Arne Beurling

Arne Karl August Beurling ( born February 3, 1905 in Gothenburg, † November 20, 1986 in Princeton ) was a Swedish mathematician who made ​​a name for himself as an analyst. Only much later, his role in deciphering the German secret writer by the Swedes in 1940 was known.

Life

Arne Beurling was Karl August in Gothenburg to school and studied from 1924 in Uppsala mathematics. In 1926 he passed the exam candidate and earned a licentiate in 1928. After military service, he was awarded his doctorate in 1933 in Uppsala with a thesis Études sur un problème de majoration Anders Wiman. His Thèse also appeared as a book, introduced him and gave him the same year a lectureship in Uppsala. In 1934 he qualified as a professor in 1937 and professor, a position he held until 1952. 1948/49, he was a visiting professor at Harvard University, where his friend Lars Ahlfors was a professor. In 1952 he went to Princeton to the Institute for Advanced Study, where he became professor in 1954 - 1965 he received even Einstein's former office at No. 115 in 1973, he retired.

In 1963 he received the Celsius Gold Medal of the Royal Swedish Academy. He was an honorary member of the Swedish Mathematical Society and its first president. 1976/77 were the seminars at the Mittag-Leffler Institute in Stockholm a whole " Arne Beurling - Year" dedicated to his work. Among his students, among others, Carl- Gustav Esseen, Göran Borg and Lennart Carleson. Beurling is buried in the family grave in Stockholm.

Work

Beurling was a leading proponent of analysis. He cooperated with about Jacques Deny, Lars Ahlfors and Paul Malliavin. He worked, among others, function theory, harmonic analysis, especially Fourier integrals, potential theory, differential equations, distribution of primes ( " Beurling zeta function") and Dirichlet series.

His dissertation of 1933 was dedicated function-theoretic issues. There he led among other things the notion of extremal distance and was able to give a new proof of a short time before proved by Ahlfors conjecture of Denjoy on asymptotic values ​​of entire functions.

Together with Ahlfors he extended it later to the concept of extremal length, that is, for example, in the theory of quasi -conformal mappings, of great importance. In the potential theory comes from him, the concept of Dirichlet spaces.

This also had great influence in the probability theory. In harmonic analysis, he followed the work of Norbert Wiener, who was one of the few contemporary mathematicians who Beurling read. His lectures were based primarily on their own work.

In 1950 he gave a plenary lecture at the International Congress of Mathematicians in Cambridge (Massachusetts ) (On zero sets in harmonic analysis and function theory ).

Deciphering the secret writer

While in England, for example, the diplomatic traffic and the news from Germany ran specifically for the deciphering of the German secret writer, over the the German - occupied Norway and Germany's ally Finland cables in Sweden, with great effort, the first computer ( " Colossus " ) were developed, managed Beurling in the summer of 1940 in Sweden, to crack the code, and in just two weeks without knowing the structure of the machine, or any plain texts. However, he could by some very serious mistakes of the German operators, by giving, for example, messages up to 40 times with the same key benefit.

The Cryptography historian David Kahn called it one of the most remarkable cryptographic services during the Second World War. His exact procedure Beurling has retained for itself, but it was described by his former colleagues at the Swedish Beckman Entzifferungsdienst in broad outline in a book. Thanks to the work of Beurling multiple copies of the secret recorder built and the systematic reconstruction of the daily changing keys could be organized. So did the Swedes, among other early knowledge of the " Barbarossa " plans of the Germans for the attack on the Soviet Union. Of the deciphering both the Soviet Union learned ( through an agent, who worked as a Swedish courier ) and the Germans in 1942 ( about the friendly with them Finns ), so that they began from 1942, incorporate difficulties in the encryption and the cable traffic over Sweden for avoided important messages. Occasionally, the Swedes were able in 1943 to break into the cipher (thanks to an error in the introduction of new cipher ), 1944 heard that but with the introduction of new cipher machines altogether.