Rolf Nevanlinna
Encyclopedia
Rolf Herman Nevanlinna was one of the most famous Finnish
mathematician
s. He was particularly appreciated for his work in complex analysis
.
in t. Petersburg],] where Otto made observations for his thesis on the spectral lines of nitrogen and oxygen.
Rolf Nevanlinna was married twice. He had four children, Kai, Harri, Arne and Sylvi with his first wife Mary Selin, and one, Kristiina, with his second wife Sinikka Kallio. Harri Nevanlinna (1922 – 94) was a prominent hematologist and director of The Finnish Red Cross Blood Service, Arne Nevanlinna (born 1925) is an architect with a second career as a novelist. His first book was Isän maa (Father's Land), which gives a rather unflattering portrayal of his father.
. 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 function
s. The roots of the theory go back to the result of Émile Picard
in 1879, showing that a 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 chrystallized 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 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 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 Bucharest
, the Giessen
, Berlin
(Free University), Glasgow
, Uppsala, Istanbul and 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.
Rolf Nevanlinna served as President of the International Mathematical Union
, IMU, in 1959–63 and as President of the International Congress of Mathematicians
, ICM, in 1962.
In 1964, Nevanlinna's connections with President Urho Kekkonen
were instrumental in bringing about a total reorganization of the Academy of Finland.
From 1954, Rolf Nevanlinna chaired the committee which set about the first computer project in Finland. When the International Mathematical Union in 1981 decided to create a prize, similar to the Fields Medal
, in theoretical computer science and the funding for the price was secured from Finland, the Union decided to give Nevanlinna's name to the prize. The Rolf Nevanlinna Prize is awarded every four years in the ICM.
party and, partly because of his half German ancestry,
was leaning towards Germany. In the spring of 1941, Finland contributed a battalion of volunteers to the Waffen SS, which then fought on the Eastern Front. At the time, the battalion was considered to form a certain bondage with Germany, as Germany and Finland both fought against the Soviet Union, without a formal alliance. In 1942, an official SS Volunteer Committee was established in Finland to take care of the battalion's somewhat strained relations with its German superiors. A special concern was a fear that the men serving in the battalion would be too much infected by the Nazi ideology. Rolf Nevanlinna was chosen to be the chairman of the committee, as a non-political person respected in Germany but loyal to Finland. The battalion was finally brought back to Finland and disbanded in 1943.
Nevanlinna's activities during the war did not affect his mathematical contacts. His election to the presidency of the IMU was almost unanimous. In the 1950 the Soviet mathematical community was isolated from their Western Colleagues. The International Colloquium on Function Theory in Helsinki in 1957, directed by Nevanlinna, was the first post-war occasion when the Soviet mathematicians could contact their Western colleagues in person. In 1965, Rolf Nevanlinna was an honorary guest in a function theory congress in Armenia.
Finland
Finland , officially the Republic of Finland, is a Nordic country situated in the Fennoscandian region of Northern Europe. It is bordered by Sweden in the west, Norway in the north and Russia in the east, while Estonia lies to its south across the Gulf of Finland.Around 5.4 million people reside...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
s. He was particularly appreciated for his work in complex analysis
Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics,...
.
The Nevanlinna family
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, Nevanlinnas 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 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 observatoryPulkovo Observatory
The Pulkovo Astronomical Observatory астрономи́ческая обсервато́рия Росси́йской акаде́мии нау́к), the principal astronomical observatory of the Russian Academy of Sciences, located 19 km south of Saint Petersburg on Pulkovo Heights...
in t. Petersburg],] where Otto made observations for his thesis on the spectral lines of nitrogen and oxygen.
Rolf Nevanlinna was married twice. He had four children, Kai, Harri, Arne and Sylvi with his first wife Mary Selin, and one, Kristiina, with his second wife Sinikka Kallio. Harri Nevanlinna (1922 – 94) was a prominent hematologist and director of The Finnish Red Cross Blood Service, Arne Nevanlinna (born 1925) is an architect with a second career as a novelist. His first book was Isän maa (Father's Land), which gives a rather unflattering portrayal of his father.
Nevanlinna as mathematician
Rolf Nevanlinna studied at the University of HelsinkiUniversity of Helsinki
The University of Helsinki is a university located in Helsinki, Finland since 1829, but was founded in the city of Turku in 1640 as The Royal Academy of Turku, at that time part of the Swedish Empire. It is the oldest and largest university in Finland with the widest range of disciplines available...
. 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
University of Zurich
The University of Zurich , located in the city of Zurich, is the largest university in Switzerland, with over 25,000 students. It was founded in 1833 from the existing colleges of theology, law, medicine and a new faculty of philosophy....
, 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
Meromorphic function
In complex analysis, a meromorphic function on an open subset D of the complex plane is a function that is holomorphic on all D except a set of isolated points, which are poles for the function...
s. The roots of the theory go back to the result of Émile Picard
Charles Émile Picard
Charles Émile Picard FRS was a French mathematician. He was elected the fifteenth member to occupy seat 1 of the Académie Française in 1924.- Biography :...
in 1879, showing that a complex-valued function which is analytic
Analytic
Generally speaking, analytic refers to the "having the ability to analyze" or "division into elements or principles."It can also have the following meanings:-Natural sciences:* In chemistry:...
in the entire complex plane
Complex plane
In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the orthogonal imaginary axis...
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
Laurent series
In mathematics, the Laurent series of a complex function f is a representation of that function as a power series which includes terms of negative degree. It may be used to express complex functions in cases where...
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 chrystallized 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
Acta Mathematica
Acta Mathematica is a journal publishing original research papers in all fields of mathematics. The journal was founded by Gösta Mittag-Leffler in 1882 and is published by Institut Mittag-Leffler, a research institute for mathematics belonging to the Royal Swedish Academy of Sciences...
. 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
Winter War
The Winter War was a military conflict between the Soviet Union and Finland. It began with a Soviet offensive on 30 November 1939 – three months after the start of World War II and the Soviet invasion of Poland – and ended on 13 March 1940 with the Moscow Peace Treaty...
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
Vilho Petter Nenonen
Vilho Petter Nenonen was a Finnish general.Received his military education in the Hamina Cadet School 1896-1901, in the Mihailov Artillery School in St Petersburg 1901-1903, and in St Petersburg Artillery Academy 1906-1909. He served in the Russian army during World War I...
, 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 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
Riemann surface
In mathematics, particularly in complex analysis, a Riemann surface, first studied by and named after Bernhard Riemann, is a one-dimensional complex manifold. Riemann surfaces can be thought of as "deformed versions" of the complex plane: locally near every point they look like patches of the...
s (the monograph Uniformisierung in 1953) and functional analysis
Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
(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
Fields Medal
The Fields Medal, officially known as International Medal for Outstanding Discoveries in Mathematics, is a prize awarded to two, three, or four mathematicians not over 40 years of age at each International Congress of the International Mathematical Union , a meeting that takes place every four...
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 Bucharest
University of Bucharest
The University of Bucharest , in Romania, is a university founded in 1864 by decree of Prince Alexander John Cuza to convert the former Saint Sava Academy into the current University of Bucharest.-Presentation:...
, the Giessen
University of Giessen
The University of Giessen is officially called the Justus Liebig University Giessen after its most famous faculty member, Justus von Liebig, the founder of modern agricultural chemistry and inventor of artificial fertiliser.-History:The University of Gießen is among the oldest institutions of...
, Berlin
Free University of Berlin
Freie Universität Berlin is one of the leading and most prestigious research universities in Germany and continental Europe. It distinguishes itself through its modern and international character. It is the largest of the four universities in Berlin. Research at the university is focused on the...
(Free University), Glasgow
University of Glasgow
The University of Glasgow is the fourth-oldest university in the English-speaking world and one of Scotland's four ancient universities. Located in Glasgow, the university was founded in 1451 and is presently one of seventeen British higher education institutions ranked amongst the top 100 of the...
, Uppsala, Istanbul and Jyväskylä
University of Jyväskylä
The University of Jyväskylä is a university in Jyväskylä, Finland. It has its origins in the first Finnish-speaking teacher training college , founded in 1863. Around 14,000 students are currently enrolled in the degree programs of the university...
. He was an honorary member of several learned societies, among them the London Mathematical Society
London Mathematical Society
-See also:* American Mathematical Society* Edinburgh Mathematical Society* European Mathematical Society* List of Mathematical Societies* Council for the Mathematical Sciences* BCS-FACS Specialist Group-External links:* * *...
and the Hungarian Academy of Sciences
Hungarian Academy of Sciences
The Hungarian Academy of Sciences is the most important and prestigious learned society of Hungary. Its seat is at the bank of the Danube in Budapest.-History:...
. — The 1679 Nevanlinna
1679 Nevanlinna
1679 Nevanlinna is a main-belt asteroid discovered on March 18, 1941 by Liisi Oterma at Turku.- External links :*...
main belt asteroid is named after him.
Administrator and Organizer
Although basically a person devoted to his science, Rolf Nevanlinna did not avoid admistrative duties. In the thirties he served as Faculty Dean and from 1941 to 1945 as Rector of the University of Helsinki. His strong inclination to Germany compelled him to leave the Rector's post in the new political situation created by the events of 1944, when Finland made peace with the Soviet Union.Rolf Nevanlinna served as President of the International Mathematical Union
International Mathematical Union
The International Mathematical Union is an international non-governmental organisation devoted to international cooperation in the field of mathematics across the world. It is a member of the International Council for Science and supports the International Congress of Mathematicians...
, IMU, in 1959–63 and as President of the International Congress of Mathematicians
International Congress of Mathematicians
The International Congress of Mathematicians is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union ....
, ICM, in 1962.
In 1964, Nevanlinna's connections with President Urho Kekkonen
Urho Kekkonen
Urho Kaleva Kekkonen , was a Finnish politician who served as Prime Minister of Finland and later as the eighth President of Finland . Kekkonen continued the “active neutrality” policy of his predecessor President Juho Kusti Paasikivi, a doctrine which came to be known as the “Paasikivi–Kekkonen...
were instrumental in bringing about a total reorganization of the Academy of Finland.
From 1954, Rolf Nevanlinna chaired the committee which set about the first computer project in Finland. When the International Mathematical Union in 1981 decided to create a prize, similar to the Fields Medal
Fields Medal
The Fields Medal, officially known as International Medal for Outstanding Discoveries in Mathematics, is a prize awarded to two, three, or four mathematicians not over 40 years of age at each International Congress of the International Mathematical Union , a meeting that takes place every four...
, in theoretical computer science and the funding for the price was secured from Finland, the Union decided to give Nevanlinna's name to the prize. The Rolf Nevanlinna Prize is awarded every four years in the ICM.
Nevanlinna and politics
Rolf Nevanlinna did not participate actively in politics, but in the thirties he was known to sympathise with the right-wing Patriotic People's MovementPatriotic People's Movement (Finland)
Patriotic People's Movement, abbreviated to IKL), was a Finnish nationalist and anti-communist political party. IKL was the successor of the previously banned Lapuan liike...
party and, partly because of his half German ancestry,
was leaning towards Germany. In the spring of 1941, Finland contributed a battalion of volunteers to the Waffen SS, which then fought on the Eastern Front. At the time, the battalion was considered to form a certain bondage with Germany, as Germany and Finland both fought against the Soviet Union, without a formal alliance. In 1942, an official SS Volunteer Committee was established in Finland to take care of the battalion's somewhat strained relations with its German superiors. A special concern was a fear that the men serving in the battalion would be too much infected by the Nazi ideology. Rolf Nevanlinna was chosen to be the chairman of the committee, as a non-political person respected in Germany but loyal to Finland. The battalion was finally brought back to Finland and disbanded in 1943.
Nevanlinna's activities during the war did not affect his mathematical contacts. His election to the presidency of the IMU was almost unanimous. In the 1950 the Soviet mathematical community was isolated from their Western Colleagues. The International Colloquium on Function Theory in Helsinki in 1957, directed by Nevanlinna, was the first post-war occasion when the Soviet mathematicians could contact their Western colleagues in person. In 1965, Rolf Nevanlinna was an honorary guest in a function theory congress in Armenia.
Biography
- Olli Lehto; Manfred Stern [translator], Erhabene Welten: Das Leben Rolf Nevanlinnas (Birkhäuser, 2008) ISBN 978-3-7643-7701-4