Although Gascoigne had always intended to study mathematics at Cambridge, an event occurred that significantly shaped his career. In 1931, an earthquake in New Zealand killed Michael Hiatt Baker, a young traveller from Bristol, and his parents established a postgraduate scholarship in his memory, for study at the University of Bristol, which Gascoigne won and took up in 1938. During his thesis studies at Bristol, Gascoigne developed a diffraction theory of the Foucault test that is used for evaluating the shape of large telescope mirrors. He completed his doctorate in physics in 1941, but by then war had broken out in Europe, and he had already returned to New Zealand on the last available ship.