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).
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.
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