I bumped into Dimi in my local pub, he was a friend of a friend. I don’t know how the conversation started but I think it was something to do with my surname, “Etter”. I was always of the opinion that it was a bit unusual in this country but he said where he came from, Switzerland, it was common as muck.
Somehow the conversation turned to mathematics, he said he’d learned maths at some London University and had a degree in it. Unlike most people, I didn’t mind maths at all. I got an O-level in it at school and remember one of my teachers telling me once that when he marked other people’s homework, he always used my results to check them against. Looking back, it was probably a trick he learned at teacher training college, but it worked on me because afterwards I always handed my homework in on time.
What this Dimi wanted to talk about was something called partitions. You take a number, say 5, and ask “How many ways are there of breaking it up, or ‘partitioning’ it?”
He showed me a simple example, like this one:
| 5 | ||||
| 4 | 1 | |||
| 3 | 2 | |||
| 3 | 1 | 1 | ||
| 2 | 2 | 1 | ||
| 2 | 1 | 1 | 1 | |
| 1 | 1 | 1 | 1 | 1 |
These are the 7 partitions of 5. There are no other ways of breaking up the number 5.
Then he said, “Well 5 is a bit of an easy example, how about counting the partitions of n?” i.e. Any number, no matter how big!
I’d never heard of partitions but I told him that I’m a bit of a whizz with a computer and could probably knock up a program to do it and I’d mail him the results.
It turned out to be not so easy after all, because of something called combinatorial growth, a phenomenon you’ll keep on encountering as you read on.
Anyway, this is the story of two guys who happened to bump into each other at the same place at the same time and thought, ”Never mind how the mainstream math community operate, let’s do our own thing!“
If you like where I’m coming from, jump on board ☺