Hellmuth Kneser (16 April 1898 – 23 August 1973) was a

Baltic German Baltic Germans (german: Deutsch-Balten or , later ) were ethnic German inhabitants of the eastern shores of the Baltic Sea, in what today are Estonia and Latvia. Since their coerced resettlement in 1939, Baltic Germans have markedly declined ...

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 made notable contributions to

group theory In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ...

and

topology In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...

. His most famous result may be his theorem on the existence of a prime decomposition for 3-manifolds. His proof originated the concept of

normal surface In mathematics, a normal surface is a surface inside a triangulated 3-manifold that intersects each tetrahedron so that each component of intersection is a ''triangle'' or a ''quad'' (see figure). A triangle cuts off a vertex of the tetrahedron wh ...

, a fundamental cornerstone of the theory of

3-manifold In mathematics, a 3-manifold is a space that locally looks like Euclidean 3-dimensional space. A 3-manifold can be thought of as a possible shape of the universe. Just as a sphere looks like a plane to a small enough observer, all 3-manifolds lo ...

s. He was born in

Dorpat Tartu is the second largest city in Estonia after the Northern European country's political and financial capital, Tallinn. Tartu has a population of 91,407 (as of 2021). It is southeast of Tallinn and 245 kilometres (152 miles) northeast of ...

Russian Empire The Russian Empire was an empire and the final period of the Russian monarchy from 1721 to 1917, ruling across large parts of Eurasia. It succeeded the Tsardom of Russia following the Treaty of Nystad, which ended the Great Northern War. ...

(now Tartu,

Estonia Estonia, formally the Republic of Estonia, is a country by the Baltic Sea in Northern Europe. It is bordered to the north by the Gulf of Finland across from Finland, to the west by the sea across from Sweden, to the south by Latvia, a ...

) and died in

Tübingen Tübingen (, , Swabian: ''Dibenga'') is a traditional university city in central Baden-Württemberg, Germany. It is situated south of the state capital, Stuttgart, and developed on both sides of the Neckar and Ammer rivers. about one in three ...

Germany Germany,, officially the Federal Republic of Germany, is a country in Central Europe. It is the second most populous country in Europe after Russia, and the most populous member state of the European Union. Germany is situated betwe ...

. He was the son of the mathematician

Adolf Kneser Adolf Kneser (19 March 1862 – 24 January 1930) was a German mathematician. He was born in Grüssow, Mecklenburg, Germany and died in Breslau, Germany (now Wrocław, Poland). He is the father of the mathematician Hellmuth Kneser and the g ...

and the father of the mathematician

Martin Kneser Martin Kneser (21 January 1928 – 16 February 2004) was a German mathematician. His father Hellmuth Kneser and grandfather Adolf Kneser were also mathematicians. He obtained his PhD in 1950 from Humboldt University of Berlin with the disser ...

. He assisted

Wilhelm Süss Wilhelm Süss (7 March 1895 – 21 May 1958) was a German mathematician. He was founder and first director of the Oberwolfach Research Institute for Mathematics. Biography He was born in Frankfurt, Germany, and died in Freiburg im Breisgau, Germ ...

in the founding of the Mathematical Research Institute of Oberwolfach and served as the director of the institute from 1958 to 1959. He was an editor of

Mathematische Zeitschrift ''Mathematische Zeitschrift'' ( German for ''Mathematical Journal'') is a mathematical journal for pure and applied mathematics published by Springer Verlag. It was founded in 1918 and edited by Leon Lichtenstein together with Konrad Knopp, Erh ...

Archiv der Mathematik '' Archiv der Mathematik'' is a peer-reviewed mathematics journal published by Springer, established in 1948. Abstracting and indexing The journal is abstracted and indexed in:

and

Aequationes Mathematicae ''Aequationes Mathematicae'' is a mathematical journal. It is primarily devoted to functional equations, but also publishes papers in dynamical systems, combinatorics, and geometry. As well as publishing regular journal submissions on these topic ...

. Kneser formulated the problem of non-integer iteration of functions and proved the existence of the entire

Abel function The Abel equation, named after Niels Henrik Abel, is a type of functional equation of the form :f(h(x)) = h(x + 1) or :\alpha(f(x)) = \alpha(x)+1. The forms are equivalent when is invertible. or control the iteration of . Equivalence The se ...

of the

exponential Exponential may refer to any of several mathematical topics related to exponentiation, including: *Exponential function, also: **Matrix exponential, the matrix analogue to the above *Exponential decay, decrease at a rate proportional to value *Expo ...

; on the base of this Abel function, he constructed the

functional square root In mathematics, a functional square root (sometimes called a half iterate) is a square root of a function with respect to the operation of function composition. In other words, a functional square root of a function is a function satisfying ...

of the exponential function as a half-iteration of the exponential, i.e. a function such that . Kneser was a student of David Hilbert. He was an advisor of a number of notable mathematicians, including

Reinhold Baer Reinhold Baer (22 July 1902 – 22 October 1979) was a German mathematician, known for his work in algebra. He introduced injective modules in 1940. He is the eponym of Baer rings and Baer groups. Biography Baer studied mechanical engineering f ...

. Hellmuth Kneser was a member of the

NSDAP The Nazi Party, officially the National Socialist German Workers' Party (german: Nationalsozialistische Deutsche Arbeiterpartei or NSDAP), was a far-right political party in Germany active between 1920 and 1945 that created and supported t ...

and also the SA. In July 1934 he wrote to

Ludwig Bieberbach Ludwig Georg Elias Moses Bieberbach (; 4 December 1886 – 1 September 1982) was a German mathematician and Nazi. Biography Born in Goddelau, near Darmstadt, he studied at Heidelberg and under Felix Klein at Göttingen, receiving his doctorat ...

a short note supporting his anti-semitic views and stating: "May God grant German science a unitary, powerful and continued political position."Sanford L. Segal
Mathematicians under the Nazis
Princeton University Press, 2003, page 276

Selected publications

* ''Funktionentheorie.'' Studia Mathematica, Göttingen, 1958; 2nd edition 1966. *Gerhard Betsch, Karl H. Hofmann (eds.): ''Gesammelte Abhandlungen'', De Gruyter 2005

References

External links

* * {{DEFAULTSORT:Kneser, Hellmuth 1898 births 1973 deaths People from Tartu People from Kreis Dorpat Baltic-German people Nazi Party members 20th-century German mathematicians Group theorists Topologists Academic staff of the University of Greifswald Sturmabteilung personnel Emigrants from the Russian Empire to Germany