February 3, 1905|
|Died||November 20, 1986(aged 81)|
Institute for Advanced Study
|Alma mater||Uppsala University|
|Doctoral advisor||Anders Wiman|
|Doctoral students||Goeran Borg
|Known for||Beurling algebra
Arne Carl-August Beurling (February 3, 1905 – November 20, 1986) was a Swedish mathematician and professor of mathematics at Uppsala University (1937–1954) and later at the Institute for Advanced Study in Princeton, New Jersey.
Beurling worked extensively in harmonic analysis, complex analysis and potential theory. The "Beurling factorization" helped mathematical scientists to understand the Wold decomposition, and inspired further work on the invariant subspaces of linear operators and operator algebras, e.g. Håkan Hedenmalm's factorization theorem for Bergman spaces.
In the summer of 1940 he single-handedly deciphered and reverse-engineered an early version of the Siemens and Halske T52 also known as the Geheimfernschreiber (secret teletypewriter) used by Nazi Germany in World War II for sending ciphered messages. The T52 was one of the so-called "Fish cyphers", that, using transposition, created nearly one quintillion (893 622 318 929 520 960) different variations. It took Beurling two weeks to solve the problem using pen and paper. Using Beurling's work, a device was created that enabled Sweden to decipher German teleprinter traffic passing through Sweden from Norway on a cable. In this way, Swedish authorities knew about Operation Barbarossa before it occurred. Since the Swedes would not reveal how this knowledge was attained, the Swedish warning was not treated as credible by Soviets.
This became the foundation for the Swedish National Defence Radio Establishment (FRA). The cypher in the Geheimfernschreiber is generally considered to be more complex than the cypher used in the Enigma machines.
Beurling was married to Karin V. Beurling, who was a distinguished PhD student from Uppsala University. When they lived in Princeton, she worked in a biochemistry lab at Princeton University. 
Beurling's great-grandfather was Per Henric Beurling (1758 (or 1763) – 1806), who founded a high quality clock factory in Stockholm in 1783.
In popular culture
- Beckman, B. (2002). Codebreakers: Arne Beurling and the Swedish crypto program during World War II. Providence, RI: American Mathematical Society.
- Rijmenants, Dirk (2008), Focus: Siemens & Halske T-52
- "Book of Members, 1780–2010: Chapter B". American Academy of Arts and Sciences. Archived from the original on 25 July 2011. Retrieved June 25, 2011.
- Arne Beurling and the success of Swedish Signal Intelligence
- O'Connor, John J.; Robertson, Edmund F., "Arne Beurling", MacTutor History of Mathematics archive, University of St Andrews.
- Arne Beurling at the Mathematics Genealogy Project
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