Now we're getting into the "define maths" part of the discussion which is always where these discussions die. It can be argued that turning a kettle on and boiling some water is "maths" or it can be as narrow as "everything above basic arithmetic is logic, not maths."
So how much of programming is maths? Before we answer that, let's answer: How much of maths is actually maths? Because first we define maths, and then we define programming based on whatever that is, but until we have that first concrete definition this discussion cannot occur.
I will add that "it is taught by the maths department in college" is a flimsy argument, and frankly one the Physics department in particular would mock.
I think for this discussion, "math is stuff you'd learn in a math department" is a pretty useful definition, even if it's not a very good one. There's a lot of math involved in the design and manufacture of the kettle, electrical grid, and water utilities, but a person's ability to put a kettle on isn't going to be improved by math classes. In that way, programming probably is a bit mathy, but good programming is more like good technical writing than it is like math.
> I think for this discussion, "math is stuff you'd learn in a math department" is a pretty useful definition
That means that definition shifts over time. For example, courses on numerical analysis, graph algorithms, programming, and on compilers used to be part of “what you’d learn in a math department”.
It likely also even today will show geographical variation.
Overlap between programming and math is quite small, e.g. halting problem is solvable in programming (by flow analysis) but isn't solvable in math. Programming deals only with practical problems and can be completely guided by practical considerations, while math requires abstract outlandish skills - exact opposite. Why talk about math at all if it's already well known that programming is engineering?
So how much of programming is maths? Before we answer that, let's answer: How much of maths is actually maths? Because first we define maths, and then we define programming based on whatever that is, but until we have that first concrete definition this discussion cannot occur.
I will add that "it is taught by the maths department in college" is a flimsy argument, and frankly one the Physics department in particular would mock.