Our first-year lectures were held in a massive lecture hall with more than two hundred students squeezing into one room. The lectures were university-wide, bringing together students from different colleges, and all the maths students entering Cambridge had to attend mandatory courses. The air would become fetid, and there were bouts of sneezing and coughing. Once a girl even fainted in the lecture hall and the students had to be evacuated. We had to take both pure and applied mathematics courses, and I did not enjoy being made to study fluid mechanics and mathematical physics. In fact, the applied mathematics courses made me almost regret not going to Yale or another US university in which one did not specialise right away, and where I could have done pure maths courses and supplemented them with other courses in literature and philosophy and languages, subjects much more to my taste.

Some of our lecturers were charismatic, like Dr JME Hyland, who taught linear algebra, and was a logician. He imbued some of the material with a philosophical and mysterious air, and even now these concepts carry for me the charge he endowed them with. He riffed on the notion of “dual of a...