Hellmuth Kneser

{{short description|German mathematician}}

{{Infobox scientist

| name = Hellmuth Kneser

| image = Hellmuth-Kneser.jpg

| image_size = 200px

| caption = Hellmuth Kneser, ca. 1930.

| birth_date = {{birth date|1898|4|16|df=y}}

| birth_place =

| death_date = {{death date and age|1973|8|23|1898|4|16|df=y}}

| death_place =

| nationality = German

| fields = Mathematics

| workplaces = University of Tübingen

| alma_mater = University of Göttingen

| doctoral_advisor = David Hilbert

| doctoral_students = Reinhold Baer,
Wolfgang Walter

| known_for = Normal function
Prime decomposition of 3-manifolds
Superfunction
Radó–Kneser–Choquet theorem

| awards =

}}

Hellmuth Kneser (16 April 1898 – 23 August 1973) was a German mathematician who made notable contributions to group theory 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, a fundamental cornerstone of the theory of 3-manifolds.

He was born in Dorpat, Russian Empire (now Tartu, Estonia) and died in Tübingen, Germany. 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 and served as the director of the institute from 1958 to 1959.

He was an editor of Mathematische Zeitschrift, Archiv der Mathematik 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; 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 {{mvar|φ}} such that {{math|φ(φ(z)) {{=}} exp(z)}}.

{{cite journal

|author=H.Kneser

|title=Reelle analytische Lösungen der Gleichung φ(φ(x)) = e^x und verwandter Funktionalgleichungen

|journal=Journal für die reine und angewandte Mathematik

|url=http://resolver.sub.uni-goettingen.de/purl?GDZPPN002175851

|volume=187

|year=1950

|pages=56–67| doi=10.1515/crll.1950.187.56 }}

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 and also the SA.[http://litten.de/fulltext/cara.htm Die Carathéodory-Nachfolge in München 1938-1944] by Freddy Litten 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, [https://books.google.com/books?id=Xa8CNCyohBQC&pg=PA276 Mathematicians under the Nazis], Princeton University Press, 2003, page 276