Rolf Nevanlinna[2] | |
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.jpg) Rolf Nevanlinna, 1958. | |
| Born | Rolf Herman Neovius (1895-10-22)22 October 1895 |
| Died | 28 May 1980(1980-05-28) (aged 84) Helsinki, Finland |
| Alma mater | University of Helsinki |
| Known for | Nevanlinna theory |
| Scientific career | |
| Fields | Mathematics |
| Thesis | Über beschränkte Funktionen die in gegebenen Punkten vorgeschriebene Werte annehmen (1919) |
| Doctoral advisor | Ernst Leonard Lindelöf |
| Doctoral students | Lars Ahlfors,Kari Karhunen,Leo Sario,Gustav Elfving,Olli Lehto,Kurt Strebel,Olli Lokki,Nazım Terzioğlu[1] |
Rolf Herman Nevanlinna (néNeovius; 22 October 1895 – 28 May 1980) was aFinnishmathematician who made significant contributions tocomplex analysis.
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 theUniversity 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 thePulkovo Observatory with the German astronomerHerman Romberg, whose daughter, Margarete Henriette Louise Romberg, he married in 1892. Otto and Margarete then settled inJoensuu, where Otto taught physics, and there their four children were born:Frithiof (born 1894; also a mathematician), Rolf (born 1895), Anna (born 1896) and Erik (born 1901).[3]
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 agrammar school in 1903 when the family moved toHelsinki, where his father took up a new post as a teacher at Helsinki High School. At the new school, Nevanlinna studiedFrench andGerman in addition to the languages he already spoke:Finnish andSwedish. He also attended an orchestra school and had a love of music, which was encouraged by his mother:
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,Bach,Beethoven,Brahms,Schubert,Schumann,Chopin andLiszt, as well as the early symphonies ofSibelius. Rolf first met Sibelius's music in 1907, when he heard hisThird Symphony. Although later he metHilbert,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 ofchamber music – lasted all their lives.[4]
Nevanlinna then progressed onto the Helsinki High School, where his main interests wereclassics andmathematics. 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 readErnst Leonard Lindelöf'sIntroduction to Higher Analysis; from that time on, Nevanlinna had an enthusiastic interest inmathematical analysis. (Lindelöf was also a cousin of Nevanlinna's father, and so a part of the Neovius-Nevanlinna mathematical family.)[3]
Nevanlinna began his studies at theUniversity of Helsinki in 1913, and received hisMaster 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 the27th Jäger Battalion, but his parents convinced him to continue with his studies. He did however join theWhite Guard in theFinnish Civil War, but did not see active military action.[5] In 1919, Nevanlinna presented his thesis, entitledÜber 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 oncomplex analysis, was of high quality and Nevanlinna was awarded hisDoctor of Philosophy on 2 June 1919.
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 aDocent of Mathematics at the University of Helsinki in 1922. During this time, he had been contacted byEdmund Landau and requested to move to Germany to work at theUniversity 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 createdfull professorship 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 asNevanlinna theory.[3]
From 1947 Nevanlinna had a chair in theUniversity 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 createdAcademy of Finland.
Rolf Nevanlinna's most important mathematical achievement is thevalue distribution theory ofmeromorphic functions. The roots of the theory go back to the result ofÉmile Picard in 1879, showing that a non-constant complex-valued function which isanalytic in the entirecomplex 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 covermeromorphic functions, i.e. functions analytic in the plane except for isolated points in which theLaurent series of the function has a finite number of terms with a negative power of the variable. Nevanlinna's value distribution theory orNevanlinna theory is crystallised in its twoMain 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 articleZur Theorie der meromorphen Funktionen[6] which contains the Main Theorems was published in 1925 in the journalActa Mathematica.Hermann Weyl has called it "one of the few great mathematical events of the [twentieth] century."[7] Nevanlinna gave a fuller account of the theory in the monographsLe théoreme de Picard – Borel et la théorie des fonctions méromorphes (1929) andEindeutige analytische Funktionen (1936).[8]
Nevanlinna theory touches also on a class of functions called the Nevanlinna class, or functions of "bounded type".
When theWinter War broke out (1939), Nevanlinna was invited to join theFinnish Army's Ballistics Office to assist in improvingartillery firing tables. These tables had been based on a calculation technique developed by GeneralVilho 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 theOrder 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 ofRiemann surfaces (the monographUniformisierung in 1953) andfunctional 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 theTheory of Relativity. His Finnish textbook on the elements of complex analysis,Funktioteoria (1963), written together withVeikko Paatero, has appeared in German, English and Russian translations.
Rolf Nevanlinna supervised at least 28 doctoral theses. His first and most famous doctoral student wasLars Ahlfors, one of the first twoFields Medal recipients. The research for which Ahlfors was awarded the prize (proving the Denjoy Conjecture, now known as theDenjoy–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 several universities: theUniversity of Heidelberg, theUniversity of Bucharest, theUniversity of Giessen, theFree University of Berlin, theUniversity of Glasgow, theUniversity of Uppsala, theUniversity of Istanbul and theUniversity of Jyväskylä. He was an honorary member of several learned societies, among them theLondon Mathematical Society and theHungarian Academy of Sciences. The1679 Nevanlinna main belt asteroid is named after him.
From 1954, Rolf Nevanlinna chaired the committee which set about the first computer project in Finland.
Rolf Nevanlinna served as President of theInternational Mathematical Union (IMU) from 1959 to 1963 and as President of theInternational Congress of Mathematicians (ICM) in 1962.[9]
In 1964, Nevanlinna's connections with PresidentUrho Kekkonen were instrumental in bringing about a total reorganization of the Academy of Finland.[10]
From 1965 to 1970 Nevanlinna was Chancellor of theUniversity of Turku.[11]
Although Nevanlinna did not participate actively in politics, he was known to sympathise with the right-wingPatriotic People's Movement and, partly because of his half-German parentage, was also sympathetic towardsNazi Germany; with many mathematics professors fired in the 1930s due to theNuremberg Laws, mathematicians sympathetic to the Nazi policies were sought as replacements, and Nevanlinna accepted a position as professor at theUniversity of Göttingen in 1936 and 1937.[12] 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.[13]
In the spring of 1941, Finland contributed aVolunteer Battalion to theWaffen-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.[10][14] He stated in his autobiography that he accepted this role due to a "sense of duty".
Nevanlinna's collaboration withNazi Germany did not prevent mathematical contacts withAllied 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.[15] In 1965, Nevanlinna was an honorary guest at a function theory congress inSoviet Armenia.[10]
When the IMU in 1981 decided to create a prize, similar to theFields 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; theRolf Nevanlinna Prize was awarded every four years at the ICM.[9] In 2018, the General Assembly of the IMU approved a resolution to remove Nevanlinna's name from the prize.[16] Starting in 2022 the prize has been called the IMU Abacus Medal.[17]
such notorious figures as ... Professor Rolf Nevanlinna (rector of Helsinki State University and one of the organisers of the first S.S. volunteers).
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