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Ernst Sejersted Selmer (11 February 1920 – 8 November 2006) was a Norwegian
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, structure, space, models, and change. History On ...
, who worked in
number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777â ...
, as well as a
cryptologist This is a list of cryptographers. Cryptography is the practice and study of techniques for secure communication in the presence of third parties called adversaries. Pre twentieth century * Al-Khalil ibn Ahmad al-Farahidi: wrote a (now lost) book ...
. The
Selmer group In arithmetic geometry, the Selmer group, named in honor of the work of by , is a group constructed from an isogeny of abelian varieties. The Selmer group of an isogeny The Selmer group of an abelian variety ''A'' with respect to an isogeny ''f ...
of an
Abelian variety In mathematics, particularly in algebraic geometry, complex analysis and algebraic number theory, an abelian variety is a projective algebraic variety that is also an algebraic group, i.e., has a group law that can be defined by regular func ...
is named after him. His primary contributions to mathematics reside within the field of
diophantine equation In mathematics, a Diophantine equation is an equation, typically a polynomial equation in two or more unknowns with integer coefficients, such that the only solutions of interest are the integer ones. A linear Diophantine equation equates to a c ...
s. He started working as a
cryptologist This is a list of cryptographers. Cryptography is the practice and study of techniques for secure communication in the presence of third parties called adversaries. Pre twentieth century * Al-Khalil ibn Ahmad al-Farahidi: wrote a (now lost) book ...
during the
Second World War World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...
; due to his work, Norway became a
NATO The North Atlantic Treaty Organization (NATO, ; french: Organisation du traité de l'Atlantique nord, ), also called the North Atlantic Alliance, is an intergovernmental military alliance between 30 member states – 28 European and two No ...
superpower in the field of encryption.


Biography


Early life

Ernest S. Selmer was born in
Oslo Oslo ( , , or ; sma, Oslove) is the capital and most populous city of Norway. It constitutes both a county and a municipality. The municipality of Oslo had a population of in 2022, while the city's greater urban area had a population of ...
in the family of Professor Ernst W. Selmer and Ella Selmer (born Sejersted). He was the brother of Knut S. Selmer who married with Elisabeth Schweigaard, as well as first cousin of
Francis Sejersted Francis Sejersted (8 February 1936 – 25 August 2015) was a Norwegian history professor and the chairman of the Norwegian Nobel Committee (which awards the Nobel Peace Prize) from 1991 until 1995. Early life Sejersted was born in Oslo. He p ...
. Already early in school, Selmer demonstrated mathematical talent. When attending
Stabekk Stabekk is a suburban centre in the municipality of Bærum, Norway, west of Oslo. It is predominantly a residential area, with many residents commuting to Oslo. As of 2005 the population was 6,261. Bærum has the highest income per capita and the hi ...
high school he was an editor of the school's magazine ''Tall og tanker'' (numbers and thoughts). In 1938, he won Crown Prince Olav's Mathematics Prize for high school graduates. From 1942–1943, he studied at the
University of Oslo The University of Oslo ( no, Universitetet i Oslo; la, Universitas Osloensis) is a public research university located in Oslo, Norway. It is the highest ranked and oldest university in Norway. It is consistently ranked among the top universit ...
. As a student at the university during
World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...
, Selmer was involved in encrypting secret messages for the
Norwegian resistance movement The Norwegian resistance (Norwegian: ''Motstandsbevegelsen'') to the occupation of Norway by Nazi Germany began after Operation WeserĂĽbung in 1940 and ended in 1945. It took several forms: *Asserting the legitimacy of the exiled government, ...
. During the autumn of 1943 when the Germans forced the University to close he escaped to
Sweden Sweden, formally the Kingdom of Sweden,The United Nations Group of Experts on Geographical Names states that the country's formal name is the Kingdom of SwedenUNGEGN World Geographical Names, Sweden./ref> is a Nordic country located on ...
, just in time before the Nazi Germany secret police
Gestapo The (), abbreviated Gestapo (; ), was the official secret police of Nazi Germany and in German-occupied Europe. The force was created by Hermann Göring in 1933 by combining the various political police agencies of Prussia into one organi ...
closed the university and arrested the male students. In 1944 Selmer was sent to
London London is the capital and largest city of England and the United Kingdom, with a population of just under 9 million. It stands on the River Thames in south-east England at the head of a estuary down to the North Sea, and has been a majo ...
, where he took technical responsibility for all Norwegian military and civilian cipher machines. The communication was mainly carried out using the Hagelin cipher machine. When the war ended, Selmer returned to Norway, and in 1946, was hired as a lecturer in the
University of Oslo The University of Oslo ( no, Universitetet i Oslo; la, Universitas Osloensis) is a public research university located in Oslo, Norway. It is the highest ranked and oldest university in Norway. It is consistently ranked among the top universit ...
. In the same year, he started working for the Cipher Department of the Armed Forces Security Service as a consultant. With colleagues, he built a communication system for Norway's equivalent of the
MI5 The Security Service, also known as MI5 ( Military Intelligence, Section 5), is the United Kingdom's domestic counter-intelligence and security agency and is part of its intelligence machinery alongside the Secret Intelligence Service (MI6), Go ...
, which was used from 1949 till 1960. Selmer spent the spring of 1949 at the
Cambridge University , mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Schola ...
working with the famous mathematician JWS Cassels. As a result of their collaboration, a group related to an
Abelian variety In mathematics, particularly in algebraic geometry, complex analysis and algebraic number theory, an abelian variety is a projective algebraic variety that is also an algebraic group, i.e., has a group law that can be defined by regular func ...
—namely, the
Selmer group In arithmetic geometry, the Selmer group, named in honor of the work of by , is a group constructed from an isogeny of abelian varieties. The Selmer group of an isogeny The Selmer group of an abelian variety ''A'' with respect to an isogeny ''f ...
—was discovered and named after Selmer. In 1993,
Andrew Wiles Sir Andrew John Wiles (born 11 April 1953) is an English mathematician and a Royal Society Research Professor at the University of Oxford, specializing in number theory. He is best known for proving Fermat's Last Theorem, for which he was awar ...
used Selmer's group in his proof of the Fermat's last theorem.


Middle years

Selmer received his dr.philos in 1952 from the University of Oslo and was at the same time hired as a lecturer for the university. Among Selmer's lectures, his lectures on
data processing Data processing is the collection and manipulation of digital data to produce meaningful information. Data processing is a form of ''information processing'', which is the modification (processing) of information in any manner detectable by an ...
is of particular note, as it helped lay the foundation for the Department of Informatics at the university. In the same year, he received a
Rockefeller Foundation The Rockefeller Foundation is an American private foundation and philanthropic medical research and arts funding organization based at 420 Fifth Avenue, New York City. The second-oldest major philanthropic institution in America, after the Carneg ...
Fellowship to study in the
United States The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 states, a federal district, five major unincorporated territorie ...
during the years 1951–1952. Selmer arrived in January 1951 as a visiting scholar at the
Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...
in Princeton, N.J. where the
IAS machine The IAS machine was the first electronic computer built at the Institute for Advanced Study (IAS) in Princeton, New Jersey. It is sometimes called the von Neumann machine, since the paper describing its design was edited by John von Neumann, a ...
was being constructed for
John von Neumann John von Neumann (; hu, Neumann János Lajos, ; December 28, 1903 â€“ February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, engineer and polymath. He was regarded as having perhaps the widest cove ...
. During his stay in Princeton he also met with people such as
Albert Einstein Albert Einstein ( ; ; 14 March 1879 â€“ 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
,
J. Robert Oppenheimer J. Robert Oppenheimer (; April 22, 1904 – February 18, 1967) was an American theoretical physicist. A professor of physics at the University of California, Berkeley, Oppenheimer was the wartime head of the Los Alamos Laboratory and is often ...
and his countryman
Atle Selberg Atle Selberg (14 June 1917 – 6 August 2007) was a Norwegian mathematician known for his work in analytic number theory and the theory of automorphic forms, and in particular for bringing them into relation with spectral theory. He was awarded t ...
. Einstein is said to have been the first person Selmer met on arrival in Princeton on a Saturday afternoon, and apparently took on the task as campus guide with open arms. From Princeton, Selmer traveled to
Berkeley Berkeley most often refers to: *Berkeley, California, a city in the United States **University of California, Berkeley, a public university in Berkeley, California * George Berkeley (1685–1753), Anglo-Irish philosopher Berkeley may also refer ...
where he contributed to Paul Morton's construction of the CALDIC computer. He was hired by
Consolidated Engineering Corporation Consolidated Engineering Corporation was a chemical instrument manufacturer from 1937 to 1960 when it became a subsidiary of Bell and Howell Corp. History CEC was founded in 1937 by Herbert Hoover Jr., eldest son of former United States president ...
(CEC) on von Neumann's recommendation in late 1951 and designed much of the logic for their
Datatron The Datatron is a family of decimal vacuum tube computers developed by ElectroData Corporation and first shipped in 1954. The Datatron was later marketed by Burroughs Corporation after Burroughs acquired ElectroData in 1956. The Burroughs models of ...
computer, working closely with other CEC employees such as Sibyl M. Rock. Later the computer was named Burroughs 205 and it was the most serious competitor of
IBM 650 The IBM 650 Magnetic Drum Data-Processing Machine is an early digital computer produced by IBM in the mid-1950s. It was the first mass produced computer in the world. Almost 2,000 systems were produced, the last in 1962, and it was the first ...
. He returned to the
Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...
again as a visiting scholar in 1952. In late 1952, Selmer returned to Oslo, and started working on a military computer. A product of this work was implemented in a computer, which was installed in the
Norwegian Defence Research Establishment The Norwegian Defence Research Establishment (''Forsvarets forskningsinstitutt'' – ''FFI'') is a research institute that conducts research and development on behalf of the Norwegian Armed Forces and provides expert advice to political and mi ...
in 1957. On September 25, 1953 Selmer applied for a
U.S. Patent Under United States law, a patent is a right granted to the inventor of a (1) process, machine, article of manufacture, or composition of matter, (2) that is new, useful, and non-obvious. A patent is the right to exclude others, for a limited ...
for an Electronic Adder. This patent, No. 2,947,479, was awarded on August 2, 1960.


Later life

At the age of mere 37 Selmer took a position of a full professor in mathematics at the
University of Bergen The University of Bergen ( no, Universitetet i Bergen, ) is a research-intensive state university located in Bergen, Norway. As of 2019, the university has over 4,000 employees and 18,000 students. It was established by an act of parliament in 194 ...
, which was a huge feat in 1957. At the university he was involved in designing two ciphers for NATO. In 1962, a hotline between the Kremlin and Washington was established via the Norwegian-developed encryption equipment ETCRRM II (Electronic Teleprinter Cryptographic Regenerative Repeater Mixer) from STK. At the University of Bergen Selmer started studying Linear Shift Registers and lectured on the subject. He commissioned a theoretical basis for linear shift register sequences in the 1960s on behalf of the Cipher Department. His lecture notes were published several times, under the title "Linear Recurrence Relations over Finite Fields". In his lecture on EUROCRYPT'93, Ernst Sejersted Selmer gave an overview of what he had contributed to the field of cryptography. From 1960–1966, Selmer served as vice dean at the Faculty of Mathematics and Natural Sciences at the University of Bergen, and dean from 1966–1968. Selmer was a member of the Council for Electronic Data Processing in the
Norwegian state Norway, officially the Kingdom of Norway, is a Nordic country in Northern Europe, the mainland territory of which comprises the western and northernmost portion of the Scandinavian Peninsula. The remote Arctic island of Jan Mayen and the ...
from its establishment in 1961 to 1973.


Personal relations

Selmer was married to Signe Randi Johanne Faanes and had one daughter, the microbiologist Johanne-Sophie Selmer who was educated at
Karlstad University Karlstad University (Swedish ''Karlstads universitet'') is a state university in Karlstad, Sweden. It was originally established as the Karlstad campus of the University of Gothenburg in 1967, and this campus became an independent university col ...
. His wife became his support throughout his life, and his great efforts in many fields would probably not have been possible without her. While work was his life, he was also a man that gave his home and family high priority. One time Selmer would not want to break a deal with his daughter in favor of a meeting with
Fields Medal The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award ho ...
winner Alan Baker. Selmer was also fond of
gardening Gardening is the practice of growing and cultivating plants as part of horticulture. In gardens, ornamental plants are often grown for their flowers, foliage, or overall appearance; useful plants, such as root vegetables, leaf vegetables, fruits ...
as a hobby and the famous botanist Knut Fægri used to make excursions to Selmer's garden. In 1990 he retired with his wife in
Ski A ski is a narrow strip of semi-rigid material worn underfoot to glide over snow. Substantially longer than wide and characteristically employed in pairs, skis are attached to ski boots with ski bindings, with either a free, lockable, or partial ...
and was in good physical and mental shape until he was hit by a stroke in the fall of 2004, after the stroke he was never the same. On the 8th of November 2006 Selmer fell asleep quietly. Selmer was elected member of the
Norwegian Academy of Science and Letters The Norwegian Academy of Science and Letters ( no, Det Norske Videnskaps-Akademi, DNVA) is a learned society based in Oslo, Norway. Its purpose is to support the advancement of science and scholarship in Norway. History The Royal Frederick Univer ...
in 1961, and became a knight of the 1st class of the Order of St. Olav in 1983. In 2020, the University of Bergen published the book "Professor in Secret Service", which is a biography on Selmer.


Legacy

In honor of Prof. Ernst Sejersted Selmer the University of Bergen established th
Selmer Center
in 2003. The Selmer Center held a leading position in the field of cryptography nationally and internationally, with roots going back 70 years. Selmer is behind the algorithm used to calculate the check digits in Norwegian birth numbers. Norwegian-developed mathematical theory became an important contribution to the modernization of crypto-algorithms in NATO and the
NSA The National Security Agency (NSA) is a national-level intelligence agency of the United States Department of Defense, under the authority of the Director of National Intelligence (DNI). The NSA is responsible for global monitoring, collectio ...
. Selmer's advanced research formed the basis for National Security Agency to develop modern crypto machines.


Publications

*


References


External links


interview with SelmerSelmer center
{{DEFAULTSORT:Selmer, Ernst Sejersted 1920 births 2006 deaths Norwegian mathematicians Number theorists Academic staff of the University of Oslo Academic staff of the University of Bergen Institute for Advanced Study visiting scholars Members of the Norwegian Academy of Science and Letters Royal Norwegian Society of Sciences and Letters