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Jakob Nielsen (mathematician)
Encyclopedia
Denmark
Denmark is a Scandinavian country in Northern Europe. The countries of Denmark and Greenland, as well as the Faroe Islands, constitute the Kingdom of Denmark . It is the southernmost of the Nordic countries, southwest of Sweden and south of Norway, and bordered to the south by Germany. Denmark...
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....
known for his work on automorphism
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 automorphisms of an object forms a group, called the automorphism...
s of surface
Surface
In mathematics, specifically in topology, a surface is a two-dimensional topological manifold. The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional Euclidean space R3 — for example, the surface of a ball...
s. He was born in the village Mjels on the island of Als in North Schleswig, in modern day Denmark
Denmark
Denmark is a Scandinavian country in Northern Europe. The countries of Denmark and Greenland, as well as the Faroe Islands, constitute the Kingdom of Denmark . It is the southernmost of the Nordic countries, southwest of Sweden and south of Norway, and bordered to the south by Germany. 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
University of Kiel
The University of Kiel is a university in the city of Kiel, Germany. It was founded in 1665 as the Academia Holsatorum Chiloniensis by Christian Albert, Duke of Holstein-Gottorp and has approximately 23,000 students today...
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
Constantinople was the capital of the Roman, Eastern Roman, Byzantine, Latin, and Ottoman Empires. Throughout most of the Middle Ages, Constantinople was Europe's largest and wealthiest city.-Names:...
as a military adviser to the Turkish Government
Ottoman Empire
The Ottoman EmpireIt was usually referred to as the "Ottoman Empire", the "Turkish Empire", the "Ottoman Caliphate" or more commonly "Turkey" by its contemporaries...
. After the war, in the spring of 1919, Nielsen married Carola von Pieverling, a German
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
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
Subgroup
In group theory, 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 G if the restriction of * to H x H is a group operation on H...
of a finitely generated free group
Free group
In mathematics, a group G is called free if there is a subset S of G such that any element of G can be written in one and only one way as a product of finitely many elements of S and their inverses...
is free. In 1926 Otto Schreier
Otto Schreier
Otto Schreier was an Austrian mathematician who made major contributions in combinatorial group theory and in the topology of Lie groups. He studied mathematics at the University of Vienna and obtained his doctorate in 1923, under the supervision of Philipp Furtwängler...
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
Nielsen–Schreier theorem
In group theory, a branch of mathematics, the Nielsen–Schreier theorem is the statement that every subgroup of a free group is itself free. It is named after Jakob Nielsen and Otto Schreier.-Statement of the theorem:...
. Also in 1921 Nielsen moved to the Royal Veterinary and Agricultural University 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.
During 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...
some efforts were made to bring Nielsen to the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
as it was feared that he would be assaulted by the Nazis. 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
University of Copenhagen
The University of Copenhagen is the oldest and largest university and research institution in Denmark. Founded in 1479, it has more than 37,000 students, the majority of whom are female , and more than 7,000 employees. The university has several campuses located in and around Copenhagen, with the...
, taking the position vacated by the death of Harald Bohr
Harald Bohr
Harald August Bohr was a Danish mathematician and football player. After receiving his doctorate in 1910, Bohr became an eminent mathematician, founding the field of almost periodic functions. His brother was the Nobel Prize-winning physicist Niels Bohr...
. He resigned this position in 1955 because of his international undertakings, in particular with UNESCO
UNESCO
The United Nations Educational, Scientific and Cultural Organization is a specialized agency of the United Nations...
, where he served on the executive board from 1952 to 1958.
See also
- Fenchel–Nielsen coordinatesFenchel–Nielsen coordinatesIn mathematics, Fenchel–Nielsen coordinates are coordinates for Teichmüller space introduced by Werner Fenchel and Jakob Nielsen.-Definition:...
- Nielsen transformationNielsen transformationIn 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 and one of the main tools used in studying free groups,...
- Nielsen theoryNielsen theoryNielsen 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....
- Nielsen–Thurston classification
- Nielsen realization problemNielsen realization problemThe 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:...