The most common intersection, IMO, is inductive reasoning. If you can write a working recursive function, you are also writing an inductive proof. The only explanation I have for why people think there's either no link to math, or that they can program but can't do math, is a cultural sledgehammer smashed into our collective skulls while we're young that tells us we can't.
This is a shame, because we spend a lot of effort in deliberately avoiding common abstractions in case it scares programmers away, but really we're just making it harder for everyone to learn all these things. We either eventually recognise the underlying pattern through our brain's capacity to extrapolate from examples (hard, slow), or learn the pattern explicitly and recognise it, or often never learn the pattern and have to learn each new language's way of doing things one by one.
And of course when we either don't know or deliberately avoid effective abstractions we make or propagate mistakes. See Java's first crack at Future, for example, which was practically useless since the only thing you could do with a Future was wait for it to be the present.
This is a shame, because we spend a lot of effort in deliberately avoiding common abstractions in case it scares programmers away, but really we're just making it harder for everyone to learn all these things. We either eventually recognise the underlying pattern through our brain's capacity to extrapolate from examples (hard, slow), or learn the pattern explicitly and recognise it, or often never learn the pattern and have to learn each new language's way of doing things one by one.
And of course when we either don't know or deliberately avoid effective abstractions we make or propagate mistakes. See Java's first crack at Future, for example, which was practically useless since the only thing you could do with a Future was wait for it to be the present.