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, who made notable contributions to

group theory In abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as ...

and topology. 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, Russian Empire (now

Tartu 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 o ...

, Estonia) and died in Tübingen, Germany. 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 gra ...

and the father of the mathematician Martin Kneser. 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, G ...

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,

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 seco ...

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 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. 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 th ...

and also the SA. In July 1934 he wrote to Ludwig Bieberbach 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