In 1930, Cartwright was awarded a Yarrow Research Fellowship and went to Girton College, Cambridge to continue working on the topic of her doctoral thesis. Attending Littlewood's lectures, she solved one of the open problems which he posed. Her mathematical theorem, now known as Cartwright's theorem, gives an estimate for the maximum modulus of an analytic function that takes the same value no more than "p" times in the unit disc. To prove the theorem she used a new approach, applying a technique introduced by Lars Ahlfors for conformal mappings.