Rolf Nevanlinna

Rolf Herman Nevanlinna (born October 22, 1895 in Joensuu , † May 28, 1980 in Helsinki ) was a Finnish mathematician . He is considered one of the leading exponents of function theory in the 20th century.

Rolf Nevanlinna

Life

Childhood and youth

Memorial plaque on the house where Rolf Nevanlinna was born, Koulukatu 25, Joensuu, Finland

Rolf Nevanlinna's father was Otto Wilhelm Neovius, who worked as a high school teacher in Joensuu. Like two of his four brothers, he had studied mathematics and physics. Rolf's mother Margareta (actually: Margarete) Romberg, the daughter of the German astronomer Hermann Romberg (1836–1898), he had met during his doctorate at the Pulkowo Observatory and married her in the summer of 1892. Rolf was born their second child in 1895, his brother Frithiof was born one year before him, and his sister Anna one year after him. In 1901 his younger brother Erik was born.

In 1906 the family changed their surname. Nevanlinna's ancestors had abandoned their original Finnish name around 1730 and adopted the Swedish name Nyman (Neumann in German) based on their origin Uusikylä (Finnish for Neudorf). This name was later Latinized to Neovius. This name was wrongly associated with Neovia, the Latinized name of a fortress on the Neva estuary. With the onset of Fennization, the family got the name Nevanlinna ( linna : Finnish for castle).

The children grew up bilingual, the main language spoken at home was Swedish, and the language of instruction at school was Finnish.

In 1902 Rolf went straight to the second grade of the private primary school in Vatanen because he had already taught himself to read and write in self-study. However, after receiving a moderate grade of conduct (a 6 in the Finnish grading system ), he refused to continue attending school. This only changed when his father was appointed senior teacher at the Swedish-language secondary school in Helsinki as the successor to his brother Lars, and the family moved there in August 1903. After a break of 1½ years, Nevanlinna started third grade at Alli Nissinen Primary School. Then he attended the Finnish Normallyceum. He was always one of the best students in his class. His own father became his math teacher last year of school.

In his free time he liked to play football and read a lot. One of his favorite authors was Zacharias Topelius . By reading Andersen's fairy tales in the original, he taught himself Danish. Later he also learned German and French in self-study. Music also played an important role in his life. He learned the violin at the Helsinki Orchestra School. There was also a lot of music at home, his mother played the piano, his brother Frithiof the cello. He remained connected to music throughout his life, and particularly valued Jean Sibelius .

Education

After studying the textbook Introduction to Higher Analysis by Ernst Lindelöf , Nevanlinna decided to study mathematics, to which he enrolled at the University of Helsinki in May 1912 . Lindelöf was also his main teacher. He passed his master's degree in mathematics, physics and astronomy, as well as chemistry. Building on his master's thesis, he also wrote his doctoral thesis at Lindelöf. For a short time he had the plan, like many comrades, to volunteer for the Royal Prussian Jäger Battalion , but on the advice of his father he abandoned it. In 1916 he retired to the countryside in Vuosaari for half a year because there was a food shortage in Helsinki as a result of the First World War and he was also ill. On his return he was drafted into the military, but classified as unfit.

The doctorate took place in May 1919 with the thesis on limited functions that assume prescribed values ​​in given points . The opponent was Jarl Lindeberg .

Marriage and profession

During his master's thesis he had already got engaged to his cousin Mary Selin, but the engagement broke up again. The two became engaged again in January 1919 and married in Vyborg in the summer of the same year .

Nevanlinna found a job as a substitute teacher at the New Coeducational School in the Helsinki district of Kruununhaka . However, the salary was not enough, so that he also became an assistant mathematician at the life insurance company Salama through the mediation of his brother Frithiof. In 1922 he became a private lecturer at the University of Helsinki.

The family's four children were born between 1920 and 1930: Kai (1920), Harri (1922), Arne (1925–2016) and Sylvi (1930).

Scientific achievements

In addition to his three positions, he continued to conduct research in the area of ​​his doctoral thesis and other functional theory topics. Sometimes he worked with his brother Frithiof. At the Scandinavian Mathematicians Congress in July 1922, both gave lectures on their research. It was on this occasion that Nevanlinna had first contact with foreign mathematicians. A joint work emerged from the lectures of the two brothers, which received exceptionally positive reviews and about which Lars Ahlfors later said that after its publication the theory of functions was no longer the same as before.

Nevanlinna's most important mathematical achievement is considered to be the value distribution theory of meromorphic functions that he developed in a work published in 1925 , which is now known as the Nevanlinna theory . Hermann Weyl later described the publication of this work as one of the few great mathematical events of our century . Nevanlinna later gave more detailed descriptions of his theory in his books Le théorème de Picard-Borel et la théorie des fonctions méromorphes (1929) and Unique analytical functions (1936). The basic idea of ​​the Nevanlinna theory is to give a quantitative version of Picard's theorem . Corresponding results for whole functions have already been given by Émile Borel and other mathematicians using the maximum amount of a whole function . The maximum amount is unsuitable for meromorphic functions, however, and Nevanlinna introduced a measure for the growth of a meromorphic function with the variable known today as the Nevanlinna characteristic, which often has better properties than the maximum amount for entire functions. Later Nevanlinna also dealt with Riemann surfaces , about which he wrote the book Uniformization . ${\displaystyle \max _{|z|=r}|f(z)|}$ ${\displaystyle f}$

Nevanlinna became a member of the Finnish Academy of Sciences in Helsinki in 1924 .

Professor in Helsinki

In 1926 he was appointed professor of mathematics at the University of Helsinki, where he prevailed against his competitor Pekka Myrberg . With the professorship he gave up his job as a substitute teacher. However, he kept his position at Salama, where he was promoted to chief mathematician in 1930.

In 1933 he became dean of the mathematics and natural sciences faculty and thus came into contact with the university administration. He also enjoyed a reputation outside of the university sector, so he became a member of the Abitur examination commission in 1935 and soon afterwards its chairman.

Trips abroad

Nevanlinna's first trip abroad took him to Göttingen in 1924 , where he met Edmund Landau , Richard Courant and David Hilbert . He made another trip to Paris in 1926 , where he met Émile Borel , Jacques Hadamard and Paul Montel . In the winter semester of 1928/1929 he represented Hermann Weyl at the ETH Zurich , where he went with his family. When it became known that Weyl would not return to Zurich because he had accepted a call to Göttingen, Nevanlinna was offered the position. Although the salary would have been three times higher than in Helsinki, he refused, justifying this with his loyalty to Helsinki and the desire that his children grow up in Finland. He also turned down a professorship at Stanford that was offered to him shortly thereafter.

From Zurich he traveled to Paris alone, for which he had received a Rockefeller grant . He had actually wanted to travel to Great Britain, but his knowledge of English was insufficient.

In the semester 1936/1937 he held a visiting professorship in Göttingen, since Helmut Hasse was urgently looking for a replacement for Professors Courant and Weyl, who had emigrated to the USA for political reasons. Nevanlinna's January 1936 political report is consistently positive. However, as before in Zurich, he refused an extension of his employment that was actually planned.

Time of war

Even during the Second World War, Nevanlinna maintained good relations with Germany and traveled there repeatedly. In a report by the communist state police, which was active after the war, they even claim that he actively supported the Finnish Nazi movement.

In 1940 he devoted himself to ballistic calculations for war purposes, he wrote a treatise on the calculation of the normal flight path of a projectile . On the Hanko front he was honored by the fact that he was allowed to fire the first cannon salvo at the Russian opponents.

Nevanlinna plays a decisive role in an episode heavily embellished by André Weil and his biographers: Weil was suspected of espionage for the Soviet Union in 1939 and arrested in Helsinki. On the evening before Weil's planned execution, the responsible police chief is said to have met Nevanlinna by chance at a gala dinner and to have complied with his request, only to expel Weil from the country. Nevanlinna, on the other hand, reports in his memoirs that although he happened to talk to the State Secretary in the Foreign Ministry about Weil, the idea of ​​expulsion did not come from him. In Weil's file with the state police there is no indication of a planned execution either.

In 1942 Nevanlinna became chairman of the SS volunteer committee at the request of the Finnish Foreign Minister Rolf Witting . However, he was no longer engaged in recruiting new volunteers, but only in returning battalions that had already been deployed. After he had traveled to Berlin in April 1943 for talks with the SS leadership, he was returned in June of the same year.

Nevanlinna was a founding member of the German-Finnish Society in November 1942; In 1944 he became a board member.

During the war, he was elected rector of the university in 1941, in which he prevailed over vice rector Edwin Linkomies . When he was elected Chancellor in 1944, however, he had to be content with third place.

When Linkomies became Prime Minister of Finland in 1943, Nevanlinna was to become Minister of Education in his cabinet, but this probably failed due to resistance from the Social Democrats.

After the war

Nevanlinna was re-elected rector in 1944, and in the years after the end of the war the main focus was on repairing the damaged buildings. After Juho Kusti Paasikivi took office, he resigned in 1945 due to political pressure.

He shifted his interest towards clarifying the physical worldview through mathematical methods. In the 1950s he developed - again together with his brother Frithiof - a coordinate-free vector calculation, the absolute analysis .

In 1950 he traveled to the USA for the first time to re-establish the International Mathematical Union in New York, and was later elected President for the period 1959 to 1962. A year later he made his first trip to Great Britain to Cambridge University .

Professor in Zurich

In 1946 Nevanlinna held another visiting professorship in Zurich, but this time it extended it. His brother Frithiof was his successor in Helsinki. In 1947 Nevanlinna had been proposed as a member of the newly founded Academy of Finland , which had the task of advising the state on future science planning and promoting science. After a few disputes, the president was appointed with the honorary title of academic in 1948 . In order to be able to work in the Academy of Finland, his full professorship in Zurich was converted into an honorary professor in 1949.

New marriage

Nevanlinna met the singer and actress Mary Hannikainen even before the war. This relationship became closer after the death of her husband, in 1944 he almost divorced his wife Mary Nevanlinna because of her. In addition to this relationship, he fell in love with the art historian Sinikka Kallio-Visapää. In 1946 their daughter Kristiina was born, who grew up with the four other children of the Visapää family, of which only Mary Nevanlinna and Sinikka's husband Niilo Visapää were informed for many years. He tried to keep the relationship with Sinikka a secret, especially from Mary Hannikainen, but she discovered it in May 1956 when she surprised the two of them in Nevanlinna's apartment in Zurich, and informed his wife about it. The marriages Nevanlinna and Visapää were divorced and in November 1958 Nevanlinna married Sinikka Kallio-Visapää in Paris.

Last years

Nevanlinna in 1976.

In 1954 he became chairman of the committee for mechanical machines, in 1960 the calculating machine ESKO ( electronic sarjakomputaattorie , Finnish for serial computer) at the computer center of the University of Helsinki was completed.

In 1963 Nevanlinna gave up his professorship in Zurich and finally returned to Finland. On his 70th birthday in 1965, he retired from his position at the Academy of Finland. On the same day he took up the post of Chancellor of the University of Turku , which he held until 1970.

He spent two semesters as a visiting professor in the USA: in 1965 at Stanford University , in 1970 at the University of California in San Diego.

In 1978 he was involved in the organization of the IMU Congress in Helsinki and also presented the Fields Medals .

In early 1980, Nevanlinna was diagnosed with liver cancer, from which he died several months later.

Honors

In addition to the Finnish Academy of Sciences , Nevanlinna was a member of ten other academies and scientific societies, including the Leopoldina .

Nevanlinna received a total of eight honorary doctorates, starting with the University of Heidelberg in 1936.

In 1940 he was awarded the Freedom Cross 2nd Class in connection with his ballistic calculations.

An asteroid and the prize of the IMU for theoretical computer science are named after him .

Others

His brother Frithiof Nevanlinna (1894-1977) was also a mathematician, who received his doctorate under Ernst Lindelöf in 1918 , went into the insurance industry and was a professor in Helsinki from 1950 to 1962, succeeding Rolf Nevanlinna.

Works

A total of 127 publications come from Nevanlinna, six of them together with his brother Frithiof, two with Veikko Paatero and one each with Hans Wittich and Paul Kustaanheimo .

Function theory

• with Frithiof Nevanlinna: About the properties of analytical functions in the vicinity of a singular point or line. Acta Societatis Scientiarum Fennicae, 1922.
• Le théorème de Picard-Borel et la théorie des fonctions méromorphes. Gauthier-Villars, Paris 1929.
• Unique analytical functions. Springer, Berlin 1936, 1953, 1974.
• Uniformization. Springer, Berlin 1953.
• with Veikko Paatero: Introduction to Function Theory . Birkhäuser, Basel 1965.

Others

• with Frithiof Nevanlinna: Absolute Analysis. Basic Teachings of Mathematical Sciences 102, Springer, Berlin 1959.
• Space, time and relativity. Birkhäuser, Basel 1964.
• with Paul Edwin Kustaanheimo: Fundamentals of Geometry. Birkhäuser, Basel 1976.

literature

• Olli Lehto : Sublime worlds - the life of Rolf Nevanlinna. From the Finnish by Manfred Stern. Birkhäuser, Basel 2008, ISBN 978-3-7643-7701-4 . Original: Korkeat Maailmat. Rolf Nevanlinnan elämä. Otava Publishing House, Helsinki 2001.
• Lars Ahlfors : The mathematical work of Rolf Nevanlinna. Annales Academiae Scientiarum Fennicae, Helsinki 1976.

Web links

• John J. O'Connor, Edmund F. Robertson :  Rolf Nevanlinna. In: MacTutor History of Mathematics archive .
• Biography of Pekonen (English)
• Literature by and about Rolf Nevanlinna in the catalog of the German National Library

Individual evidence

1. ↑ Olli Lehto: Sublime Worlds. P. 16.
2. ↑ Olli Lehto: Sublime Worlds. P. 2, 23.
3. ↑ Olli Lehto: Sublime Worlds. P. 25 f.
4. ↑ Olli Lehto: Sublime Worlds. P. 31.
5. ↑ Olli Lehto: Sublime Worlds. P. 32.
6. ↑ Olli Lehto: Sublime Worlds. P. 33.
7. ↑ Olli Lehto: Sublime Worlds. P. 37
8. ↑ Olli Lehto: Sublime Worlds. P. 40
9. ↑ Gábor Szegő : Review on About the properties of analytical functions in the vicinity of a singular point or line. In: Yearbook on the Progress of Mathematics . 1922 ( online ).
10. ↑ Olli Lehto: Sublime Worlds. P. 59
11. ^ R. Nevanlinna, On the theory of meromorphic functions, Acta Mathematica, Volume 46, pp. 1-99, 1925.
12. ^ H. Weyl, Meromorphic functions and analytic curves , Princeton University Press, 1943. On page 8, Weyl writes: The appearance of this paper has been one of the few great mathematical events of our century.
13. ↑ Olli Lehto: Sublime Worlds. P. 114
14. ↑ Olli Lehto: Sublime Worlds. P. 76.
15. ↑ Letter from Rudolf Hess to the Reich Minister of Education of January 10, 1936, German Federal Archives Berlin, quoted from: Olli Lehto: Eröhee Welten. P. 124.
16. ↑ Olli Lehto: Sublime Worlds. P. 159
17. ↑ Olli Lehto Sublime Worlds , p. 148
18. ↑ Osmo Pekonen: L'affaire Because à Helsinki 1939. In: Gazette des Mathématiciens. Société mathématique de France, No. 52, April 1992.
19. ↑ Olli Lehto: Sublime Worlds. P. 144ff.
20. ↑ Olli Lehto: Sublime Worlds. P. 156
21. ↑ Olli Lehto: Sublime Worlds. P. 164ff.
22. ↑ Olli Lehto: Sublime Worlds. P. 173.
23. ↑ Olli Lehto: Sublime Worlds. P. 175.
24. ↑ Olli Lehto: Sublime Worlds. P. 176 ff.
25. ↑ Olli Lehto: Sublime Worlds. P. 275
26. ↑ Olli Lehto: Sublime Worlds. P. 130
27. ↑ Olli Lehto: Sublime Worlds. P. 277