Rolf Nevanlinna

Rolf Nevanlinna
Rolf Nevanlinna with his friend Erik Tawaststjerna at the piano (1962).
Born	(1895-10-22)22 October 1895 Joensuu
Died	28 May 1980(1980-05-28) (aged 84) Helsinki
Nationality	Finnish
Fields	Mathematics
Institutions	University of Helsinki
Alma mater	University of Helsinki
Doctoral advisor	Ernst Leonard Lindelöf
Doctoral students	Lars Ahlfors Kari Karhunen Gustav Elfving Olli Lehto Ilppo Simo Louhivaara Leo Sario Inkeri Simola
Known for	Nevanlinna theory

Rolf Herman Nevanlinna (22 October 1895 – 28 May 1980) was one of the most famous Finnish mathematicians. He was particularly appreciated for his work in complex analysis.

The Nevanlinna family

The Neovius-Nevanlinna family boasts mathematicians in at least five generations. Rolf Nevanlinna's grandfather Edavard Engelbert Neovius (1823–88), a major general in the Czar's army, taught mathematics in the Hamina Cadet School, Nevanlinna's father Otto Neovius-Nevanlinna (1867–1927) was a prominent mathematics teacher while one of his uncles was a mathematics professor and another a mathematics teacher. Rolf Nevanlinna's brother Frithiof Nevanlinna (1894–1977) was a mathematics professor, whose son and grandson are mathematics professors. A part of the family changed their name from Neovius to Nevanlinna in 1906, participating in the patriotic campaign to change Swedish and other foreign surnames into Finnish ones. Rolf Nevanlinna's mother Margareta Romberg was German; she was the daughter of the German astronomer Herman Romberg. Margareta Romberg and Otto Neovius met at the Pulkovo observatory in St. Petersburg, where Otto made observations for his thesis on the spectral lines of nitrogen and oxygen.

Rolf Nevanlinna was married twice. He had four children, Kai, Harri, Arne and Sylvi with his first wife Mary Selin, and one, Kristiina, with his second wife Sinikka Kallio. Harri Nevanlinna (1922 – 94) was a prominent hematologist and director of The Finnish Red Cross Blood Service, Arne Nevanlinna (born 1925) is an architect with a second career as a novelist. His first book was Isän maa (Father's Land), which gives a rather unflattering portrayal of his father.

Nevanlinna as mathematician

Rolf Nevanlinna studied at the University of Helsinki. He graduated in 1917. He obtained his doctorate in 1919 with the thesis Über beschränkte Funktionen die in gegebenen Punkten vorgeschriebene Werte annehmen; his thesis advisor was Ernst Lindelöf. In 1922 he was appointed a docent in the University of Helsinki, and in 1926 he was given a newly created full professorship in Helsinki. From 1947 Nevanlinna had a chair in the University of Zurich, which he held on a half-time basis after receiving in 1948 a permanent position as one of the 12 salaried Academicians in the newly created Academy of Finland.

Rolf Nevanlinna's most important mathematical achievement is the value distribution theory of meromorphic functions. The roots of the theory go back to the result of Émile Picard in 1879, showing that a non-constant complex-valued function which is analytic in the entire complex plane assumes all complex values save at most one. In the early 1920s Rolf Nevanlinna, partly in collaboration with his brother Frithiof, extended the theory to cover meromorphic functions, i.e. functions analytic in the plane except for isolated points in which the Laurent series of the function has a finite number of terms with a negative power of the variable. Nevanlinna's value distribution theory or Nevanlinna theory is crystallized in its two Main Theorems. Qualitatively, the first one states that if a value is assumed less frequently than average, then the function comes close to that value more often than average. The Second Main Theorem, more difficult than the first one tells that there are relatively few values which the function assumes less often than average.

Rolf Nevanlinna's article Zur Theorie der meromorphen Funktionen which contains the Main Theorems was published in 1925 in the journal Acta Mathematica. Nevanlinna gave a fuller account of the theory in the monographs La théoreme de Picard – Borel et la théorie des fonctions méromorphes (1929) and Eindeutige analytische Funktionen (1936).^[1]

When the Winter War broke out, Nevanlinna was invited to join the Finnish Army's Ballistics Office to assist in improving artillery firing tables. These tables had been based on a calculation technique developed by General Vilho Petter Nenonen, but Nevanlinna now came up with a new method which made them considerably faster to compile. In recognition of his work he was awarded the Order of the Cross of Liberty, Second Class, and throughout his life he held this honour in especial esteem.

Among Rolf Nevanlinna's later interests in mathematics were the theory of Riemann surfaces (the monograph Uniformisierung in 1953) and functional analysis (Absolute analysis in 1959, written in collaboration with his brother Frithiof). Nevanlinna also published in Finnish a book on the foundations of geometry and a semipopular account of the Theory of Relativity. His Finnish textbook on the elements of complex analysis, Funktioteoria (1963), written together with Veikko Paatero, has appeared in German, English and Russian translations.

Rolf Nevanlinna supervised at least 28 doctoral theses. His first and most famous doctoral student was Lars Ahlfors, one of the two first Fields Medal recipients. The research for which Ahlfors was awarded the prize was strongly based on Nevanlinna's work.

Nevanlinna's work was recognized in the form of honorary degrees which he held from the universities of Heidelberg, the University of Bucharest, the University of Giessen, the Free University of Berlin, the University of Glasgow, the University of Uppsala, the University of Istanbul and the University of Jyväskylä. He was an honorary member of several learned societies, among them the London Mathematical Society and the Hungarian Academy of Sciences. — The 1679 Nevanlinna main belt asteroid is named after him.

Administrator and organizer

Nevanlinna and his portrait.

Although basically a person devoted to his science, Rolf Nevanlinna did not avoid administrative duties. Politically, he was in the 1930s a supporter of the National Socialist Germany: With a remarkable number of mathematics professors removed through the racial laws of the Nazi period, people sympathetic to the Nazi policies were sought all over Europe as replacements, and Nevanlinna accepted a professor's position in Göttingen for the year 1936-37. In Finland, he served in the thirties as Faculty Dean and from 1941 to 1945 as Rector of the University of Helsinki. His support of Nazi Germany^[2] led to his being removed from the Rector's post in the new political situation created by the events of 1944, when Finland made peace with the Soviet Union. Most importantly, his political commitments during the Nazi period included presiding the commission of voluntary Finnish SS-officers.^[3] Remarkably, his autobiography includes that this was done out of a "sense of duty."

Rolf Nevanlinna served as President of the International Mathematical Union, IMU, in 1959–63 and as President of the International Congress of Mathematicians, ICM, in 1962.^[4]

In 1964, Nevanlinna's connections with President Urho Kekkonen were instrumental in bringing about a total reorganization of the Academy of Finland.^[5]

From 1954, Rolf Nevanlinna chaired the committee which set about the first computer project in Finland. When the International Mathematical Union in 1981 decided to create a prize, similar to the Fields Medal, in theoretical computer science and the funding for the prize was secured from Finland, the Union decided to give Nevanlinna's name to the prize.^[4] The Rolf Nevanlinna Prize is awarded every four years in the ICM.

Nevanlinna and politics

Rolf Nevanlinna did not participate actively in politics, but in the thirties he was known to sympathise with the right-wing Patriotic People's Movement party and, partly because of his half German ancestry, was leaning towards Germany. In the spring of 1941, Finland contributed a battalion of volunteers to the Waffen SS, which then fought on the Eastern Front. At the time, the battalion was considered to form a certain bondage with Germany, as Germany and Finland both fought against the Soviet Union, without a formal alliance. In 1942, an official SS Volunteer Committee was established in Finland to take care of the battalion's somewhat strained relations with its German superiors. Rolf Nevanlinna was chosen to be the chairman of the committee, as a person respected in Germany but loyal to Finland. The battalion was finally brought back to Finland and disbanded in 1943.^[5]

Nevanlinna's Nazi sympathies during the war did not affect his mathematical contacts. His election to the presidency of the IMU was almost unanimous. In the 1950 the Soviet mathematical community was isolated from their Western colleagues. The International Colloquium on Function Theory in Helsinki in 1957, directed by Nevanlinna, was the first post-war occasion when the Soviet mathematicians could contact their Western colleagues in person. In 1965, Rolf Nevanlinna was an honorary guest in a function theory congress in Armenia.^[5]

See also

• Nevanlinna theory
• Nevanlinna–Pick interpolation
• Nevanlinna's criterion
• Nevanlinna Prize

References

Sources

• Olli Lehto; Manfred Stern [translator], Erhabene Welten: Das Leben Rolf Nevanlinnas (Birkhäuser, 2008) ISBN 978-3-7643-7701-4

External links

• O'Connor, John J.; Robertson, Edmund F., "Rolf Nevanlinna", MacTutor History of Mathematics archive, University of St Andrews .
• Rolf Nevanlinna at the Mathematics Genealogy Project