Writing autobiography is hard; I have found it one of the hardest things I have done. (You can find the first chapter of my autobiography, covering the first twenty-one years of my life, here on my web page. That was written while I was on sabbatical and living on my own in a flat in Cambridge, so I was able to immerse myself in my past and let odd items float to the surface. I couldn’t do this in the bustle of normal life.)

Here, then, is a brief account. I was born in Toowoomba, an inland city in Queensland, Australia. After being taught by correspondence for a few years, I went to the local one-teacher primary school (it was upgraded to two teachers the following year), then to boarding school in Toowoomba, and then to the University of Queensland in Brisbane. I won a scholarship to Oxford, and came to Britain intending to take my DPhil (Oxford-speak for PhD) and return home; but things didn’t work out that way, and I am still here more than forty years later.

I never really wanted to do anything but mathematics. At first, I didn’t know that a career as a “mathematician” was possible; once I discovered this (by being interviewed by mathematicians before going to the University), I was in no more doubt.

As a student, I had other interests: running (I was in the University athletics and cross-couontry teams, and secretary of the Athletics Club for a year); music (I played in a band called, variously, The Black Stumps and the Sixteenth Precinct Repair Shoppe); reading (I went off reading at school but rediscovered it at university and am now a confirmed bibliogle – if I see print, I must read it); and so on. But nothing really took the place of mathematics.

Some psychologists say that the module in our brains responsible for counting is separate from the module that does geometry and estimates magnitudes. If that is so, then the first of these modules is better developed in my brain than the second. Mathematicians are divided up in various ways; I think the most meaningful division is between discrete and continuous mathematicians, and I definitely fall on the discrete side of the divide. I have even developed ways of doing topology as a branch of discrete mathematics!

I was delighted when I stumbled upon Richard Brautigan’s novel *The Hawkline Monster: A Gothic Western*. (I thoroughly recommend this book, by the way.) One of the heroes is a gunslinger called Cameron, and his trademark is that he counts things. At one point we read:

“I count a lot of things that there’s no need to count,” Cameron said. “Just because that’s the way I am. But I count all the things that need to be counted.”

Anyway, career-wise, after my PhD I held a Junior Research Fellowship at Merton College, Oxford, to which I returned as a tutorial fellow after a year and a half teaching in the University of London. I returned to the University of London after eleven years teaching in Oxford. The experience as a tutorial fellow was extremely demanding, but also very valuable for me; I taught a wide range of pure mathematics in depth to some very good students, and in doing so could not help learning a lot myself.

I have been here ever since. I never imagined when I was younger that I could ever bear to stay in the same place for more than twenty years, but it has happened. With retirement just a few years away, it looks like I will stay. (Actually, I don’t think mathematicians really can retire; but that is another matter.)

Mathematically, I have always been broad rather than deep; my most cited works have established connections between apparently very different areas, rather than answering difficult but specialised questions in one area. I have a lot of respect for people who can work at great depth, but that is not the way I am.

I began blogging in 2009, quite by accident. There was a debate in the London Mathematical Society about whether to merge with the Institute for Mathematics and its Applications to form a unified mathematics society for Britain. (I will not go into the arguments here!) A group of mathematicians whom I respected were opposed to the merger, and had set up a blog entitled “Save the LMS”. When things on LMS council got rough and lawyers were called in, one of these mathematicians asked me to take over as an administrator of the blog. I decided that I would need some practice, so signed up for a blog of my own as a practice. “Save the LMS” was already getting a lot of traffic, and I thought that if I were going to screw things up it would be better on an unadvertised blog of my own.

Now “Save the LMS” has disappeared following the loss of the motion for the merger, to be replaced by “Future of the LMS”. It would have been natural to close down my own blog at that point. But, as several people have pointed out, blogging is addictive!

Also, as I said in the preceding post, it is a good and painless way to practice writing. When I was a student, I wrote poetry (as many people do), which was not very good (again like that of many people), but always at the back of my mind was a secondary motivation: practice makes perfect. One of my colleagues has the following “learning tip” on her module web page:

Watching your friend do a work-out at the gym will not make you any fitter.

Listening to Ashkenazy playing *The Moonlight Sonata* will not make you a better pianist.

So why do you think that looking at my model solutions will improve your mathematical ability?

Perhaps questionable, but containing a lot of truth; and to an extent, the same is true for writing. With a blog, I can produce any old rant and make it public. Some people may find it useful, and if they do, I am pleased; but I gain benefit from it even if nobody reads it.

Over time, I hope to expand on some things touched on above, and on other topics too. I have a few things in mind, but am open to suggestions!

Thanks for the post. I also started blogging a couple of months ago. The reason for this is that I had been reading various mathematical blogs in the summer (which were very useful to me as a school student) and that I wanted to practise writing up mathematics. Of course I could have just done that by writing on paper, but this was an easy way to keep it organised and also for others to see.

I have a question: What do you perfer in combinatorics that’s not in other fields? I am currently starting to read material in additive combinatorics (e.g. connection between harmonic analysis and additive combinatorics) and it is fascinating. I would like to know what interests you most in the theory of combinatorics.

That’s a big question; let me try to answer. (I was talking to a student this morning who has discovered that there are connections between combinatorics and algebraic geometry, and wanted to know exactly what they are.) Most branches of mathematics are fairly easy to define. The subject begins with some definitions or axioms saying exactly what it is about, and there is no disagreement. Combinatorics is not like that. The only possible definition is “Combinatorics is what combinatorialists do”. It is criticised by some as being too broad and sprawling; but really combinatorics is more about techniques than about big theorems. (I certainly want to return to this topic.) The group theorist Roger Lyndon, when asked “whether there was a common thread to the diverse work in so many different fields of mathematics, he replied that he felt the problems on which he had worked had all been combinatorial in nature”.

I don’t know where you live, but if you are within reach of London, I urge you to come to two talks this Friday and next by Olof Sisask, a research fellow at Queen Mary, on “Fourier analysis and approximate structure in additive combinatorics”. The first talk will be a gentle introduction to the field, and then he will go on to talk about his own work. The talks are at 4:30pm in room 103 in the Mathematical Sciences building at Queen Mary, in the Mile End Road: the web page is here.

Thanks for the reply. This question is certainly deeper than I thought. Although I live in Cambridge, (so I am within reach of London) there is this annoying little thing called school which I am afraid I have to attend, and since I board, I cannot go out of school for over a couple of hours at a time, therefore I’m afraid I cannot come to the talks.

Not sure if you got the reply I sent. Let me have your email address and I will try to send you notes from the talk.

I’ve sent it by email, hope you don’t mind.