The mathematician's dilemma

There were a number of reasons mathematics was my most difficult subject, not least among them a peculiar habit common to maths lecturers. They would speak with a kind of soporific slowness when introducing a topic, then blitz through the workup on the board so quickly you couldn't follow it at all. It would have been hilarious if it wasn't so disorienting. It's like they had been told at some point, "you need to slow down so that the students have time to understand", and the lecturers had dutifully slowed down everything – except the actual mathematics.

It took me a while before I realised the problem: they didn't actually understand what was difficult! I mean, these were serious researchers teaching first-year mathematics, roughly the equivalent of Tolkien teaching people how to use adjectives. Whatever difficulty there was had long ago been internalised, leaving only a kind of faint confusion. What, exactly, are you finding difficult here? It's "big red house", not "red big house". Yes, of course there's a rule. You can look it up or whatever, but you shouldn't need to. Can we move on to the interesting stuff and stop worrying about which way around the adjectives go?

As you might imagine, this shows up in many more places than mathematics lectures. It's important not to forget that programming is just typing with more rules, but I see a lot of people try to teach programming without spending enough time on syntax or other simple mechanics we take for granted. I've made the same mistake myself. Inside each of us, it seems, is a tiny frustrated mathematician who just wants to skip to the good part. But, if we want to convey our ideas clearly, we have to give time to the obvious.

How else will it become obvious to others?