Arne Beurling

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Arne Beurling
Born (1905-02-03)3 February 1905
Died 20 November 1986(1986-11-20) (aged 81)
Nationality Swedish
Fields Mathematics
Institutions Uppsala University
Institute for Advanced Study
Alma mater Uppsala University
Doctoral advisor Anders Wiman
Doctoral students Göran Borg
Lennart Carleson
Yngve Domar
Carl-Gustav Esseen
Known for Beurling algebra
Beurling factorization
Beurling–Lax theorem
Beurling–Nyman criterion

Arne Carl-August Beurling (3 February 1905 – 20 November 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.[1] 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.[2]

Beurling was elected a Fellow of the American Academy of Arts and Sciences in 1970.[3] He was the doctoral advisor of Lennart Carleson and Carl-Gustav Esseen.

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.[4]

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[edit]

Beurling's prowess as a cryptanalysist is the subject of the 2005 short opera Krypto CEG by Jonas Sjöstrand and Kimmo Eriksson.

See also[edit]


  1. ^ Beckman, B. (2002). Codebreakers: Arne Beurling and the Swedish crypto program during World War II. Providence, RI: American Mathematical Society. 
  2. ^ Rijmenants, Dirk (2008), Focus: Siemens & Halske T-52 
  3. ^ "Book of Members, 1780–2010: Chapter B" (PDF). American Academy of Arts and Sciences. Archived (PDF) from the original on 25 July 2011. Retrieved 25 June 2011. 
  4. ^

External links[edit]