinavian congress of mathematicians, Kristiania [Oslo] 1913.

^{1} It later turned out that Abel's large Parisian memoir (see the biography) had been in some of the same collections, but was never offered for sale. The Parisian manuscript eventually landed in the Moreniana Library of Florence, where in 1952 it was rediscovered by the Norwegian mathematician Viggo Brun. Today the memoir is regarded as a treasure in the collections of the venerable library.