# In Praise of Idlework

My client was concerned. Not for the usual reason a client might be concerned - in fact, I’d just come up with a key insight that fixed our biggest problem. He was concerned that I’d come up with the insight while out for a walk with my family. He was worried I was thinking about the intersection of Bayesian statistics and 3D geometry instead of focussing on family time.

But that’s not how my mind works. It has two modes for thinking about maths: the sort of deep work you’re probably thinking of, focussed in front of the computer or a notebook, arranging ideas, calculating, looking for difficulties. And then there’s idlework. Once I’ve thought hard about a problem and got properly stuck, deliberately thinking any more about it is probably counterproductive. But letting my mind work away at it in the background is another kettle of worms.

Just this last week, I’ve come up with unblocking ideas while in the shower, while cooking, and while asleep. During my PhD, my go-to was Tetris (to the point where I was, briefly. in the top 20 on the world high score table for ksirtet.) Stopping to think is a powerful tactic for solving mathematical problems - but stopping to not think is often effective, too.

It might be that the mathematician you’re working with is spending hours staring into space, or wandering off for long strolls when they’re “meant to be working.” But mathematical work does not proceed on the clock. Sometimes, busy work is a workable tactic, but if your mathematician needs time to let ideas percolate, then getting on their case about it won’t help.

I’m not goofing off. I’m idle working.