Arne Beurling
Encyclopedia
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 subspace
s of linear operators and operator algebras, e.g. Håkan Hedenmalm's factorization theorem for Bergman space
s.
In the summer of 1940 he single-handedly decipher
ed and reverse-engineer
ed 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 cipher
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
traffic passing through Sweden from Norway
on a cable. In this way, Swedish authorities knew about Operation Barbarossa
before it occurred. Not wanting to 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 elected a Fellow of the American Academy of Arts and Sciences
in 1970. He was the doctoral advisor
of Lennart Carleson
and Carl-Gustav Esseen
.
Beurling's great-grandfather was Per Henric Beurling (1758 (or 1763) – 1806), who founded a high quality clock factory in Stockholm in 1783.
Sweden
Sweden , officially the Kingdom of Sweden , is a Nordic country on the Scandinavian Peninsula in Northern Europe. Sweden borders with Norway and Finland and is connected to Denmark by a bridge-tunnel across the Öresund....
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and professor
Professor
A professor is a scholarly teacher; the precise meaning of the term varies by country. Literally, professor derives from Latin as a "person who professes" being usually an expert in arts or sciences; a teacher of high rank...
of mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
at Uppsala University
Uppsala University
Uppsala University is a research university in Uppsala, Sweden, and is the oldest university in Scandinavia, founded in 1477. It consistently ranks among the best universities in Northern Europe in international rankings and is generally considered one of the most prestigious institutions of...
(1937–1954) and later at the Institute for Advanced Study
Institute for Advanced Study
The Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...
in Princeton, New Jersey
Princeton Township, New Jersey
Also Princeton Borough is an independent municipality completely surrounded by the township.Princeton North is a census-designated place and unincorporated area located within Princeton Township....
.
Beurling worked extensively in harmonic analysis
Harmonic analysis
Harmonic analysis is the branch of mathematics that studies the representation of functions or signals as the superposition of basic waves. It investigates and generalizes the notions of Fourier series and Fourier transforms...
, complex analysis
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 useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics,...
and potential theory
Potential theory
In mathematics and mathematical physics, potential theory may be defined as the study of harmonic functions.- Definition and comments :The term "potential theory" was coined in 19th-century physics, when it was realized that the fundamental forces of nature could be modeled using potentials which...
. The "Beurling factorization" helped mathematical scientists to understand the Wold decomposition
Wold decomposition
In operator theory, the Wold decomposition, named after Herman Wold, or Wold-von Neumann decomposition, after Wold and John von Neumann, is a classification theorem for isometric linear operators on a given Hilbert space...
, and inspired further work on the invariant subspace
Invariant subspace
In mathematics, an invariant subspace of a linear mappingfrom some vector space V to itself is a subspace W of V such that T is contained in W...
s of linear operators and operator algebras, e.g. Håkan Hedenmalm's factorization theorem for Bergman space
Bergman space
In complex analysis, a branch of mathematics, 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 they are absolutely integrable...
s.
In the summer of 1940 he single-handedly decipher
DECIPHER
DECIPHER is a web-based resource and database of array comparative genomic hybridization data from analysis of patient DNA. It documents submicroscopic chromosome abnormalities, including microdeletions and duplications, from over 6000 patients and maps them to the human genome using the Ensembl...
ed and reverse-engineer
Reverse engineering
Reverse engineering is the process of discovering the technological principles of a device, object, or system through analysis of its structure, function, and operation...
ed an early version of the Siemens and Halske T52
Siemens and Halske T52
The Siemens and Halske T52, also known as the Geheimfernschreiber , or Schlüsselfernschreibmaschine , was a World War II German teleprinter cipher machine...
also known as the Geheimfernschreiber (secret teletypewriter) used by Nazi Germany
Nazi Germany
Nazi Germany , also known as the Third Reich , but officially called German Reich from 1933 to 1943 and Greater German Reich from 26 June 1943 onward, is the name commonly used to refer to the state of Germany from 1933 to 1945, when it was a totalitarian dictatorship ruled by...
in World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
for sending cipher
Cipher
In cryptography, a cipher 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. In non-technical usage, a “cipher” is the same thing as a “code”; however, the concepts...
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
Teleprinter
A teleprinter is a electromechanical typewriter that can be used to communicate typed messages from point to point and point to multipoint over a variety of communication channels that range from a simple electrical connection, such as a pair of wires, to the use of radio and microwave as the...
traffic passing through Sweden from Norway
Norway
Norway , officially the Kingdom of Norway, is a Nordic unitary constitutional monarchy whose territory comprises the western portion of the Scandinavian Peninsula, Jan Mayen, and the Arctic archipelago of Svalbard and Bouvet Island. Norway has a total area of and a population of about 4.9 million...
on a cable. In this way, Swedish authorities knew about Operation Barbarossa
Operation Barbarossa
Operation Barbarossa was the code name for Germany's invasion of the Soviet Union during World War II that began on 22 June 1941. Over 4.5 million troops of the Axis powers invaded the USSR along a front., the largest invasion in the history of warfare...
before it occurred. Not wanting to 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
Swedish National Defence Radio Establishment
The National Defence Radio Establishment is a civilian establishment subordinate to the Ministry of Defence. The two main tasks of FRA are signals intelligence and support to government authorities and state owned companies regarding IT security.Interception of signals is done from fixed sites on...
(FRA). The cypher in the Geheimfernschreiber is generally considered to be more complex than the cypher used in the Enigma machines.
Beurling was elected a Fellow of the American Academy of Arts and Sciences
American Academy of Arts and Sciences
The American Academy of Arts and Sciences is an independent policy research center that conducts multidisciplinary studies of complex and emerging problems. The Academy’s elected members are leaders in the academic disciplines, the arts, business, and public affairs.James Bowdoin, John Adams, and...
in 1970. He was the doctoral advisor
Doctoral advisor
A doctoral advisor is an advanced member of a university faculty whose role is to guide a graduate student who is a candidate for a doctorate degree, helping them select coursework, as well as shaping, refining and directing the students' choice of sub-discipline...
of Lennart Carleson
Lennart Carleson
Lennart Axel Edvard Carleson is a Swedish mathematician, known as a leader in the field of harmonic analysis.-Life:He was a student of Arne Beurling and received his Ph.D. from Uppsala University in 1950...
and Carl-Gustav Esseen
Carl-Gustav Esseen
Carl-Gustav Esseen was a Swedish mathematician. His work was in the theory of probability. The Berry–Esseen theorem is named after him.-Life:...
.
Beurling's great-grandfather was Per Henric Beurling (1758 (or 1763) – 1806), who founded a high quality clock factory in Stockholm in 1783.