Roger, however, was set on research in mathematics and on entering St John's College he began research in algebraic geometry supervised by Hodge . However, after one year of study at Cambridge, finding that his interests were not particularly central to those of Hodge, he changed his supervisor to John Todd . Penrose was awarded his Ph.D. for his work in algebra and geometry from the University of Cambridge in 1957 but by this time he had already become interested in physics.
Roger, gayunman, ay naka-set sa pananaliksik sa matematika at sa pagpasok St John's College siya nagsimulang pananaliksik sa algebraic geometry supervised by Hodge. Subalit, pagkatapos ng isang taon ng pag-aaral sa Cambridge, paghanap na ang kanyang mga interes ay hindi lalo na sa mga central ng Hodge, siya ay nagbago sa kanyang superbisor sa John Todd. Penrose ay iginawad sa kanyang Ph.D. para sa kanyang trabaho sa algebra at geometry mula sa University of Cambridge sa 1957 ngunit sa pamamagitan ng oras na ito niya na maging interesado sa physics.