Hellmuth Kneser
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Hellmuth Kneser (16 April 1898 – 23 August 1973) was a German
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 ...
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 Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...
. 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 (topology), surface inside a triangulated 3-manifold that intersects each tetrahedron in several components called normal disks. Each normal disk is either a ''triangle'' which cuts off a vertex of the t ...
, a fundamental cornerstone of the theory of
3-manifold In mathematics, a 3-manifold is a topological space that locally looks like a three-dimensional Euclidean space. A 3-manifold can be thought of as a possible shape of the universe. Just as a sphere looks like a plane (geometry), plane (a tangent ...
s. He was born in
Dorpat Tartu is the second largest city in Estonia after Tallinn. Tartu has a population of 97,759 (as of 2024). It is southeast of Tallinn and 245 kilometres (152 miles) northeast of Riga, Latvia. Tartu lies on the Emajõgi river, which connects the ...
,
Russian Empire The Russian Empire was an empire that spanned most of northern Eurasia from its establishment in November 1721 until the proclamation of the Russian Republic in September 1917. At its height in the late 19th century, it covered about , roughl ...
(now
Tartu Tartu is the second largest city in Estonia after Tallinn. Tartu has a population of 97,759 (as of 2024). It is southeast of Tallinn and 245 kilometres (152 miles) northeast of Riga, Latvia. Tartu lies on the Emajõgi river, which connects the ...
,
Estonia Estonia, officially the Republic of Estonia, is a country in Northern Europe. It is bordered to the north by the Gulf of Finland across from Finland, to the west by the Baltic Sea across from Sweden, to the south by Latvia, and to the east by Ru ...
) and died in
Tübingen Tübingen (; ) is a traditional college town, 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 (Neckar), Ammer rivers. about one in ...
,
Germany Germany, officially the Federal Republic of Germany, is a country in Central Europe. It lies between the Baltic Sea and the North Sea to the north and the Alps to the south. Its sixteen States of Germany, constituent states have a total popu ...
. He was the son of the mathematician Adolf Kneser and the father of the mathematician Martin Kneser. He assisted Wilhelm Süss in the founding of the
Mathematical Research Institute of Oberwolfach The Oberwolfach Research Institute for Mathematics () is a center for mathematical research in Oberwolfach, Germany. It was founded by mathematician Wilhelm Süss in 1944. It organizes weekly workshops on diverse topics where mathematicians and ...
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. History The journal was founded in 1917, with its first issue appearing in 1918. It wa ...
,
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. Kneser formulated the problem of non-integer iteration of functions and proved the existence of the entire Abel function 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 * Ex ...
; 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 fo ...
of the exponential function as a half-iteration of the exponential, i.e. a function such that . Kneser was a student of
David Hilbert David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician and philosopher of mathematics and one of the most influential mathematicians of his time. Hilbert discovered and developed a broad range of fundamental idea ...
. 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, Baer groups, and Baer subplanes. Biography Baer studied mecha ...
. Hellmuth Kneser was a member of the
NSDAP The Nazi Party, officially the National Socialist German Workers' Party ( or NSDAP), was a far-right political party in Germany active between 1920 and 1945 that created and supported the ideology of Nazism. Its precursor, the German Workers ...
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 leading representative of National Socialist German mathematics (" Deutsche Mathematik"). Biography Born in Goddelau, near Darmstadt, ...
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 Scientists from Tartu People from Kreis Dorpat People of Baltic German descent Emigrants from the Russian Empire to Germany Nazi Party members 20th-century German mathematicians Group theorists German topologists Academic staff of the University of Greifswald Sturmabteilung personnel Presidents of the German Mathematical Society