He was successful at the "ten plus" examination and subsequently won a Scholarship to study mathematics at Cambridge University. During his first three years at Magdalene College, Cambridge, where he was a scholar, Pedoe was tutored in mathematics by Arthur Stanley Ramsey, the father of Frank P. Ramsey. He attended lectures by Ludwig Wittgenstein and Bertrand Russell, although he was unimpressed by the teaching style of either great man. Geometry became his main interest and, advised by Henry Baker, he started work on his doctorate and published several papers. In 1935 he took a break from Cambridge and went to the Institute for Advanced Study at Princeton where he worked with Solomon Lefschetz. On his return to England in 1936, Pedoe was appointed as an assistant lecturer of the mathematics department at the University College, Southampton. More of his papers were published and after(?) 1937, he was awarded his PhD on the strength of his thesis, "The Exceptional Curves on an Algebraic Surface", which was based on Henry Baker's work on the Italian theory of algebraic surfaces; he was examined by W. V. D. Hodge and Baker at Cambridge. In the late 1930s, Pedoe married Mary Tunstall, an English geographer and the couple had a daughter, Naomi, and identical twin sons, Dan and Hugh, born in December 1939. By 1941, Winchester College had lost several teachers to the army and had become unable to meet its teaching commitments. They requested help and Pedoe was asked to assist with the teaching of mathematics. He taught junior and senior classes (the juniors could be unruly) and in the senior class one of the students was Freeman Dyson who showed enormous early talent and was strongly encouraged by Pedoe with extra work and reading. Their friendship lasted more than fifty more years until Pedoe's death in 1998 and Dyson's list of people who have most influenced him begins "Hardy, Pedoe...". In 1941 a collaboration with W. V. D. Hodge started which lasted some twelve years and included the writing of the huge three-volume work, "Methods of Algebraic Geometry". Although the book was originally designed as a geometric counterpart of G. H. Hardy's "A Course of Pure Mathematics" it was never intended as a textbook and contains original material. First published in the 1940s, all three volumes were reprinted by Cambridge University Press in 1995. Pedoe published three more papers in 1942: "A remark on a property of a special pencil of quadrics", "On some geometrical inequalities" and "An inequality for two triangles".