Jakob Nielsen (15 October 1890 in Mjels,
Als
Amyotrophic lateral sclerosis (ALS), also known as motor neuron disease (MND) or Lou Gehrig's disease, is a neurodegenerative disease that results in the progressive loss of motor neurons that control voluntary muscles. ALS is the most comm ...
– 3 August 1959 in
Helsingør) was a Danish
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 ...
known for his work on
automorphism
In mathematics, an automorphism is an isomorphism from a mathematical object to itself. It is, in some sense, a symmetry of the object, and a way of mapping the object to itself while preserving all of its structure. The set of all automorphis ...
s of
surface
A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. It is the portion or region of the object that can first be perceived by an observer using the senses of sight and touch, and is ...
s. He was born in the village Mjels on the island of
Als
Amyotrophic lateral sclerosis (ALS), also known as motor neuron disease (MND) or Lou Gehrig's disease, is a neurodegenerative disease that results in the progressive loss of motor neurons that control voluntary muscles. ALS is the most comm ...
in
North Schleswig
Southern Jutland ( da, Sønderjylland; German: Südjütland) is the name for the region south of the Kongeå in Jutland, Denmark and north of the Eider (river) in Schleswig-Holstein, Germany. The region north of the Kongeå is called da, Nørr ...
, in modern-day Denmark. His mother died when he was 3, and in 1900 he went to live with his aunt and was enrolled in the Realgymnasium. In 1907 he was expelled for membership to an illicit student club. Nevertheless, he matriculated at the
University of Kiel
Kiel University, officially the Christian-Albrecht University of Kiel, (german: Christian-Albrechts-Universität zu Kiel, abbreviated CAU, known informally as Christiana Albertina) is a university in the city of Kiel, Germany. It was founded in ...
in 1908.
Nielsen completed his doctoral dissertation in 1913. Soon thereafter, he was drafted into the German Imperial Navy. He was assigned to coastal defense. In 1915 he was sent to
Constantinople
la, Constantinopolis ota, قسطنطينيه
, alternate_name = Byzantion (earlier Greek name), Nova Roma ("New Rome"), Miklagard/Miklagarth (Old Norse), Tsargrad ( Slavic), Qustantiniya (Arabic), Basileuousa ("Queen of Cities"), Megalopolis (" ...
as a military adviser to the
Turkish Government. After the war, in the spring of 1919, Nielsen married Carola von Pieverling, a German medical doctor.
In 1920 Nielsen took a position at the
Technical University of Breslau. The next year he published a paper in Mathematisk Tidsskrift in which he proved that any
subgroup
In group theory, a branch of mathematics, given a group ''G'' under a binary operation ∗, a subset ''H'' of ''G'' is called a subgroup of ''G'' if ''H'' also forms a group under the operation ∗. More precisely, ''H'' is a subgroup ...
of a finitely generated
free group
In mathematics, the free group ''F'S'' over a given set ''S'' consists of all words that can be built from members of ''S'', considering two words to be different unless their equality follows from the group axioms (e.g. ''st'' = ''suu''−1' ...
is free. In 1926
Otto Schreier would generalize this result by removing the condition that the free group be finitely generated; this result is now known as the
Nielsen–Schreier theorem
In group theory, a branch of mathematics, the Nielsen–Schreier theorem states that every subgroup of a free group is itself free. It is named after Jakob Nielsen and Otto Schreier.
Statement of the theorem
A free group may be defined from a gr ...
. Also in 1921 Nielsen moved to the
Royal Veterinary and Agricultural University
The Royal Veterinary and Agricultural University ( da, Kongelige Veterinær- og Landbohøjskole, abbr. KVL) was a veterinary and agricultural science university in Denmark. It was founded in 1856 and operated until 2007, when it became a part of ...
in Copenhagen, where he would stay until 1925, when he moved to the
Technical University in Copenhagen.
He also proved the
Dehn–Nielsen theorem In mathematics, and more precisely in topology, the mapping class group of a surface, sometimes called the modular group or Teichmüller modular group, is the group of homeomorphisms of the surface viewed up to continuous (in the compact-open topo ...
on mapping class groups.
Nielsen was a Plenary Speaker of the
ICM in 1936 in Oslo.
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 World War II by country, vast majority of the world's countries—including all of the great power ...
some efforts were made to bring Nielsen to the United States as it was feared that he would be assaulted by the
Nazis
Nazism ( ; german: Nazismus), the common name in English for National Socialism (german: Nationalsozialismus, ), is the far-right totalitarian political ideology and practices associated with Adolf Hitler and the Nazi Party (NSDAP) in N ...
. Nielsen would, in fact, stay in Denmark during the war without being harassed by the Nazis.
In 1951 Nielsen became professor of mathematics at the
University of Copenhagen
The University of Copenhagen ( da, Københavns Universitet, KU) is a prestigious public university, public research university in Copenhagen, Copenhagen, Denmark. Founded in 1479, the University of Copenhagen is the second-oldest university in ...
, taking the position vacated by the death of
Harald Bohr
Harald August Bohr (22 April 1887 – 22 January 1951) was a Danish mathematician and footballer. After receiving his doctorate in 1910, Bohr became an eminent mathematician, founding the field of almost periodic functions. His brother was the ...
. He resigned this position in 1955 because of his international undertakings, in particular with
UNESCO
The United Nations Educational, Scientific and Cultural Organization is a List of specialized agencies of the United Nations, specialized agency of the United Nations (UN) aimed at promoting world peace and security through international coope ...
, where he served on the executive board from 1952 to 1958.
Bibliography
2011 pbk edition*
*
[
*
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See also
* Fenchel–Nielsen coordinates In mathematics, Fenchel–Nielsen coordinates are coordinates for Teichmüller space introduced by Werner Fenchel and Jakob Nielsen.
Definition
Suppose that ''S'' is a compact Riemann surface of genus
Genus ( plural genera ) is a taxonomic ra ...
* Nielsen transformation
In mathematics, especially in the area of abstract algebra known as combinatorial group theory, Nielsen transformations, named after Jakob Nielsen, are certain automorphisms of a free group which are a non-commutative analogue of row reduction a ...
* Nielsen theory Nielsen theory is a branch of mathematical research with its origins in topological fixed-point theory. Its central ideas were developed by Danish mathematician Jakob Nielsen, and bear his name.
The theory developed in the study of the so-called ' ...
* Nielsen–Thurston classification
In mathematics, Thurston's classification theorem characterizes homeomorphisms of a compact orientable surface. William Thurston's theorem completes the work initiated by .
Given a homeomorphism ''f'' : ''S'' → ''S'', ther ...
* Nielsen realization problem
The Nielsen realization problem is a question asked by about whether finite subgroups of mapping class groups can act on surfaces, that was answered positively by .
Statement
Given an oriented surface, we can divide the group Diff(''S''), the gr ...
References
External links
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{{DEFAULTSORT:Nielsen, Jakob
1890 births
1959 deaths
20th-century Danish mathematicians
People from Sønderborg Municipality