Editing Rolf Nevanlinna

{{Short description|Finnish mathematician (1895–1980)}}
{{Infobox scientist
| name              = Rolf Nevanlinna<ref name=mathgen1>{{cite web|url=http://genealogy.math.ndsu.nodak.edu/id.php?id=18689|website=Mathematics Genealogy Project|publisher=North Dakota State University Department of Mathematics|access-date=27 August 2017|title=The Mathematics Genealogy Project – Rolf Nevanlinna}}</ref>
| birth_name        = Rolf Herman Neovius
| image             = Rolf-Nevanlinna-1958 (cropped).jpg
| image_size        = 
| caption           = Rolf Nevanlinna, 1958.
| birth_date        = {{birth date|1895|10|22|df=y}}
| birth_place       = [[Joensuu]], [[Grand Duchy of Finland]], [[Russian Empire]]
| death_date        = {{death date and age|1980|05|28|1895|10|22|df=y}}
| death_place       = [[Helsinki]], Finland
| nationality       = [[Finns|Finnish]]
| fields            = [[Mathematics]]
| workplaces        = 
| alma_mater        = [[University of Helsinki]]
| thesis_title      = Über beschränkte Funktionen die in gegebenen Punkten vorgeschriebene Werte annehmen
| thesis_year       = 1919
| doctoral_advisor  = [[Ernst Leonard Lindelöf]]
| doctoral_students = [[Lars Ahlfors]], [[Kari Karhunen]], [[Leo Sario]], [[Gustav Elfving]], [[Olli Lehto]], [[Kurt Strebel]], [[Olli Lokki]], [[Nazim Terzioglu|Nazım Terzioğlu]]<ref name=mathgen2>{{cite web|url=http://genealogy.math.ndsu.nodak.edu/id.php?id=148430|website=Mathematics Genealogy Project|publisher=North Dakota State University Department of Mathematics|access-date=27 August 2017|title=The Mathematics Genealogy Project – Nazım Terzioğlu}}</ref>
| known_for         = [[Nevanlinna theory]]
| awards            = 
}}
'''Rolf Herman Nevanlinna''' (né '''Neovius'''; 22 October 1895 – 28 May 1980) was a [[Finns|Finnish]] [[mathematician]] who made significant contributions to [[complex analysis]].

==Background==
Nevanlinna was born Rolf Herman Neovius, becoming Nevanlinna in 1906 when his father changed the family name.

The Neovius-Nevanlinna family contained many mathematicians: Edvard Engelbert Neovius (Rolf's grandfather) taught mathematics and topography at a military academy; Edvard Rudolf Neovius (Rolf's uncle) was a professor of mathematics at the [[University of Helsinki]] from 1883 to 1900; Lars Theodor Neovius-Nevanlinna (Rolf's uncle) was an author of mathematical textbooks; and Otto Wilhelm Neovius-Nevanlinna (Rolf's father) was a physicist, astronomer and mathematician.

After Otto obtained his Ph.D. in physics from the University of Helsinki, he studied at the [[Pulkovo Observatory]] with the German astronomer [[Herman Romberg]], whose daughter, Margarete Henriette Louise Romberg, he married in 1892. Otto and Margarete then settled in [[Joensuu]], where Otto taught physics, and there their four children were born: [[Frithiof Nevanlinna|Frithiof]] (born 1894; also a mathematician), Rolf (born 1895), Anna (born 1896) and Erik (born 1901).<ref name=MacTutor>{{cite web|url=http://www-history.mcs.st-and.ac.uk/Biographies/Nevanlinna.html|title=Nevanlinna Biography|first1=John J.|last1=O'Connor|first2=Edmund F.|last2=Robertson|publisher=MacTutor History of Mathematics archive|date=January 2012}}</ref>

==Education==
Nevanlinna began his formal education at the age of 7. Having already been taught to read and write by his parents, he went straight into the second grade but still found the work boring and soon refused to attend the school. He was then homeschooled before being sent to a [[grammar school]] in 1903 when the family moved to [[Helsinki]], where his father took up a new post as a teacher at Helsinki High School. At the new school, Nevanlinna studied [[French language|French]] and [[German language|German]] in addition to the languages he already spoke: [[Finnish language|Finnish]] and [[Swedish language|Swedish]]. He also attended an orchestra school and had a love of music, which was encouraged by his mother:

{{Blockquote|Margarete was an excellent pianist and Frithiof and Rolf would lie under the piano and listen to her playing. At 13 they went to orchestra school and became accomplished musicians – Frithiof on the cello and Rolf on the violin. Through free tickets from the orchestra school they got to know and love the music of the great composers, [[Johann Sebastian Bach|Bach]], [[Ludwig van Beethoven|Beethoven]], [[Johannes Brahms|Brahms]], [[Franz Schubert|Schubert]], [[Robert Schumann|Schumann]], [[Frédéric Chopin|Chopin]] and [[Franz Liszt|Liszt]], as well as the early symphonies of [[Jean Sibelius|Sibelius]]. Rolf first met Sibelius's music in 1907, when he heard his [[Symphony No. 3 (Sibelius)|Third Symphony]]. Although later he met [[David Hilbert|Hilbert]], [[Albert Einstein|Einstein]], [[Thomas Mann]] and other famous people, Rolf said that none had had such a strong effect on him as Sibelius. The boys played trios with their mother and their love of music – in particular of [[chamber music]] – lasted all their lives.<ref>{{cite book|title=Rolf Nevanlinna|first=W K|last=Hayman|series=Bulletin of the London Mathematical Society|volume=14|date=1982|pages=419–436}}</ref>}}

Nevanlinna then progressed onto the Helsinki High School, where his main interests were [[classics]] and [[mathematics]]. He was taught by a number of teachers during this time but the best of them all was his own father, who taught him physics and mathematics. He graduated in 1913 having performed very well, although he was not the top student of his year. He then went beyond the school syllabus in the summer of 1913 when he read [[Ernst Leonard Lindelöf]]'s ''Introduction to Higher Analysis''; from that time on, Nevanlinna had an enthusiastic interest in [[mathematical analysis]]. (Lindelöf was also a cousin of Nevanlinna's father, and so a part of the Neovius-Nevanlinna mathematical family.)<ref name=MacTutor/>

Nevanlinna began his studies at the [[University of Helsinki]] in 1913, and received his [[Master of Philosophy]] in mathematics in 1917. Lindelöf taught at the university and Nevanlinna was further influenced by him. During his time at the University of Helsinki, [[World War I]] was underway and Nevanlinna wanted to join the [[27th Jäger Battalion (Finland)|27th Jäger Battalion]], but his parents convinced him to continue with his studies. He did however join the [[White Guard (Finland)|White Guard]] in the [[Finnish Civil War]], but did not see active military action.<ref name=ICMI>{{cite web|url=http://www.icmihistory.unito.it/portrait/nevanlinna.php|title=Rolf Nevanlinna: Brief scientific biography|publisher=International Commission on Mathematical Instruction|first=Osmo|last=Pekonen|date=2013}}</ref> In 1919, Nevanlinna presented his thesis, entitled ''Über beschränkte Funktionen die in gegebenen Punkten vorgeschriebene Werte annehmen'' ("On limited functions prescribed values at given points"), to Lindelöf, his doctoral advisor. The thesis, which was on [[complex analysis]], was of high quality and Nevanlinna was awarded his [[Doctor of Philosophy]] on 2 June 1919.

==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.

==Administrative activities==
[[File:Rolf Nevanlinna.jpg|thumb|right|Nevanlinna and his portrait.]]

From 1954, Rolf Nevanlinna chaired the committee which set about the first computer project in Finland. 

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.<ref name="Without_Borders">Lehto, Olli: ''Mathematics Without Borders: A History of the International Mathematical Union.'' Springer 1998.</ref>

In 1964, Nevanlinna's connections with President [[Urho Kekkonen]] were instrumental in bringing about a total reorganization of the Academy of Finland.<ref name="korkeat_maailmat">{{cite book | last = Lehto | first = Olli |author-link= Olli Lehto | year = 2001 |title = Korkeat maailmat: Rolf Nevanlinnan elämä |publisher= [[Otava (publisher)|Otava]] |oclc= 58345155 |isbn=951-1-17200-X |trans-title=High Worlds: The life of Rolf Nevanlinna |language = fi }}</ref>

From 1965 to 1970 Nevanlinna was Chancellor of the [[University of Turku]].<ref name="Chancellors">{{cite web |url=https://www.utu.fi/en/university/traditions/history/Pages/chancellors.aspx |title=Chancellors of the University of Turku  |author=<!--Not stated--> |website=University of Turku  |access-date=22 October 2019 }}</ref>

==Political activities==
Although Nevanlinna did not participate actively in politics, he was known to sympathise with the right-wing [[Patriotic People's Movement (Finland)|Patriotic People's Movement]] and, partly because of his half-German parentage, was also sympathetic towards [[Nazi Germany]]; with many mathematics professors fired in the 1930s due to the [[Nuremberg Laws]], mathematicians sympathetic to the Nazi policies were sought as replacements, and Nevanlinna accepted a position as professor at the [[University of Göttingen]] in 1936 and 1937.<ref>{{citation|contribution=A Failure Revisited: The First Finnish Computer Construction Project|title=IFIP WG9.7 First Working Conference on the History of Nordic Computing (HiNC1), June 16–18, 2003, Trondheim, Norway|pages=79–94|year=2005|doi=10.1007/0-387-24168-X_7|first=Petri|last=Paju|series=IFIP International Federation for Information Processing|volume=174|publisher=Springer|doi-access=free}}. 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.&nbsp;139."</ref> His sympathy towards the Nazis led to his removal from his position as Rector of the University of Helsinki after Finland made peace with the Soviet Union in 1944.<ref>{{Cite journal |last=Lehto |first=Olli |year=1997 |title=Nevanlinna, Rolf |url=http://urn.fi/urn:nbn:fi:sks-kbg-007111 |journal=Studia Biographica 4, Helsinki: Suomalaisen Kirjallisuuden Seura, 1997}}</ref>

In the spring of 1941, Finland contributed a [[Finnish Volunteer Battalion of the Waffen-SS|Volunteer Battalion]] to the [[Waffen-SS]]. In 1942, a committee was established for the Volunteer Battalion to take care of the battalion's somewhat strained relations with its German commanders, and Nevanlinna was chosen to be the chairman of the committee, as he was a person respected in Germany but loyal to Finland.<ref name="korkeat_maailmat" /><ref>{{citation|title=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|first1=Kenneth|last1=Bourne|first2=D. Cameron|last2=Watt|first3=Paul|last3=Preston|first4=Anita|last4=Prazmowska|publisher=University Publications of America|year=1997|isbn=1-55655-670-5 |page=71|quote=such notorious figures as ... Professor Rolf Nevanlinna (rector of Helsinki State University and one of the organisers of the first S.S. volunteers)}}.</ref> He stated in his autobiography that he accepted this role due to a "sense of duty".

Nevanlinna's collaboration with [[Nazi Germany]] did not prevent mathematical contacts with [[Allies of World War II|Allied countries]]; after World War II, the Soviet mathematical community was isolated from the Western mathematical community and the International Colloquium on Function Theory in Helsinki in 1957, directed by Nevanlinna, was one of the first post-war occasions when Soviet mathematicians could contact their Western colleagues in person.<ref>The Soviet Union did not participate in the 1950 ICM, but was represented by five mathematicians at the 1954 ICM in Amsterdam</ref> In 1965, Nevanlinna was an honorary guest at a function theory congress in [[Soviet Armenia]].<ref name="korkeat_maailmat"/>

== IMU Abacus Medal (formerly Nevanlinna Prize)==

When the IMU 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;  the [[Rolf Nevanlinna Prize]] is awarded every four years at the ICM.<ref name="Without_Borders"/> In 2018, the General Assembly of the IMU approved a resolution to remove Nevanlinna's name from the prize.<ref>[https://www.mathunion.org/fileadmin/IMU/Organization/GA/Resolutions/RESOL2018.pdf Resolutions of the IMU General Assembly 2018: Resolution 7] International Mathematical Union</ref> Starting in 2022 the prize has been called the IMU Abacus Medal.<ref>{{cite web |title=IMU Abacus Medal |url=https://www.mathunion.org/imu-awards/imu-abacus-medal |website=International Mathematical Union (IMU) |access-date=5 July 2022}}</ref>

==See also==
*[[Harmonic measure]]
*[[Nevanlinna theory]]
*[[Nevanlinna class]] (functions of bounded type)
*[[Nevanlinna function]]
*[[Nevanlinna invariant]]
*[[Nevanlinna–Pick interpolation]]
*[[Nevanlinna's criterion]]
*[[Nevanlinna Prize]]

==References==
{{Reflist}}

==Sources==
*{{cite book | last = Lehto | first = Olli |author-link= Olli Lehto |translator= Manfred Stern | year = 2008 |title = Erhabene Welten: Das Leben Rolf Nevanlinnas |publisher= Birkhäuser |isbn= 978-3-7643-7701-4 |trans-title= High Worlds: The life of Rolf Nevanlinna |language = de }}

==External links==
*{{Commons category inline}}
* {{MathGenealogy|id=18689}}
* [http://www.kansallisbiografia.fi/english/person/7111 Nevanlinna, Rolf.] National Biography of Finland.

{{Authority control}}

{{DEFAULTSORT:Nevanlinna, Rolf}}
[[Category:1895 births]]
[[Category:1980 deaths]]
[[Category:People from Joensuu]]
[[Category:People from Kuopio Province (Grand Duchy of Finland)]]
[[Category:20th-century  Finnish mathematicians]]
[[Category:Academic staff of the University of Helsinki]]
[[Category:Finnish mathematicians]]
[[Category:Finnish Nazis]]
[[Category:Finnish people of German descent]]
[[Category:Recipients of the Order of the Cross of Liberty, 2nd Class]]
[[Category:University of Helsinki alumni]]
[[Category:Members of the German Academy of Sciences at Berlin]]
[[Category:Rectors of the University of Helsinki]]
[[Category:Chancellors of the University of Turku]]
[[Category:Academic staff of ETH Zurich]]
[[Category:People of the Finnish Civil War (White side)]]
[[Category:Academic journal editors]]
[[Category:Presidents of the International Mathematical Union]]
[[Category:Members of the Royal Swedish Academy of Sciences]]