Joys of mathematics

I am reading a book called Mathematics: A very short introduction.

I am reading this book because a mathematician at Homerton recommended it last year when I listened to his lecture. I was fascinated by what he was saying and asked whether there was something an ignoramus like me could read to learn more. It took me a long time to get the book, but here I am. Among many other brilliant things, it explains why so many people hate mathematics, or think they hate it. If I had been taught in school all these wonderful, mystical things, instead of boring sums and equations, I would have loved it, just as I loved physics. I hated sums, but I was in love with irrational numbers and the square root of 2. I hated the routine, I loved the weirdness.

Already from that lecture, and still more when I am reading the book, I understand that mathematics is about abstract thinking. About patterns and ideas, and never mind the exact facts. Gowers says explicitly that mathematicians do not use computers, that their tools are a piece a paper and a pencil. He doesn't say it, but I would guess that he does most of his work walking, biking or gardening. Or maybe not. Maybe he sits in his office in Wilberforce Road and thinks.

I admire people who can explain complicated things in a comprehensible way. I have always been fascinated by high-level dimensions, but Gowers has explained them so that I can explain it to someone else, and then you have really understood it. He says that in mathematics you just have to ignore the physicality of space and dimensions. He shows how to go on from three dimensions to four to five to thirty-seven. He shows how to multiply very large numbers without caring about errors in the region of a million. I love it.

And I have learned a new word, torus. It is the surface of an object in the shape of a doughnut.

Beautiful equations

Last Tuesday I went to a lecture on mathematics.

I may have mentioned before that among many things I like about Cambridge are all these lectures. At Homerton, there is a lecture every week, by one of the Fellows, on a level accessible for other Fellows.


When I was nine and wanted to be an astronomer, my mother told me that I was lousy in maths and so could forget it. I was doubtless lousy in maths, and still am (I cannot do a simple sum - three cheers for calculators when I have to pay bills). But I have always been fascinated by pure mathematics that has nothing to do with sums and calculations, but is just an exercise of thought. A game of glass beads, for its own sake. Cannot be applied. Cannot be used for anything practical. There is no social importance in knowing how many primes there are in the first billion. But it is sublime. I wish there was something like this in my field. Maybe there is. I just need to think of it. I have a weird feeling that a popular lecture at Homerton this week has changed my life.

Old friends

Many, many years ago when I was a teenager my parents had a friend whom we mostly met during summer holidays in Karelia. He was a scientist and a true Russian intellectual. My mother first met him during a rainy walk when they discovered that they had lots of common friends, and they decided to meet again next day and introduce their spouses. As they were about to part, this man said: "To be honest, I must warn you: I am a Party member". They became close friends, and one of the favourite pastimes was fishing. I spent hours upon hours in a boat with him, rowing and listening to his stories about theories of universe. Pulsars had just been discovered. Big Bang wasn't common knowledge. It was very exciting. I had always been fascinated by astronomy (I wanted to become an astronomer, but that's another story). But in the first place I was fascinated by this man's genius. It's easy to have a crush when you are a teenager, but it's easiest when you meet a brilliant mind. At least for me.

He was already then internationally famous, member of dozens of academies and learned societies, honorary doctor everywhere, award-winner, but he was bitter about the Nobel prize, because there wasn't any in astronomy.

Many years later he and his wife called me in Stockholm where he was giving a lecture. We invited them for dinner. Staffan, who was as good then as he is now at cooking, made oven-backed fish with spinach. The great scientist looked at the green mess on his plate and asked: "Do I have to eat this?" Staffan was a bit upset.

One day I was sitting in front of the TV and suddenly saw my childhood love and fishing companion. He had just been awarded the Nobel Prize. Astronomy or not.

If you want to know more, read this.