As an undergraduate at Cambridge Turnbull had become fascinated by the topic of invariant theory. He published two papers on classical algebra problems in 1910 and 1911, then a further paper in 1916 after his return to England.
Bilang isang undergraduate at Cambridge Turnbull had maging nabighani sa pamamagitan ng ang paksa ng invariant theory. Nai-publish na siya ng dalawang mga papeles sa klasiko algebra problema sa 1910 at 1911, at pagkatapos ng isang karagdagang papel sa 1916 matapos ang kanyang bumalik sa England.