Roger John Tayler was born in Birmingham on 25 October 1929, the elder son of Richard Henry Tayler and his wife Frances Florence Bessie (nee Redup). His father was a commercial traveller, his mother an elementary school teacher. Both he and his brother Clive (now a circuit court judge) received strong encouragement from their parents to develop their respective academic talents. At Solihull School Roger's interest in science was stimulated by the mathematical staff, especially by B.M. Peek, a well-known amateur astronomer who served as President of the British Astronomical Association and on the Council of The Royal Astronomical Society. In 1946, Roger won a state scholarship, and then a major open scholarship in mathematics to Clare College, Cambridge. In 1949, he became a wrangler, and in 1950 passed part III of the mathematical tripos with distinction, sharing the Mayhew Prize awarded for the best performance in applied mathematics. Clare College awarded him the Robins Prize and the Owst Prize.