By David Acheson
Why do so many people think they hate mathematics?
All too often, I suspect, the truth is that they were never let anywhere near it, but were fobbed off instead with something that was called mathematics, but which had none of the attractions of the real thing. In particular, they may have had no ‘big picture’ of the subject to help them along.
For what it’s worth, my own big picture of mathematics can be summed up in just six words: (i) surprising theorems, (ii) beautiful proofs and (iii) great applications.
While the subject started with applications to the physical world, mathematicians soon found beauty, too, in mathematics for its own sake, not least because of some of the elegant logical reasoning involved. My own personal view of mathematics at its best is in fact (i), (ii) and (iii) all at once, in one piece of work. That, in my view, is when you really open the champagne.
But above all, perhaps, it is the element of surprise that characterises much of mathematics at its best, and I got my first big mathematical surprise at the age of ten, in 1956. I was keen on conjuring at the time, and one day I came across the following ‘mind-reading’ trick in a magic book.
- Write down a 3-figure number. Any such number will do, provided the first and last figures differ by two or more.
- Now reverse your number, and subtract the smaller 3-figure number from the larger.
- Finally, reverse the result of that calculation, and add.
- Then the final answer will always be 1089, no matter which number you start with!
Okay, it’s not very ‘serious’ mathematics, but I have to tell you this: if you first see it as a 10-year old boy in 1956, it blows your socks off.
David Acheson is a Fellow at Jesus College, Oxford. He is the author of 1089 and All That: A Journey into Mathematics, which aims to make mathematics accessible to everyone. On the way, via Kepler and Newton, he explains what calculus really means, gives a brief history of pi, and even takes us to chaos theory and imaginary numbers, but ensures that no one gets lost along the way.