During this period, he was a research assistant under the famous chemist, Hans von Euler-Chelpin, with whom he published his first five articles from 1913 to 1914.

He eventually began his work on his doctoral studies in mathematics which were supervised by Marcel Riesz at the University of Stockholm.

His most famous paper on this subject is entitled "On the order of magnitude of the difference between consecutive prime numbers",[3] which provided a rigorous account of the constructive role in which probability applied to number theory[4] and included an estimate for prime gaps that became known as Cramér's conjecture.

"[5] Cramér took an interest in the rigorous mathematical formulation of probability in the work of French and Russian mathematicians such as Kolmogorov, Lévy, Bernstein, and Khinchin in the early 1930s.

[7][8] This text was one that "showed the way in which statistical practice depended on a body of rigorous mathematical analysis as well as Fisherian intuition.

[10] During his tenure at Stockholm University, Cramér was a PhD advisor for 10 students, most notably Herman Wold and Kai Lai Chung.

A large portion of Cramér's work concerned the field of actuarial science and insurance mathematics.

His actuarial work during this time led him to study probability and statistics which became the main area of his research.