Born and raised in Lüdenscheid, Nöbeling studied mathematics and physics at University of Göttingen between 1927 and 1929 and University of Vienna, where he was a student of Karl Menger and received his PhD in 1931 on a generalization of the embedding theorem, which for one special case can be visualized by the Menger sponge.

[2] Nöbeling worked and researched in Menger's Mathematical Colloquium with Kurt Gödel, Franz Alt, Abraham Wald, Olga Taussky-Todd and others.

In 1933, he moved to the University of Erlangen, where he habilitated in 1935 under Otto Haupt and obtained a professorship at the same place in 1940.

As Rector (1962–1963) of the University of Erlangen he oversaw the merge with the business college in Nuremberg.

[3] He also served twice as the chairman of the German Mathematical Society and is a member of the Bavarian Academy of Sciences and Humanities.