Shortly after his arrival in 1905 at University of Göttingen, Grelling began a collaboration with philosopher Leonard Nelson, with whom he tried to solve Russell's paradox, which had shaken the foundations of mathematics when it was announced in 1903.

He received his doctorate in mathematics from the same university in 1910 with a PhD dissertation on the development of arithmetic in axiomatic set theory, advised by David Hilbert.

Unable to find a university position in either Göttingen or Berlin, Grelling had to teach mathematics, philosophy and physics in secondary schools.

Although many of his relatives and friends had fled Germany, he did not think seriously about leaving until 1937, in which year he went to Brussels to work with Paul Oppenheim, this time writing several papers on the analysis of scientific explanation and on Gestalt psychology.

News of the position and a visa to the United States reached the camp where Grelling had been joined by his wife Greta, who had refused to divorce him for safety reasons.