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.