Rolf Herman Nevanlinna was one of the most famous Finnish mathematicians. He was particularly appreciated for his work in complex analysis.
Background
Rolf Nevanlinna was born in 1895 in Joensuu, Finland.
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.
Education
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.
Career
In 1922 Rolf Nevanlinna 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. In the early 1920s Rolf Nevanlinna, partly in collaboration with his brother Frithiof, extended the theory to cover meromorphic functions. 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 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 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 and functional analysis.
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.