Horst Schubert (11 June 1919 – 2001) was a German mathematician. Schubert was born in

Chemnitz Chemnitz (; from 1953 to 1990: Karl-Marx-Stadt , ) is the third-largest city in the German state of Saxony after Leipzig and Dresden. It is the 28th largest city of Germany as well as the fourth largest city in the area of former East Germany a ...

and studied mathematics and physics at the Universities of Frankfurt am Main, Zürich and Heidelberg, where in 1948 he received his PhD under

Herbert Seifert Herbert Karl Johannes Seifert (; 27 May 1897, Bernstadt – 1 October 1996, Heidelberg) was a German mathematician known for his work in topology. Biography Seifert was born in Bernstadt auf dem Eigen, but soon moved to Bautzen, where he attend ...

with thesis ''Die eindeutige Zerlegbarkeit eines Knotens in Primknoten''. From 1948 to 1956 Schubert was an assistant in Heidelberg, where he received in 1952 his

habilitation Habilitation is the highest university degree, or the procedure by which it is achieved, in many European countries. The candidate fulfills a university's set criteria of excellence in research, teaching and further education, usually including a ...

qualification. From 1959 he was a ''professor extraordinarius'' and from 1962 a ''professor ordinarius'' at the

University of Kiel Kiel University, officially the Christian-Albrecht University of Kiel, (german: Christian-Albrechts-Universität zu Kiel, abbreviated CAU, known informally as Christiana Albertina) is a university in the city of Kiel, Germany. It was founded in ...

. From 1969 to 1984 he was a professor at the

University of Düsseldorf A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, the ...

. In 1949 he published his proof that every oriented knot in

S^3

decomposes as a connect-sum of

prime knot In knot theory, a prime knot or prime link is a knot that is, in a certain sense, indecomposable. Specifically, it is a non-trivial knot which cannot be written as the knot sum of two non-trivial knots. Knots that are not prime are said to be co ...

s in a unique way, up to reordering. After this proof he found a new proof based on his study of incompressible tori in knot complements; he published this work ''Knoten und Vollringe'' in ''

Acta Mathematica ''Acta Mathematica'' is a peer-reviewed open-access scientific journal covering research in all fields of mathematics. According to Cédric Villani, this journal is "considered by many to be the most prestigious of all mathematical research journ ...

'', where he defined satellite and companion knots. His doctoral students include Theodor Bröcker.

World War II work

During

World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...

Schubert worked as a mathematician and cryptoanalyst in the

Wehrmacht The ''Wehrmacht'' (, ) were the unified armed forces of Nazi Germany from 1935 to 1945. It consisted of the ''Heer'' (army), the ''Kriegsmarine'' (navy) and the ''Luftwaffe'' (air force). The designation "''Wehrmacht''" replaced the previous ...

signals intelligence Signals intelligence (SIGINT) is intelligence-gathering by interception of ''signals'', whether communications between people (communications intelligence—abbreviated to COMINT) or from electronic signals not directly used in communication ( ...

organisation,

General der Nachrichtenaufklärung ''General der Nachrichtenaufklärung'' was the signals intelligence agency of the German Army (1935-1945), Heer (German Army), before and during World War II. It was the successor to the former cipher bureau known as Inspectorate 7/VI in operatio ...

as an expert on

Russian Russian(s) refers to anything related to Russia, including: *Russians (, ''russkiye''), an ethnic group of the East Slavic peoples, primarily living in Russia and neighboring countries *Rossiyane (), Russian language term for all citizens and peo ...

and

Polish Army The Land Forces () are the land forces of the Polish Armed Forces. They currently contain some 62,000 active personnel and form many components of the European Union and NATO deployments around the world. Poland's recorded military history stret ...

Ciphers In cryptography, a cipher (or cypher) is an algorithm for performing encryption or decryption—a series of well-defined steps that can be followed as a procedure. An alternative, less common term is ''encipherment''. To encipher or encode i ...

and

Codes In communications and information processing, code is a system of rules to convert information—such as a letter, word, sound, image, or gesture—into another form, sometimes shortened or secret, for communication through a communication ...

as well as Agents codes and ciphers, obtaining the rank of

lieutenant A lieutenant ( , ; abbreviated Lt., Lt, LT, Lieut and similar) is a commissioned officer rank in the armed forces of many nations. The meaning of lieutenant differs in different militaries (see comparative military ranks), but it is often sub ...

(german: Leutnant).TICOM I-15 Introgation Report of Oberleutnant Horst Schubert

Selected works

* ''Kategorien''. 2 vols. Springer, 1970 (trans. into Eng. by Eva Gray: ''Categories''. Springer-Verlag, 1972 ) * ''Topologie- Eine Einführung''. Teubner, 1969, 3rd edn. 1971 (trans. into Eng. by Siegfried Moran: ''Topology''. Macdonald & Co. 1968 )
''Knoten'', Jahresbericht DMV, vol. 69, 1967/68, p. 184

References

{{DEFAULTSORT:Schubert, Horst 1919 births 2001 deaths 20th-century German mathematicians Topologists German cryptographers

World War II work

Selected works

See also

References