# Reviews of *Gösta Mittag-Leffler. A Man of Conviction*

We give two reviews of Arild Stubhaug's wonderful book

*Gösta Mittag-Leffler. A Man of Conviction*. The first is a review by Sigurdur Helgason that appears in the*Notices of the American Mathematical Society***60**(8) (2013), 1054-1055. The second is a review by Peter Giblin that is published in The Mathematical Gazette 96 (536) (2012), 368-370.**1. Sigurdur Helgason's review**

The author of this book, Arild Stubhaug, is well known among mathematicians for his superb biographies of Abel and Lie. Being a cand. mag. in mathematics as well as in literature, he was in fact singularly qualified for such undertakings. He managed to convey the flavour of the mathematics involved without discouraging the nonmathematician reader.

It is therefore a matter of great interest that Stubhaug has undertaken the job of writing a biography of Mittag-Leffler. While Mittag-Leffler does not compare to Abel and Lie in mathematical output or creativity, the mathematician G H Hardy in 1927 maintained that no one had done more for mathematics during the preceding fifty years. And in fact many consider Mittag-Leffler to be the father of mathematics in Sweden. Most mathematicians know his name from the Mittag-Leffler theorem in complex analysis. It is a counterpart to Weierstrass's theorem about constructing a holomorphic function with prescribed zeros; in Mittag-Leffler's theorem the poles and the singular part at each end pole are prescribed.

Stubhaug's book traces Gösta Mittag-Leffler's life from childhood on. However, the first chapter starts with a kind of an appetiser, "Journey at the Turn of the Century", which describes a trip Mittag-Leffler took to Egypt with his wife, Signe, accompanied by his personal physician. This is one example of many extensive trips he took during his life for health reasons. In fact, he suffered from serious health problems throughout his life. As a child he suffered from serious pneumonia of a kind where the survival prospects were 0.1 percent. He credited his mother's care for his survival and kept very warm contact with her all her life. He added her name, Mittag, to his father's name, Leffler.

After his professorship in Helsingfors, 1877-1881, Mittag-Leffler accepted a professorship at Stockholm's Högskola. His principal activities can be divided into four parts: (i) reforming Stockholm's Högskola toward a more research-oriented program in mathematics; (ii) founding in 1882 and developing the journal Acta Mathematica, which even today is a highly respected mathematical journal; (iii) investing in highly varied enterprises, carbide factories, railroads, waterfalls for hydroelectric production, etc.; and (iv) founding the Mathematical Institute in Djursholm in 1916 jointly with his wife: "The married couple Signe and Mittag-Leffler".

At the time of the founding of the institute their fortune was estimated at four million krona, down from seven million two years earlier. This would decline even further after the First World War. Toward the end of his life he had little left, partly because Signe's inheritance (she died six years before him) had been in large part diverted elsewhere due to another inheritor whom Mittag-Leffler called "The Witch [Hexan] W". After his death the institute was rather dormant except for the continued publication of

*Acta Mathematica*. However, around 1970 Lennart Carleson managed to obtain funding whereby the institute could function in the way Mittag-Leffler had planned, and Carleson served for sixteen years as the scientific director.

Activities (ii) and (iii) were connected with very extensive travels all over Europe (and Egypt and Algeria). Many of these trips were taken for reasons of health and necessitated the company of a doctor.

Clearly Mittag-Leffler expected his biography would be written after his death. He always kept a diary, finally totalling ninety-three volumes. He wrote about 20,000 letters to about three thousand correspondents, collected hundreds of articles and drafts thereof, as well as records of business dealings. Every item involved was kept. The "Nachlass" filled about seventy-five shelf-meters. At the Mittag-Leffler Institute one can find series of leather-bound volumes filled with nothing but visiting cards. The list of his

*Vitenskapelige Utmerkelser*(honorary degrees and memberships in scientific academies) fills two pages.

After defending his doctoral thesis in Uppsala in 1872 he got a stipend to travel to Berlin and Paris for two to three years. He started in Paris and dutifully attended Hermite's lectures. These turned out to be a real challenge to Mittag-Leffler's familiarity with French, because Hermite had difficulty walking so he did not use a blackboard. He just stood at the lectern and read the lectures from his manuscripts, most of which consisted of formulas for elliptic functions. He lectured 9:00-10:00 p.m. on Christmas Eve and continued Christmas Day at the same time. But Mittag-Leffler was clearly a dashing, charming fellow, and Hermite took a great liking to him, inviting him to dinner

*en famille*with his two unmarried daughters present. But he advised Mittag-Leffler to go to Berlin and learn from Weierstrass ("he is the master of us all"). In Berlin Mittag-Leffler had a very productive time and established contact with members of the brilliant Berlin school, particularly Weierstrass. While Weierstrass would have liked to keep him in Berlin, Mittag-Leffler instead applied successfully for a professorship in Helsingfors. From Weierstrass he had heard about his brilliant student, Sofia Kovalevskaya. Shortly before taking the position at Helsingfors, Mittag-Leffler met her on a trip to St. Petersburg. To his mother he wrote: "Som quinna är hun forjusande. . . .Denne dag er en af de márkligsta i mitt liv. (As a woman she is enchanting. ...This day is one of the most remarkable of my life.)" Through Mittag-Leffler's efforts Sofia was appointed professor at Stockholm's Högskola, and he did his best to make a pleasant life for her. This was often a difficult task.

Another woman scientist receiving significant support from Mittag-Leffler was Marie Curie. As a member of the Royal Swedish Academy he knew that Pierre Curie was a likely candidate for the Nobel Prize and was aware that her name had not been mentioned. Mittag-Leffler then wrote to Pierre Curie and asked whether she was not a fully worthy partner in his work. Curie answered quite positively that if such a prize was contemplated she would be equally deserving. So they did indeed share the Nobel Prize in physics in 1903. A couple of years later Pierre Curie died in a traffic accident, and in 1911 the chemistry prize was accorded to Marie Curie. At that time the Nobel committee was unaware of the scandal circulating in Paris concerning Marie Curie and Paul Langevin. Arrhenius, another member of the Swedish Academy, then wrote to Marie Curie expressing his opinion that it would be best if she did not come to Stockholm to receive the prize. Mittag-Leffler took quick action and in several telegrams to Langevin insisted that she should come to Stockholm. She followed his advice with deep gratitude. Thus Mittag-Leffler has the honour of arranging the first female professorship in mathematics and the first Nobel Prize to a female.

Stubhaug's description of these scientific political matters makes for fascinating reading. One also gets a clear image of Mittag-Leffler's business and investment affairs, which during some difficult times caused him much grief and criticism. A marital crisis around 1897 caused by jealousies is described with great tact and sensitivity. While reading this book three times I often felt that I was back in Djursholm wandering through the institute or along the paths near the seashore. The book is thoroughly captivating.

While Mittag-Leffler might have thought that his diaries could make an account of his life easy for a biographer, it took almost a century until Stubhaug had the courage to tackle this enormous challenge with reasonable completeness. The result is a fascinating account of Mittag-Leffler's life which at the same time gives a vivid picture of the European mathematical milieu and activities during the period 1887-1920.

**2. Peter Giblin's review**

Arild Stubhaug has written biographies of the two Norwegian mathematicians Niels Henrik Abel (1802-1829) and Sophus Lie (1842-1899). Why should Gazette readers be interested in a biography of the much less well-known Swedish analyst G Mittag-Leffler (1846-1927)? His most famous theorem, which bears his name, asserts, in rough terms, that a meromorphic function of one complex variable exists with any closed discrete (possibly infinite) set of prescribed poles. In various forms it dates from 1876 to 1884 and belongs to the Weierstrass school of complex function theory; indeed Mittag-Leffler was a student and friend of Weierstrass until the latter's death in 1897. The theorem had about it an air of controversy since it touched on the somewhat scandalous ideas of Cantor on the theory of infinite sets. G H Hardy, in his 1928 obituary, declared Mittag-Leffler to be a mathematician of the first rank. He was the founder in 1882, and for many years after that a financial sponsor, of the first truly international mathematical journal

*Acta Mathematica*, which is still going strong and is one of the world's most respected journals. Its early volumes contain seminal papers by Poincaré, Darboux, Hermite, Cantor, Laguerre and many other famous names, as well as by Mittag-Leffler himself. In 1916 he founded the Institut Mittag-Leffler, donating his villa in Djursholm, close to Stockholm, a community founded in 1889 when the villa was constructed, and now 'enjoying' the highest property prices in Sweden. The villa has an excellent library and still operates as 'the world's oldest mathematics research institute' (the Princeton institute, for example, was founded in 1930). Mittag-Leffler was wealthy, but close to bankruptcy several times because of his very large borrowing in order to invest in vast Swedish industrial projects; he also helped to found an insurance company and for most of his professional life acted as its actuary. He was one of the first academic members of staff at Stockholm College, which was founded in 1878 and granted university status in 1960; he was a prime mover in the appointment of Sofia Kovalevskaya, the first woman in the modem world to hold a university position in mathematics, starting with a temporary docent position and moving to a chair in 1889. Though not on the Nobel Committee he exerted a good deal of pressure, sometimes in vain, on the choice of laureates and for many years he gave spectacular receptions and dinners following the Nobel ceremonies, at his villa in Djursholm.

Is this enough to fill a biography of 733 pages, weighing a kilogram? The biography is minutely detailed, almost a day-by-day account of Mittag-Leffier's life, derived from access to huge quantities of correspondence, diaries, official and private papers. Only rarely does the author step back and give us the social history, or tackle a particular theme in the life of his subject.

We learn of his family, including his sister Anne who was a novelist, close friend of Sofia Kovalevskaya, and later wife of the mathematician Pasquale del Pezzo, Duke of Cajanello and Marquis of Campodisola, and of the family of his wife Signe whom he met while in his first academic post in Finland - the machinations necessary to secure this post, ending in the agreement of the Tsar of Russia, exceed even the bureaucracy present nowadays in some south American countries.

We learn of the many battles which Mittag-Leffler lost, for example to secure a Nobel Prize for Poincaré or to keep Stockholm College as a purely research organisation which did not offer formal courses or award degrees - he did hold back the floodgates until 1904 when the College started to award Master's degrees and above. In the course of the story we also learn a little of the politics of the time: of Finland, at the time an autonomous Grand Duchy of the Russian Empire, and of Norway and Sweden, whose union was peacefully dissolved in 1905. We learn that Mittag-Leffler was frequently ill, spending much time at 'cures' in Germany and Switzerland; he was also often the subject of scandalous gossip, but on the whole we don't find out what was the truth of the matter. This is a factual, not an analytical biography. We don't learn either about Mittag-Leffier's mathematics, apart from mentions in passing, occasionally using technical words but without context or explanation: 'In the days before the fall semester began he worked with linear differential equations of the second order'.

Mittag-Leffler was a man of conviction, as the title states, and also a man of strong opinions: Marconi was a scientific swindler; Klein was fourth or fifth rate; Swedes were a small-minded and envious people incapable of action.

The figure of Sofia (Sonya) Kovalevskaya (1850-1891) is certainly one of the most interesting in the book. Readers of Alice Munro's excellent short story

*Too much happiness*will already know that her husband, whom she married in order to escape from Russia and attend university courses in Germany (without of course any prospect of graduating there), committed suicide leaving her with a daughter; that she was treated very kindly by Weierstrass; and that she died of influenza following a harrowing journey back to Stockholm after a trip to Italy. Even more interesting is the book from which Alice Munro obtained both the idea for her story and the title, the biography

*Little sparrow*by Don H Kennedy (University of Ohio Press, 1983). There is a well-known story about the rivalry between Mittag-Lcffler and Alfred Nobel, leading possibly to the absence of a Nobel Prize for Mathematics; in Stubhaug's biography the author concludes, on the basis of all available evidence, that the rivalry was probably over Sonya.

There are many photographs in Stubhaug's book, in some of which Mittag-Leffler bears a striking resemblance to Mark Twain, The index of names, though full, is not conceptual and therefore less useful than it might be: for example

*Weierstrass, Karl*is followed by a list of 76 page references without separation into topics. The translation from Norwegian is mostly very smooth, though sometimes it combines very colloquial phrases, for example 'several attorneys had to swing into action' , with words that fall heavily on an English ear, such as the constant use of 'treatise' for what we would call 'paper' or 'article'. As a biography of a complex, controversial, highly gifted man who interacted with many of the great figures of his time, this is (somewhat to my surprise) a very good read.

Last Updated June 2024