Arne Beurling

Bust in memory of Arne Beurling in the park of Uppsala University

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 primarily as an analyst. His role in the deciphering of the German secret writer by the Swedes in 1940 did not become known until much later .

Life

Arne Karl August Beurling went to school in Gothenburg and studied mathematics in Uppsala from 1924. In 1926 he passed the candidate examination and obtained his licentiate in 1928 . After military service, he received his doctorate in Uppsala in 1933 with the dissertation Études sur unproblemème de majoration with Anders Wiman . His Thèse also appeared as a book, made him known and in the same year gave him a teaching position in Uppsala. He completed his habilitation in 1934 and became a professor in 1937, which he remained until 1952. 1948/49 he was visiting professor at Harvard University , where his friend Lars Ahlfors was professor. In 1952 he went to Princeton to the Institute for Advanced Study , where he became a professor in 1954 - in 1965 he even got Einstein's former office 115 there. In 1973 he retired.

In 1963 he received the Celsius gold medal from the Royal Swedish Academy. He was an honorary member of the Swedish Mathematical Society and its first president. In 1976/77 the seminars at the Mittag-Leffler Institute in Stockholm devoted an entire "Arne Beurling year" to his work. His students include Carl-Gustav Esseen , Göran Borg and Lennart Carleson . Beurling is buried in the family grave in Stockholm.

plant

Beurling was a leading proponent of analysis. He collaborated with Jacques Deny , Lars Ahlfors and Paul Malliavin . Among other things, he dealt with function theory, harmonic analysis, in particular Fourier integrals, potential theory, differential equations, the distribution of prime numbers (“Beurling zeta function”) and Dirichlet series.

His 1933 dissertation was devoted to functional theory topics. There he led, among other things, the concept of extremal distance and was thus a new proof of a short time before proved by Ahlfors conjecture of Denjoy on asymptotic values of entire type functions.

Together with Ahlfors, he later expanded this to include the concept of extreme length , which is of great importance, for example, in the theory of quasi-conformal mapping. In potential theory, he developed the concept of Dirichlet spaces.

This also had a major impact on probability theory. In harmonic analysis he followed the work of Norbert Wiener , who was one of the few contemporary mathematicians who read Beurling. Most of his lectures were based on his own work.

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

Decipherment of the secretary

While in England, especially for the deciphering of the German secret writer, via which, for example, diplomatic communications and messages from Germany to German-occupied Norway and to German ally Finland ran over cables in Sweden, the first computers ("Colossus") cost a lot of effort. were developed, Beurling managed to crack the code in Sweden as early as the summer of 1940, and in just two weeks without knowing the structure of the machine or any plaintext. However, he was able to benefit from some very gross errors made by the German operators who, for example, passed messages up to 40 times with the same key.

The cryptography historian David Kahn called this one of the most notable cryptographic accomplishments during World War II. Beurling kept his exact procedure to himself, but it was described in rough outline in a book by his former colleague Beckman at the Swedish deciphering service. Thanks to Beurling's work, several copies of the secretary could be made and the systematic reconstruction of the keys, which changed every day, was organized. Among other things, the Swedes had early knowledge of the Germans' “Barbarossa” plans for the attack on the Soviet Union. Both the Soviet Union (through an agent who worked as a Swedish courier) and the Germans found out about the decipherments in 1942 (through their Finns friends), so that from 1942 they began to incorporate difficulties in the encryption and the cable traffic via Sweden for avoid important messages. Occasionally the Swedes were still able to break into the cipher in 1943 (thanks to a mistake in the introduction of new cipher machines), but in 1944 this stopped altogether with the introduction of new cipher machines.

literature

• Bengt Beckman: Arne Beurling and Hitler's secret writer. Springer-Verlag 2006, ISBN 3-540-23720-8 (with an interview by Carleson and other memoirs, including Ahlfors in the Mathematical Intelligencer); the English translation of the book Svenska Kryptobedrifter originally published in Sweden in 1996 was published by the AMS in 2002.
• Ahlfors: The story of a friendship - recollections of Arne Beurling. Mathematical Intelligencer 1993, volume 3 (and recollections by Bo Kjellberg and John Wermer in the same volume).
• Ahlfors, Carleson: Arne Beurling in memoriam. Acta Mathematica, Vol. 161, 1988, p. 1.
• Beurling: Collected Works. Birkhäuser Verlag (Vol. 1 1989).

Web links

• Portrait photo
• Literature by and about Arne Beurling in the catalog of the German National Library
• Description of Beurling's cryptographic work by Lars Ulfving , translated from Swedish to English by Frode Weierud
• John J. O'Connor, Edmund F. Robertson :  Arne Beurling. In: MacTutor History of Mathematics archive .
• Review of Beckman's book by Bauer, PDF file, 72 kB, English, first in Mitteilungen DMV 2003

Individual evidence

1. ^ Siemens cipher telex T 52 a
2. ↑ Beurling kept his Swedish citizenship all his life.
3. ↑ Before that, during a visit to Finland, he had already broken into the code book of the Russian Baltic Fleet, and as early as 1931 during his military service, during which he attended cryptographic courses, he “cracked” an early cipher machine from Boris Hagelin, which the Swedes used themselves .
4. ↑ In contrast to the English, he did not even know the published patents
5. ^ Kahn: The Codebreakers. 1967, p. 482. However, the Anglo-Polish efforts to decipher Enigma were still secret at the time.
6. ↑ After Beckman, loc. Cit. P. 283, that was also a general attitude of Beurling in mathematics. He was hot-tempered and resentful about the use of research that was otherwise fairly generous with his students and colleagues. Like Gauss, he used to cover up the traces of how he arrived at his results.
7. ↑ But he was only in the Swedish decryption office FRA from 1946. Before retiring in 1991, he headed the cryptographic department.