At the age of 10, I was run over by a Rolls Royce, no less. It was an extraordinary incident. A boy in school snatched the cap off my head and ran across the road. I was angry and ran after him. I didn't notice the on-coming Rolls Royce. ... what happened was that I had a long period of recuperation, much of which was spent in a hospital bed with plaster of Paris on my left leg, all the way up, in fact, to my navel. So I had this sort of white board permanently available to me sitting on my stomach. It simply turned out that I spent a lot of my leisure time doing mathematical problems, writing them on the plaster of Paris, and erasing them each morning. It gave me the opportunity to realize that I had this intensive love of mathematics. I realized earlier that I had a certain proficiency, but I hadn't realized before that it was the sort of thing I would do when I had the choice of doing other things. So then it came to me that I really loved mathematics and thoroughly enjoyed doing it. I recall even having unkind thoughts about visitors who came to see if I was all right, as they would interrupt me when I was really enjoying what I was doing.

My tutor recommended me to attend the interview although I was not a mathematician - merely an undergraduate of mathematics - and my knowledge of German was rudimentary, since I had merely been teaching myself for a year.

... two of my colleagues [at Bletchley Park] were Henry Whitehead and Max Newman. Due to the peculiar circumstances of the war, I was on an equal footing with them. In fact, I was simply a young man who had taken a wartime degree and they were eminent mathematicians. I became, in particular, very, very friendly with Henry Whitehead, on first-name, beer-drinking terms. After the war, Henry Whitehead invited me to come back to Oxford and be his first post-war research student. I said, "But I don't know anything about topology." And he said, "Oh, don't worry, Peter, you'll like it." So in fact, I didn't even know what the subject was. I went back to Oxford, and I studied topology. Whatever Henry Whitehead had specialized in, I would have studied. His personality was so attractive, that it was clear that it was going to be great fun to work with him. It turned out to be not only fun but extremely exacting and demanding - it was a marvellous experience. I really took up topology because it was Whitehead's field.

To supplement my income next year, in the hope, eventually, of being able to put down the deposit for a house, I have offered to give a course of extra-mural lectures on "The Development of Mathematics". Messrs Styler and Pedley seemed interested and asked me to give a syllabus, which I based on the course I gave in Oxford in 1947-48. They want me to give an extension course (once a week) starting in October, but I thought before agreeing I should make sure that you have no objections. I think I can promise that neither the preparation time nor the lecturing time would eat into my research time!

This admirable book is designed to make the transition between the elementary textbook and the research-level treatise in algebraic topology. It begins with concrete geometrical fundamentals and manages nevertheless to introduce its reader to enough of the heavyweight machinery of modern topology so that he may hope to attack the contemporary literature of the field. The plan of the book is bipartite. The first portion is concerned principally with the homology theory of simplicial polyhedra, the second with singular homology. ... [An] account of the contents does not convey the richness of the discussion and the plenitude of examples which indeed are calculated not only to illuminate the systematic discussion but also to introduce the reader to the atmosphere of algebraic topology. This aim is even more evident in the very extensive collection of problems, which range from straightforward exercises to items out of the recent literature ... This is a badly needed book. It does an excellent job of carrying the serious beginning student of algebraic topology to a genuine acquaintance with the field, and seems to this reviewer likely to become a standard work in a domain where indeed it is essentially without a rival.

At the moment, no textbook of homotopy theory exists at any level, with the result that the newcomer to this branch of mathematics is obliged to plunge straight into the study of original papers, often of very considerable complexity. This monograph is designed to fill the gap. It does not claim to be a comprehensive treatment of its subject (the recent work of the French school, for example, is not included, except for a brief introduction to it in the last section of Chapter V); but it is hoped that the reader familiar with Lefschetz's 'Introduction to Topology' will obtain an understanding of the fundamental ideas of homotopy theory from the first six chapters of this book.

This book occupies an important place in the literature of topology. ... It is a book for the serious student. For such a person, it is excellent, both in the clarity and discipline of the presentation and for the range of results covered.

This book is intended to provide the university student in the physical sciences with information about the differential calculus which he is likely to need ... The emphasis is on detailed discussion of the ideas ... rather than on complete proofs.

I had been appointed head of department at Birmingham University in 1958, and it looked as if I would be there for the rest of my career. That is to say that I would have approximately another 35 years as head of department. ... I was doing a lot of committee work. I was very conscientious and I don't believe unusually proficient, and I realized that it was having a very deleterious effect on my research. I saw no escape, because I certainly wasn't a big enough person to downgrade myself again, say to the rank of senior lecturer, to halve my salary and lose my position. And yet on the other hand I could not see the possibility of my aspiring to one of the very few positions in the country, at that time, where you could have professorial status without departmental and university-wide responsibilities. ... I had visited Cornell and thoroughly enjoyed it. When an offer came from Cornell, my wife Meg and I talked it over seriously. Then we realized that this was really the unique way of escaping from the situation. So we decided to try it experimentally, and it worked very well.

I would not have accepted the position at Case Western Reserve University.

I think I have made more of a contribution as an expositor in algebraic topology than as a researcher, in bringing ideas into good order so that they would be accessible to students of algebraic topology and homological algebra. In my own research I think the best paper I ever wrote is a paper I wrote under the influence of Jean-Pierre Serre on the homotopy groups of the union of spheres [On the homotopy groups of the union of spheres (1955)]. This was, I think, the first time that Lie algebras were used in homotopy theory in an effective way. It was basic and it is a paper very frequently cited. I think then I would have to jump and say that a series of papers I did with Joseph Roitberg and later also with Guido Mislin on questions relating to failures of cancellation in homotopy theory are good papers. There are two sorts of cancellation you can ask about in homotopy theory. You can take the union of two spaces with a single common point - it's like addition - so you're asking about failure of cancellation under addition. We were able to show systematically how to construct examples where one could take two different spaces, and add on the same space to each, so that the two unions had the same homotopy type; and then, what turned out to be a more difficult problem, we showed how to construct examples with the topological product replacing the union. In the course of that work Joe Roitberg and I were able to construct the first new example of a Hopf manifold. And that, I think, began a whole new industry in mathematics. So I was very happy about that paper. Then I would say the work that the three of us did on localization theory - the new results and the systematization of known results - was a very significant contribution to the whole structure of the subject. I think also that Eckmann and I did significant work in applying categorical notions. Both of us felt these notions were appropriate for looking at concepts and problems in algebraic topology and homological algebra. We were neither of us pure category- theorists and I think that these series of papers we wrote on group-like structures in general categories, and on general homotopy theory and duality, were two very significant contributions to the applications of these categorical notions that suggested ideas and problems. I always feel enormously grateful to Norman Steenrod, that he not only encouraged us, but also when he compiled his list of papers in algebraic topology, he gave Eckmann-Hilton duality a special heading for the papers that had been written in that area. I do think that Eckmann and I did in that way systematize some ideas and we showed how certain ideas are naturally related. Some of these things were intuitively clear to certain people but had not been systematized. By systematizing them, we made them more readily accessible to students, but also we broadened and extended them substantially.

This book is written by two men who have each contributed much to the development of mathematical education in universities, as well as to mathematics itself. Both of these activities have aided in the writing of the book, whose starting point was an in-service course of mathematics for teachers at Birmingham University in 1961-62. There is a long introduction, which should be read with care, for it reveals as few other textbooks the existence of opinions about the presentation of mathematical ideas, their communication, and their importance. This leads to a personal commitment to sharing mathematics which pervades the whole body of the book.

The two books are dedicated to the same principal purpose - to stimulate the interest of bright people in mathematics.

Just as any sensitive human being can be brought to appreciate beauty in art, music or literature, so that person can be educated to recognize the beauty in a piece of mathematics. The rarity of that recognition is not due to the "fact" that most people are not mathematically gifted but to the crassly utilitarian manner of teaching mathematics and of deciding syllabi and curricula, in which tedious, routine calculations, learned as a skill, are emphasized at the expense of genuinely mathematical ideas, and in which students spend almost all their time answering someone else's questions rather than asking their own.