Soon afterwards, an interviewing board was searching for a mathematician with a strong knowledge of European languages. Given the high degree of specialisation in the educational system of the time, this was asking a lot. Only one candidate presented himself for interview, an undergraduate studying for a mathematics degree who had been teaching himself German for a year. His name was Peter Hilton, and he was appointed, even though neither he nor the interviewers knew what the job was. His official position was in the foreign office.

As a student at Oxford University, Hilton had trained for the Royal Artillery. However, he decided that if he followed that career path, he was likely to die young, "of sheer boredom", as he wrote in 1998 in Reminiscences of a Codebreaker.

So, on 12 January 1942, the young mathematician presented himself at Hut 8, Bletchley Park, where Turing asked him if he played chess. A day later he was told what his real job was: decoding secret German messages encrypted by the famous Enigma machines. Though he lived until the age of 87, Hilton always maintained that Bletchley Park was the most exciting part of his career. For most of his professional life he was a researcher and teacher specialising in an esoteric branch of pure mathematics, topology, at a number of British and then US universities.

Hilton was born in London, the son of Elizabeth Freedman and Mortimer Hilton. His interest in mathematics was inspired by an unfortunate incident. At the age of 10 he was run over by a Rolls-Royce. Spending many weeks in hospital with his leg in plaster to the waist, he made use of what he later described as "this sort of whiteboard, permanently available to me sitting on my stomach". He used it to solve mathematical problems.

In 1940 he finished his studies at St Paul's school, Hammersmith, where he began to teach himself German, not realising where that would lead. He won a scholarship to the Queen's College, Oxford, to read mathematics, and there, at the start of his second year, came the offer he could not refuse.

Many of Britain's most brilliant mathematicians were assigned to Bletchley Park: Turing, Henry Whitehead and Max Newman among them. Hilton got on especially well with Whitehead they often shared a beer or two and when the war ended, he was invited to return to Oxford as Whitehead's research student.

Whitehead worked in topology, often described as "rubber sheet geometry" because it deals with those properties of geometric shapes that remain unchanged when the shape is bent, twisted, stretched or shrunk. Examples are whether the shape is connected or falls into several pieces, or more subtly, whether a closed curve is knotted.

Topology is now one of the central pillars of mathematics, with applications to astronomy, quantum physics and the biology of DNA. Whitehead worked in algebraic topology, which used the abstract structures of modern algebra to characterise and distinguish basic topological forms. "But I don't know anything about topology," Hilton pointed out. "Oh, don't worry, Peter, you'll like it," Whitehead replied.

Hilton accepted the invitation, wrote his PhD thesis, and took a position at Manchester University. Even then, his mathematical interests were broad. In 1949 he wrote to Newman that he had offered an extramural lecture course on the development of mathematics, hoping to earn the deposit on a house. There was a good reason: he was about to marry Margaret Mostyn. They would have two sons, Nicholas and Timothy. The couple shared a love of the theatre and acting; Peter as an amateur, Margaret as a professional.

After three years in Cambridge, Hilton returned to Manchester, becoming senior lecturer in 1956. He was often influenced by people he had met at Bletchley Park, among them Shaun Wylie. Together, they wrote Homology Theory: An Introduction to Algebraic Topology. Published in 1960, it quickly became one of the classics of the subject. Hilton went on to write several more research texts.

By 1958 he had become Mason professor of pure mathematics at Birmingham University, where he anticipated spending the rest of his career, mostly as head of department. Seeking to escape an increasing burden of committee work, he accepted an offer from Cornell University at Ithaca in the US. From there he moved to the University of Washington, then to Case Western Reserve University in Ohio, and finally, in 1982, became a professor at the State University of New York in Binghamton.

Hilton's mathematical legacy consists of 15 books and more than 600 papers. In later life he took an increasing interest in education, and he was the first vice-president of the Mathematical Association of America, primarily an organisation for teachers. He was a consultant to the Children's Television Workshop (now the Sesame Workshop). He received numerous awards, including the silver medal of the University of Helsinki and three honorary doctorates. Several international conferences have been held in his honour. Despite his dislike of such work, he belonged to a variety of key committees, and was chair of the National Research Council committee on graduate and postdoctoral training in mathematics.

Hilton was a man of boundless energy, a genial personality who had time to spare for anyone who shared his love of mathematics. He contributed on every level, from public understanding to the frontiers of research. He is survived by his wife and sons.

*Peter Hilton, mathematician, born* 7 *April* 1923; *died* 6 *November* 2010

**Ian Stewart**

2 December 2010 © Guardian News and Media Limited