This book is a biography of Gösta Mittag-Leffler comprising more than 750 pages. It was written by Arild Stubhaug, who is also the author of biographies of Niels Henrik Abel and Sophus Lie and originally published in Norwegian under the title “Med viten og vilje” (Aschehoug 2007); an English edition is in preparation with Springer-Verlag and due in 2009. Arild Stubhaug has a background both in mathematics and literature, making him ideally suited to embark on the monumental task of writing a biography of such a complex and at times controversial person as Gösta Mittag-Leffler.

The book starts in the middle of events, with a description of a visit to Egypt by Gösta Mittag-Leffler and his wife Signe. They were also accompanied by a personal physician. Mittag-Leffler was 53 years old and his wife was 38. The trip lasted from the end of 1899 until Easter 1900. The main reason for the trip was Mittag-Leffler’s health problems (in particular stomach problems). This is a recurring theme throughout the biography. The dry desert air seems to have had a beneficial influence.

As can be inferred from this short summary of the introductory chapter, the biography brings us very close to Mittag-Leffler and his daily life, routines and cares. The biography is based on the wealth of material that Mittag-Leffler left behind. Some documents are kept in the National Library of Sweden (Kungliga biblioteket), Stockholm, while other documents are at the Mittag-Leffler Institute in the suburb of Djursholm. The documents include diaries, letters, newspaper clippings, etc. Arild Stubhaug has carefully researched this wealth of material and distilled out of it a fascinating account of a complex personality.

Mittag-Leffler was born in 1846, the son of Johan Olof Leffler and Gustava Wilhelmina, née Mittag. He had one sister Anne Charlotte (born 1849) and two brothers Fritz (born 1847) and Arthur (born 1854). His father developed a mental disorder and was committed to care from 1870 until his death. This illness might be one of the reasons why Gösta Mittag-Leffler had no children. He was very close to his mother and wrote her many letters. From these letters (and the replies) Arild Stubhaug has gained access to some of his personal thoughts during formative periods of his life. This has given a view of him that would otherwise not be available.

Mittag-Leffler received his doctorate from Uppsala University in 1872. His thesis was on some results in complex analysis. One characteristic of this biography is that it does not provide any details on his mathematical achievements. As a mathematician one may regret this. However, it is not for his mathematical achievements that he deserves a well researched biography.

Probably one of the most important events in his life was the award of a travel grant (Bysantinska resestipendiet) in 1873, allowing him to visit mathematicians in Paris and Berlin. In Paris he visited Hermite and also became acquainted with other French mathematicians. These contacts were to play an important role in his career, for example leading to a close acquaintance with Hermite’s student Poincaré. After a semester in Paris he moved to Berlin and met Weierstrass. This connection was to determine the direction of many of his activities in the future. In particular, he heard about Sonja Kovalevsky for the first time.

Mittag-Leffler was called to a professorship at the newly established Stockholms Högskola (later Stockholm University) in 1881 and from that time his base was Stockholm. However he kept up contacts with a large number of European mathematicians during the rest of his career. He often travelled and reports on his travels take up a large part of the biography. See the accompanying translation of a selected chapter in this newsletter issue.

Many of the high points of his career after returning to Stockholm are probably known to many mathematicians. He managed to get Sonja Kovalevsky appointed to a professorship at Stockholms Högskola, he founded the journal Acta Mathematica, and he educated and promoted a number of brilliant Swedish mathematicians, including I. Fredholm. All this, and much more, is meticulously related. Many details are added that most of us probably never knew. For example that the economy of Acta Mathematica was precarious for many years and that Mittag-Leffler paid part of the expenses from his own funds.

Apart from mathematics Mittag-Leffler also had a career as a business man. He invested in many businesses and made and lost money. This is a fascinating part of his life that is exposed in detail for the first time. Again the wealth of written material makes this possible.

At some points in his career he was very wealthy. Towards the end of his life he had very little left. In 1916 on his 70th birthday he and his wife Signe announced in a testament the formation of Makarna Mittag-Lefflers Matematiska Stiftelse under the Royal Academy. The purpose was the formation of a mathematical research institute . The donation included his library and his villa in Djursholm. Extracts of the testament were published in Acta Mathematica.

Downturns in his financial situation and other events meant that the vision was not realized for many years. It is fortunate that the donation in 1916 of the library and the villa put those out of reach of his creditors. It was only in the late 1960s that Lennart Carleson managed to secure funding for turning the villa in Djursholm into a world class mathematical research institute.

The impression one gets after reading this comprehensive account is of a very complex personality. So many facets are revealed that it is clear he must have been at times both very charming and able to get close to people of very different personalities, for example Hermite, Painlevé and Weierstrass, and at other times not a person one would like to go up against.

I will not say anything about Gösta Mittag-Leffler and Alfred Nobel. To find out about this you will have to read the book. The account given changed the picture I had of the two and their relations.

The reader is also rewarded with a lively picture of the life and social activities of the upper segment of Swedish society during that period. It is important to see the mathematics and the mathematicians in their contemporary context.

I enjoyed reading this book very much and hope you will do the same.

Arne Jensen [matarne@math.aau.dk] got his PhD from the University of Aarhus in 1979. He has been a professor of mathematics at Aalborg University since 1988. He served as acting director of the Mittag-Leffler Institute from 1993 to the beginning of 1995. In 2000-01 he was a visiting professor at the University of Tokyo. His research interests are spectral and scattering theory for Schrödinger operators.