Rolf Nevanlinna

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Rolf Nevanlinna
Rolf Nevanlinna with his friend Erik W. Tawaststjerna at the piano (1962).
Born (1895-10-22)22 October 1895
Died 28 May 1980(1980-05-28) (aged 84)
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.

Memorial plaque of Rolf Nevanlinna's birth home, Koulukatu 25, Joensuu, Finland. Text: Academician Rolf Nevanlinna's (1895-1980) birth home was in a house which was located here.

Nevanlinna as mathematician[edit]

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, states roughly 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. Hermann Weyl has called it "one of the few great mathematical events of the [twentieth] century."[1] Nevanlinna gave a fuller account of the theory in the monographs Le théoreme de Picard – Borel et la théorie des fonctions méromorphes (1929) and Eindeutige analytische Funktionen (1936).[2]

Nevanlinna theory touches also on a class of functions called the Nevanlinna class, or functions of "bounded type".

When the Winter War broke out (1939), 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 first two Fields Medal recipients. The research for which Ahlfors was awarded the prize (proving the Denjoy Conjecture, now known as the Denjoy–Carleman–Ahlfors theorem) 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[edit]

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 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 in 1936 and 1937. 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[3] 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 over the commission of voluntary Finnish SS-officers.[4] 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, from 1959 to 1963 and as President of the International Congress of Mathematicians, ICM, in 1962.[5]

In 1964, Nevanlinna's connections with President Urho Kekkonen were instrumental in bringing about a total reorganization of the Academy of Finland.[6]

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.[5] The Rolf Nevanlinna Prize is awarded every four years in the ICM.

Nevanlinna and politics[edit]

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 bond 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.[6]

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 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.[6]

See also[edit]


  1. ^ H. Weyl (1943). Meromorphic functions and analytic curves. Princeton University Press. p. 8. 
  2. ^ Hille, Einar (1939). "Review: Eindeutige analytische Funktionen, by R. Nevanlinna". Bull. Amer. Math. Soc. 45 (1): 52–55. doi:10.1090/s0002-9904-1939-06916-4. 
  3. ^ Paju, Petri (2005), "A Failure Revisited: The First Finnish Computer Construction Project", IFIP WG9.7 First Working Conference on the History of Nordic Computing (HiNC1), June 16–18, 2003, Trondheim, Norway, IFIP International Federation for Information Processing, 174, Springer, pp. 79–94, doi:10.1007/0-387-24168-X_7 . Footnote 20, p. 86: "Nevanlinna had also been a visiting mathematics professor in Göttingen in 1936–1937. At that time, Nevanlinna was a known Nazi-sympathiser. On this topic, see O. Lehto, Korkeat maailmat, on p. 139."
  4. ^ Bourne, Kenneth; Watt, D. Cameron; Preston, Paul; Prazmowska, Anita (1997), British documents on foreign affairs: reports and papers from the Foreign Office confidential print : Kenneth. Bourne. From 1940 through 1945. Series A: The Soviet Union and Finland, Part 3, University Publications of America, p. 71, ISBN 9781556556708, such notorious figures as ... Professor Rolf Nevanlinna (rector of Helsinki State University and one of the organisers of the first S.S. volunteers) .
  5. ^ a b Lehto, Olli: Mathematics Without Borders. A History of the International Mathematical Union. Springer 1998
  6. ^ a b c Lehto, Olli (2001). Korkeat maailmat. Rolf Nevanlinnan elämä [High Worlds. The life of Rolf Nevanlinna] (in Finnish). Otava. 317 pages. OCLC 58345155. 


  • Lehto, Olli (2008). Erhabene Welten: Das Leben Rolf Nevanlinnas [High Worlds. The life of Rolf Nevanlinna] (in German). Translated by Manfred Stern. Birkhäuser. 299 pages. ISBN 978-3-7643-7701-4. 

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