My insomnia, as far as I can remember, began when I became a boarding at my 'prep' school, aged nine. As I have mentioned here before, I was terrified of needing to pee (or worse, wet my bed) so I stayed awake until everyone else was asleep, then crept to the bathroom - which, strictly speaking was Breaking a School Rule...
Anyway, it meant I spent a lot of time in bed awake, thinking. And one of the things I thought about was Arithmetic. Five times five is twenty five. Subtract one and add one - so multiply four by six - and you get twenty four. Just one less. Six times six is 36. Six minus one multiplied by six plus one (7x5) is 35 - again one less. It works every time! I was very pleased with myself.
A few years later, I learnt algebra. It took me some time to see the relevance. Then I realised my little insomniac discovery was expressed in a very common equation - (n+1) x (n-1) = n sqaured minus 1 [excuse my inability for find the right keys to press for superscript].
So I was right! What I had stumbled across empirically (to use a grown-up word) could be proved in theory.
On the other hand, I was a bit disappointed that my name would not be set in lights as a mathematical genius.
