Arne Carl-August Beurling (3 February 1905 – 20 November 1986) was a

Swedish Swedish or ' may refer to: Anything from or related to Sweden, a country in Northern Europe. Or, specifically: * Swedish language, a North Germanic language spoken primarily in Sweden and Finland ** Swedish alphabet, the official alphabet used by ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

and

professor Professor (commonly abbreviated as Prof.) is an Academy, academic rank at university, universities and other tertiary education, post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin ...

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

Uppsala University Uppsala University (UU) () is a public university, public research university in Uppsala, Sweden. Founded in 1477, it is the List of universities in Sweden, oldest university in Sweden and the Nordic countries still in operation. Initially fou ...

(1937–1954) and later at the

Institute for Advanced Study The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...

Princeton, New Jersey The Municipality of Princeton is a Borough (New Jersey), borough in Mercer County, New Jersey, United States. It was established on January 1, 2013, through the consolidation of the Borough of Princeton, New Jersey, Borough of Princeton and Pri ...

. Beurling worked extensively in

harmonic analysis Harmonic analysis is a branch of mathematics concerned with investigating the connections between a function and its representation in frequency. The frequency representation is found by using the Fourier transform for functions on unbounded do ...

complex analysis Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic ...

and

potential theory In mathematics and mathematical physics, potential theory is the study of harmonic functions. The term "potential theory" was coined in 19th-century physics when it was realized that the two fundamental forces of nature known at the time, namely g ...

. The " Beurling factorization" helped mathematical scientists to understand the

Wold decomposition In mathematics, particularly in operator theory, Wold decomposition or Wold–von Neumann decomposition, named after Herman Wold and John von Neumann, is a classification theorem for isometric linear operators on a given Hilbert space. It states t ...

, and inspired further work on the

invariant subspace In mathematics, an invariant subspace of a linear mapping ''T'' : ''V'' → ''V '' i.e. from some vector space ''V'' to itself, is a subspace ''W'' of ''V'' that is preserved by ''T''. More generally, an invariant subspace for a collection of ...

s of linear operators and

operator algebras In functional analysis, a branch of mathematics, an operator algebra is an algebra of continuous linear operators on a topological vector space, with the multiplication given by the composition of mappings. The results obtained in the study o ...

, e.g. Håkan Hedenmalm's factorization theorem for

Bergman space In complex analysis, functional analysis and operator theory, a Bergman space, named after Stefan Bergman, is a function space of holomorphic functions in a domain ''D'' of the complex plane that are sufficiently well-behaved at the boundary that ...

s. He is perhaps most famous for single-handedly decrypting an early version of the German cipher machine

Siemens and Halske T52 The Siemens & Halske T52, also known as the Geheimschreiber ("secret teleprinter"), or ''Schlüsselfernschreibmaschine'' (SFM), was a World War II German cipher machine and teleprinter produced by the electrical engineering firm Siemens & Halske. ...

in a matter of two weeks during 1940, using only pen and paper. This machine's cipher is generally considered to be more complicated than that of the more famous

Enigma machine The Enigma machine is a cipher device developed and used in the early- to mid-20th century to protect commercial, diplomatic, and military communication. It was employed extensively by Nazi Germany during World War II, in all branches of the W ...

. Beurling's method of decrypting military telegrams between Norway and Germany worked from June 1940 right up until 1943 when the Germans changed equipment.

Early life

Beurling was born on 3 February 1905 in

Gothenburg Gothenburg ( ; ) is the List of urban areas in Sweden by population, second-largest city in Sweden, after the capital Stockholm, and the fifth-largest in the Nordic countries. Situated by the Kattegat on the west coast of Sweden, it is the gub ...

, Sweden and was the son of the landowner Konrad Beurling and baroness Elsa Raab. After

graduating A graduation is the awarding of a diploma by an educational institution. It may also refer to the ceremony that is associated with it, which can also be called commencement, congregation, convocation or invocation. The date of the graduation ...

in 1924, he was enrolled at the

where he received a Bachelor of Arts degree in 1926 and two years later a Licentiate of Philosophy degree.

Career

Early career

Beurling was assistant teacher at Uppsala University from 1931 to 1933. He received his doctorate in mathematics in 1933 for his dissertation ''Études sur un problème de majoration''. Beurling was a

docent The term "docent" is derived from the Latin word , which is the third-person plural present active indicative of ('to teach, to lecture'). Becoming a docent is often referred to as habilitation or doctor of science and is an academic qualifi ...

of mathematics at Uppsala University from 1933 and then professor of mathematics from 1937 to 1954.

World War II

In the summer of 1940 he single-handedly

decipher DECIPHER is a web-based resource and database of genomic variation data from analysis of patient DNA. It documents submicroscopic Chromosome abnormality, chromosome abnormalities (Deletion (genetics), microdeletions and Gene duplication, duplic ...

ed and

reverse-engineer Reverse engineering (also known as backwards engineering or back engineering) is a process or method through which one attempts to understand through deductive reasoning how a previously made device, process, system, or piece of software accompl ...

ed an early version of the

also known as the ''Geheimfernschreiber'' ("secret teletypewriter") used by

Nazi Germany Nazi Germany, officially known as the German Reich and later the Greater German Reich, was the German Reich, German state between 1933 and 1945, when Adolf Hitler and the Nazi Party controlled the country, transforming it into a Totalit ...

World War II World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...

for sending

cipher In cryptography, a cipher (or cypher) is an algorithm for performing encryption or decryption—a series of well-defined steps that can be followed as a procedure. An alternative, less common term is ''encipherment''. To encipher or encode i ...

ed 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 A teleprinter (teletypewriter, teletype or TTY) is an electromechanical device that can be used to send and receive typed messages through various communications channels, in both point-to-point (telecommunications), point-to-point and point- ...

traffic passing through Sweden from

Norway Norway, officially the Kingdom of Norway, is a Nordic countries, Nordic country located on the Scandinavian Peninsula in Northern Europe. The remote Arctic island of Jan Mayen and the archipelago of Svalbard also form part of the Kingdom of ...

on a cable. In this way, Swedish authorities knew about

Operation Barbarossa Operation Barbarossa was the invasion of the Soviet Union by Nazi Germany and several of its European Axis allies starting on Sunday, 22 June 1941, during World War II. More than 3.8 million Axis troops invaded the western Soviet Union along ...

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 The National Defence Radio Establishment (, FRA) is a Swedish government agency organised under the Ministry of Defence. The two main tasks of FRA are signals intelligence (SIGINT), and support to government authorities and state-owned companie ...

(''FRA''). The cypher in the ''Geheimfernschreiber'' is generally considered to be more complex than the cypher used in the Enigma machines.

Later life

He was visiting professor at

Harvard University Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyma ...

from 1948 to 1949. From 1954 he was professor at the

in Princeton, New Jersey,

United States The United States of America (USA), also known as the United States (U.S.) or America, is a country primarily located in North America. It is a federal republic of 50 U.S. state, states and a federal capital district, Washington, D.C. The 48 ...

, where he took over

Albert Einstein Albert Einstein (14 March 187918 April 1955) was a German-born theoretical physicist who is best known for developing the theory of relativity. Einstein also made important contributions to quantum mechanics. His mass–energy equivalence f ...

's office. He was the

doctoral advisor A doctoral advisor (also dissertation director, dissertation advisor; or doctoral supervisor) is a member of a university faculty whose role is to guide graduate students who are candidates for a doctorate, helping them select coursework, as well ...

Lennart Carleson Lennart Axel Edvard Carleson (born 18 March 1928) is a Swedish mathematician, known as a leader in the field of harmonic analysis. One of his most noted accomplishments is his proof of Lusin's conjecture. He was awarded the Abel Prize in 200 ...

and Carl-Gustav Esseen.

Personal life

Arne Beurling was first married (1936–40) to Britta Östberg (born 1907), daughter of Henrik Östberg and Gerda Nilsson. In 1950 he married Karin Lindblad (1920–2006), daughter of ironmonger Henric Lindblad and Wanja Bengtsson. Karin was a distinguished Ph.D. student from Uppsala University. When they lived in Princeton, she worked in a biochemistry lab at Princeton University. He had two children from his first marriage — Pehr-Henrik (1936–1962) and Jane (1938–1992). Beurling's great-grandfather was Pehr Henrik Beurling (1758 or 1763–1806), who founded a high quality clock factory in

Stockholm Stockholm (; ) is the Capital city, capital and List of urban areas in Sweden by population, most populous city of Sweden, as well as the List of urban areas in the Nordic countries, largest urban area in the Nordic countries. Approximately ...

in 1783.

Death

Arne Beurling died in 1986 and was buried at

Norra begravningsplatsen Norra begravningsplatsen, literally "The Northern Burial Place" in Swedish, is a major cemetery of the Stockholm urban area, located in Solna Municipality. Inaugurated on 9 June 1827, it is the burial site for a number of Swedish notables. Th ...

Solna Solna ( or , ), also known as Solna Municipality, is a municipality in central Stockholm County, Sweden, located just north of Stockholm City Centre. Its seat is located in the town of Solna, which is a part of the Stockholm urban area. Solna i ...

In popular culture

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

Kimmo Eriksson Kimmo is a Finnish given name for males. Notable people with the name include: * Kimmo Kapanen (born 1974), Finnish professional ice hockey goaltender * Kimmo Kiljunen (born 1951), member of the Finnish parliament * Kimmo Kinnunen (born 1968), fo ...

Awards and decorations

*Knight of the

Order of the Polar Star The Royal Order of the Polar Star (Swedish language, Swedish: ''Kungliga Nordstjärneorden''), sometimes translated as the Royal Order of the North Star, is a Swedish order of chivalry created by Frederick I of Sweden, King Frederick I on 23 F ...

*Knight of the

Order of Vasa The Royal Order of Vasa () is a Swedish order of chivalry founded on 29 May 1772 by Gustav III, King Gustav III. It is awarded to Swedish citizens for service to state and society especially in the fields of agriculture, mining and commerce. His ...

Honours

*Honorary member of the Göteborgs nation at

(1937) *Member of the

Royal Swedish Academy of Sciences The Royal Swedish Academy of Sciences () is one of the Swedish Royal Academies, royal academies of Sweden. Founded on 2 June 1739, it is an independent, non-governmental scientific organization that takes special responsibility for promoting nat ...

(1937) *Member of the Royal Society of the Humanities at Lund (''Kungliga Humanistiska Vetenskapssamfundet i Lund'') (1937) *Member of the

Finnish Society of Sciences and Letters The Finnish Society of Sciences and Letters (, , ) is a Finnish learned society for natural sciences, social sciences and humanities. It is a bilingual (Swedish and Finnish) science academy and the oldest of the four science academies in Finland. ...

(1942) *Member of the

Royal Physiographic Society in Lund The Royal Physiographic Society in Lund (), is one of the Royal Academies in Sweden. It was founded in Lund, on December 2, 1772, and received a Royal Charter by Gustav III, on March 6, 1778. *Member of the

Royal Danish Academy of Sciences and Letters The Royal Danish Academy of Sciences and Letters ({{Langx, da, Det Kongelige Danske Videnskabernes Selskab or ''Videnskabernes Selskab'') is a Danish academy of science. The Royal Danish Academy was established on 13 November 1742, and was create ...

(1951) *Fellow of the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (The Academy) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and other ...

(1970)

References

External links

Arne Beurling and the success of Swedish Signal Intelligence
* * {{DEFAULTSORT:Beurling, Arne 1905 births 1986 deaths 20th-century cryptographers 20th-century Swedish mathematicians Uppsala University alumni Institute for Advanced Study faculty Members of the Royal Swedish Academy of Sciences Members of the Royal Physiographic Society in Lund Members of the Royal Danish Academy of Sciences and Letters Fellows of the American Academy of Arts and Sciences Scientists from Gothenburg Knights of the Order of the Polar Star Knights of the Order of Vasa Burials at Norra begravningsplatsen Swedish cryptographers Members of the Royal Society of Sciences in Uppsala