Jakob Nielsen (15 October 1890 in Mjels,
Als
Amyotrophic lateral sclerosis (ALS), also known as motor neuron disease (MND) or—in the United States—Lou Gehrig's disease (LGD), is a rare, terminal neurodegenerative disorder that results in the progressive loss of both upper and low ...
– 3 August 1959 in
Helsingør
Helsingør ( , ; ), classically known in English as Elsinore ( ), is a coastal city in northeastern Denmark. Helsingør Municipality had a population of 63,953 on 1 January 2025, making it the 23rd most populated municipality in Denmark. Helsin ...
) 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, mathematical structure, structure, space, Mathematica ...
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 automorphism ...
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—in the United States—Lou Gehrig's disease (LGD), is a rare, terminal neurodegenerative disorder that results in the progressive loss of both upper and low ...
in
North Schleswig
North is one of the four compass points or cardinal directions. It is the opposite of south and is perpendicular to east and west. ''North'' is a noun, adjective, or adverb indicating direction or geography.
Etymology
The word ''north'' is ...
, 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 being a member of an illicit student club. Nevertheless, he matriculated at the
University of Kiel
Kiel University, officially the Christian Albrecht University of Kiel, (, abbreviated CAU, known informally as Christiana Albertina) is a public research university in the city of Kiel, Germany. It was founded in 1665 as the ''Academia Holsator ...
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
Constantinople (#Names of Constantinople, see other names) was a historical city located on the Bosporus that served as the capital of the Roman Empire, Roman, Byzantine Empire, Byzantine, Latin Empire, Latin, and Ottoman Empire, Ottoman empire ...
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, a subset of a group G is a subgroup of G if the members of that subset form a group with respect to the group operation in G.
Formally, given a group (mathematics), group under a binary operation ...
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''− ...
is free. In 1926
Otto Schreier
Otto Schreier (3 March 1901 in Vienna, Austria – 2 June 1929 in Hamburg, Germany) was a Jewish-Austrian mathematician who made major contributions in combinatorial group theory and in the topology of Lie groups.
Life
His parents were the arch ...
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 gro ...
. Also in 1921 Nielsen moved to the
Royal Veterinary and Agricultural University
The Royal Veterinary and Agricultural University (, abbr. KVL, , abbr. RVA) was a veterinary and agricultural science university in Denmark. It was founded in 1856 and operated until 2007, when it became a part of the University of Copenhagen. It ...
in Copenhagen, where he would stay until 1925, when he moved to the
Technical University in Copenhagen.
He also proved the
Dehn–Nielsen theorem 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 (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 ...
some efforts were made to bring Nielsen to the United States as it was feared that he would be assaulted by the
Nazis
Nazism (), formally named National Socialism (NS; , ), is the far-right politics, far-right Totalitarianism, totalitarian socio-political ideology and practices associated with Adolf Hitler and the Nazi Party (NSDAP) in Germany. During H ...
. 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 (, KU) is a public university, public research university in Copenhagen, Copenhagen, Denmark. Founded in 1479, the University of Copenhagen is the second-oldest university in Scandinavia, after Uppsala University.
...
, 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 (UNESCO ) is a List of specialized agencies of the United Nations, specialized agency of the United Nations (UN) with the aim of promoting world peace and International secur ...
, where he served on the executive board from 1952 to 1958.
Bibliography
2011 pbk edition*
*
[
*
]
See also
* Fenchel–Nielsen coordinates
* Nielsen transformation
* 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'', there ...
* Nielsen realization problem
References
External links
*
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{{DEFAULTSORT:Nielsen, Jakob
1890 births
1959 deaths
20th-century Danish mathematicians
People from Sønderborg Municipality