Editing Rolf Nevanlinna (section)

==Career==
When Nevanlinna earned his doctorate in 1919, there were no university posts available so he became a school teacher. His brother, Frithiof, had received his doctorate in 1918 but likewise was unable to take up a post at a university, and instead began working as a mathematician for an insurance company. Frithiof recruited Rolf to the company, and Nevanlinna worked for the company and as a school teacher until he was appointed a [[Docent]] of Mathematics at the University of Helsinki in 1922. During this time, he had been contacted by [[Edmund Landau]] and requested to move to Germany to work at the [[University of Göttingen]], but did not accept.

After his appointment as Docent of Mathematics, he gave up his insurance job but did not resign his position as school teacher until he received a newly created [[full professor]]ship at the university in 1926. Despite this heavy workload, it was between the years of 1922–25 that he developed what would become to be known as [[Nevanlinna theory]].<ref name=MacTutor/>

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 function]]s. The roots of the theory go back to the result of [[Charles Émile Picard|Émile Picard]] in 1879, showing that a non-constant complex-valued function which is [[Analytic function|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 crystallised 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''<ref name="Nevanlinna 1925 Meromorphen">{{cite journal | last=Nevanlinna | first=Rolf | title=Zur Theorie der Meromorphen Funktionen | journal=Acta Mathematica | volume=46 | issue=1-2 | date=1925 | issn=0001-5962 | doi=10.1007/BF02543858 | pages=1–99}}</ref> 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."<ref name="weyl">{{cite book|author=H. Weyl| author-link=Hermann Weyl|title=Meromorphic functions and analytic curves 
|publisher=[[Princeton University Press]]|year=1943|page=8}}</ref> 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).<ref>{{cite journal|author=Hille, Einar|author-link=Einar Hille|title=Review: ''Eindeutige analytische Funktionen'', by R. Nevanlinna|journal=Bull. Amer. Math. Soc.|year=1939|volume=45|issue=1|pages=52–55|url=https://www.ams.org/journals/bull/1939-45-01/S0002-9904-1939-06916-4/|doi=10.1090/s0002-9904-1939-06916-4|doi-access=free}}</ref>

Nevanlinna theory touches also on a class of functions called the Nevanlinna class, or functions of "[[Bounded type (mathematics)|bounded type]]".

[[File:Memorial plaque of Rolf Nevanlinna's birth home, Koulukatu 25, Joensuu, Finland.jpg|thumb|Memorial plaque of Rolf Nevan&shy;linna's birth home, Koulu&shy;katu 25, Joensuu, Finland. “Academician Rolf Nevan&shy;linna's (1895–1980) birth home was in a house located here.”]]
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 surface]]s (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 recognised in the form of honorary degrees which he held from the universities of [[University of Heidelberg|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.