[Refefer]

I considered editing my other comment but decided instead to break it out.

There are a couple of complexities that your comment illustrates well:

First, continuous math _is_ available and immediately applicable today. The problem is that we often reason in and program to the implementation, not the abstraction - a subtle difference, but an important one. Not only that, but by reasoning in a flawed representation, we often miss important derivations that result in dramatic simplifications and reductions in the problem domain. I would also argue that we already do use continuous math regularly - for example, linear algebra, combinatorics, and set theor: most of us only know them as arrays, random, and SQL.

Secondly, not enough effort is made in formal education for applying 'pure' math to computer science. Some branches, such as linear algebra, have obvious implementations and analogies already available but others are quite a bit less clear - I fault this more on curriculum silos than an engineer's innate abilities. It's a learned skill that just isn't often taught.

[syncopatience]

This might be beside the point, but combinatorics, set theory and algebra are prime examples of discrete mathematics, not continuous.