Hellmuth Kneser

Who was Hellmuth Kneser?

Hellmuth Kneser was a Baltic 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 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.

Kneser had formulated the problem or 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 φ such that φ = exp.; although this superexponential is not real and cannot be considered as a tetration.

Kneser was a student of David Hilbert. He was an advisor of a number of notable mathematicians, including Reinhold Baer.