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I suppose that I'm tired—I was up at four-thirty and I've still got a couple of hours of work to go—but there really can't be any excuse for having to plug actual numbers into a modulus function. I should know this stuff by heart.

My problem is that I thought that I saw a clean way to solve a problem, but I ended up with an inequality that was just plain wrong. There will be a clean way to do it, I just can't see it at the moment.

What do I mean by clean?

With maths and computing and poetry and words you often know when you've got things right—it feels apt, you've rung the bell, received the prize. There's a concision, and a focus, and that deep joy of rightness in the-you that we all crave.

True, sometimes you write pages for very few marks, sometimes you have to. But every now-and-again you produce that half-a-page which you just know is the business.

I had this experience on my last TMA: I lucked into something that just nailed the proof [sequential] of the continuity of a trig function. I remember writing it out, Max would cry it the flex, it all just fell into place. My hand ached. My wife asked me what I was smiling so loudly about.

Too often, lately, I've forgotten how lucky I am to be given such wonderful nonsense.