[auggierose]

Of course mathematicians also think in terms of logic. It’s what you learn when you study mathematics, you soak it up automatically, although few study logic explicitly. And before 2015 a machine beating worlds best go player also seemed pretty unlikely.

[eru]

I've studied mathematics.

You only do (formal) logic as an afterthought when communicating your proofs to other people or writing them down. Otherwise it's mostly intuition.

[auggierose]

I've studied mathematics, too. Yes, formal logic is an afterthought when you do mathematics. But formal logic is just an explicit representation of what goes on internally in a mathematician. Or at least that's how I approach formal logic (most logicians don't). I would describe these internal processes inside a mathematician (and outside, when used for communication) as intuition + "logic to keep intuition in check". Sounds like ML + logic to me.