Book Review

Gösta Mittag-Leffler.A Man of ConvictionReviewed by Sigurdur Helgason

Gösta Mittag-Leffler. A Man of ConvictionArild StubhaugSpringer-Verlag, 2010US$79.95, 810 pagesISBN-13: 978-3642116711

The author of this book, Arild Stubhaug, is wellknown among mathematicians for his superb bi-ographies of Abel and Lie. Being a cand. mag.in mathematics as well as in literature, he wasin fact singularly qualified for such undertak-ings. He managed to convey the flavor of themathematics involved without discouraging thenonmathematician reader.

It is therefore a matter of great interest thatStubhaug has undertaken the job of writing abiography of Mittag-Leffler. While Mittag-Lefflerdoes not compare to Abel and Lie in mathematicaloutput or creativity, the mathematician G. H. Hardyin 1927 maintained that no one had done more formathematics during the preceding fifty years. Andin fact many consider Mittag-Leffler to be the fatherof mathematics in Sweden. Most mathematiciansknow his name from the Mittag-Leffler theoremin complex analysis. It is a counterpart to Weier-strass’s theorem about constructing a holomorphicfunction with prescribed zeros; in Mittag-Leffler’stheorem the poles and the singular part at eachend pole are prescribed.

Sigurdur Helgason is professor of mathematics at the Mas-sachusetts Institute of Technology. His email address ishelgason@mit.edu.

This is a slightly revised version of a piece that originallyappeared in Matilde, the news publication of the DanishMathematical Society (number 41, December 2010). It isreprinted here with permission.

DOI: http://dx.doi.org/10.1090/noti1037

Stubhaug’s book traces Gösta Mittag-Leffler’slife from childhood on. However, the first chapterstarts with a kind of an appetizer, “Journey atthe Turn of the Century”, which describes a tripMittag-Leffler took to Egypt with his wife, Signe,accompanied by his personal physician. This is oneexample of many extensive trips he took duringhis life for health reasons. In fact, he suffered fromserious health problems throughout his life. As achild he suffered from serious pneumonia of a kindwhere the survival prospects were 0.1 percent. Hecredited his mother’s care for his survival and keptvery warm contact with her all her life. He addedher name, Mittag, to his father’s name, Leffler.

After his professorship in Helsingfors, 1877–1881, Mittag-Leffler accepted a professorship atStockholm’s Högskola. His principal activities canbe divided into four parts: (i) reforming Stock-holm’s Högskola toward a more research-orientedprogram in mathematics; (ii) founding in 1882and developing the journal Acta Mathematica,which even today is a highly respected mathe-matical journal; (iii) investing in highly variedenterprises, carbide factories, railroads, waterfallsfor hydroelectric production, etc.; and (iv) foundingthe Mathematical Institute in Djursholm in 1916jointly with his wife: “The married couple Signeand Mittag-Leffler”.

At the time of the founding of the institutetheir fortune was estimated at four million krona,down from seven million two years earlier. Thiswould decline even further after the First WorldWar. Toward the end of his life he had little left,partly because Signe’s inheritance (she died sixyears before him) had been in large part divertedelsewhere due to another inheritor whom Mittag-Leffler called “The Witch [Hexan] W”. After hisdeath the institute was rather dormant except forthe continued publication of Acta Mathematica.

1054 Notices of the AMS Volume 60, Number 8

However, around 1970 Lennart Carleson managedto obtain funding whereby the institute couldfunction in the way Mittag-Leffler had planned, andCarleson served for sixteen years as the scientificdirector.1

Activities (ii) and (iii) were connected with veryextensive travels all over Europe (and Egypt andAlgeria). Many of these trips were taken for reasonsof health and necessitated the company of a doctor.

Clearly Mittag-Leffler expected his biographywould be written after his death. He always kepta diary, finally totalling ninety-three volumes.He wrote about 20,000 letters to about threethousand correspondents, collected hundreds ofarticles and drafts thereof, as well as recordsof business dealings. Every item involved waskept. The “Nachlass” filled about seventy-five shelf-meters. At the Mittag-Leffler Institute one can findseries of leather-bound volumes filled with nothingbut visiting cards. The list of his VitenskapeligeUtmerkelser (honorary degrees and membershipsin scientific academies) fills two pages.

After defending his doctoral thesis in Uppsalain 1872 he got a stipend to travel to Berlin andParis for two to three years. He started in Parisand dutifully attended Hermite’s lectures. Theseturned out to be a real challenge to Mittag-Leffler’sfamiliarity with French, because Hermite haddifficulty walking so he did not use a blackboard.He just stood at the lectern and read the lecturesfrom his manuscripts, most of which consistedof formulas for elliptic functions. He lectured9:00–10:00 p.m. on Christmas Eve and continuedChristmas Day at the same time. But Mittag-Leffler was clearly a dashing, charming fellow,and Hermite took a great liking to him, invitinghim to dinner en famille with his two unmarrieddaughters present. But he advised Mittag-Lefflerto go to Berlin and learn from Weierstrass (“he isthe master of us all”). In Berlin Mittag-Leffler had avery productive time and established contact withmembers of the brilliant Berlin school, particularlyWeierstrass. While Weierstrass would have liked tokeep him in Berlin, Mittag-Leffler instead appliedsuccessfully for a professorship in Helsingfors.From Weierstrass he had heard about his brilliantstudent, Sonja Kowalevski. Shortly before taking theposition at Helsingfors, Mittag-Leffler met her on atrip to St. Petersburg. To his mother he wrote: “Somquinna är hun forjusande. . . .Denne dag er en af demárkligsta i mitt liv. (As a woman she is enchanting.. . .This day is one of the most remarkable of mylife.)” Through Mittag-Leffler’s efforts Sonja wasappointed professor at Stockholm’s Högskola, and

1Information about the Mittag-Leffler Institute and its his-tory may be found in “The dream of a Swedish mathemati-cian: The Mittag-Leffler Institute”, by Allyn Jackson, Notices,October 1999.

he did his best to make a pleasant life for her. Thiswas often a difficult task.

Another woman scientist receiving significantsupport from Mittag-Leffler was Marie Curie. As amember of the Royal Swedish Academy he knewthat Pierre Curie was a likely candidate for theNobel Prize and was aware that her name hadnot been mentioned. Mittag-Leffler then wrote toPierre Curie and asked whether she was not a fullyworthy partner in his work. Curie answered quitepositively that if such a prize was contemplatedshe would be equally deserving. So they didindeed share the Nobel Prize in physics in 1903.A couple of years later Pierre Curie died in atraffic accident, and in 1911 the chemistry prizewas accorded to Marie Curie. At that time theNobel committee was unaware of the scandalcirculating in Paris concerning Marie Curie andPaul Langevin. Arrhenius, another member ofthe Swedish Academy, then wrote to Marie Curieexpressing his opinion that it would be best if shedid not come to Stockholm to receive the prize.Mittag-Leffler took quick action and in severaltelegrams to Langevin insisted that she shouldcome to Stockholm. She followed his advice withdeep gratitude. Thus Mittag-Leffler has the honorof arranging the first female professorship inmathematics and the first Nobel Prize to a female.

Stubhaug’s description of these scientific polit-ical matters makes for fascinating reading. Onealso gets a clear image of Mittag-Leffler’s businessand investment affairs, which during some difficulttimes caused him much grief and criticism. Amarital crisis around 1897 caused by jealousiesis described with great tact and sensitivity. Whilereading this book three times I often felt that I wasback in Djursholm wandering through the instituteor along the paths near the seashore. The book isthoroughly captivating.

While Mittag-Leffler might have thought that hisdiaries could make an account of his life easy for abiographer, it took almost a century until Stubhaughad the courage to tackle this enormous challengewith reasonable completeness. The result is afascinating account of Mittag-Leffler’s life which atthe same time gives a vivid picture of the Europeanmathematical milieu and activities during theperiod 1887–1920.

September 2013 Notices of the AMS 1055