My response to a questionnaire from the Maths Club at Bury Grammar School Boys:
1) At what age did you decide that you wanted to become a professional mathematician, and what inspired you to make this decision?
At 14, as a result of participation in mathematical olympiads.
2) How successful were you at Maths in primary and secondary school?
3) What aspect of Maths do you think is most important to understand deeply?
The concept of proof and fundamentals of technique of proof.
4) What type of Maths are you currently working on, and have you developed any theories of your own?
5. Which bit of Mathematics has proved most useful to you and why?
All mathematics is useful. The most useful is the first one that you learn independently. For me, it was projective geometry that I learnt from the first edition of Robin Harsthorne’s wonderful book when I was still at secondary school. Interestingly, I started to use projective geometry in my research twelve years later. In mathematics, if you learn something serious, it always sooner or later turns out to be useful.
6. Do you work with Mathematicians from other countries and do you get the opportunity to travel and meet them?
Oh yes, quite a lot. In my other blog, A Sentimental Journey, almost all “places I visited” were visited because I did mathematics there.
7. Would you encourage you own children to become professional Mathematicians?
I would love too — but they had chosen other paths in their lives. However, both my children benefit in their professional lives from some basic skills of mathematical thinking (as opposed to mere numeracy).