Once you understand the math, continuous functions are much simpler than discrete maths (the CS-y things like how many strings with such and such a property are there, or how many ways can you program a Turing machine to take a long time but eventually finish work).

Especially if they are complex differentiable functions - then they are wholly determined by their values in any tiny (complex) neighborhood around 1 (complex) value. Basically just equivalent to power series at that point.

While even finding the number of ways to give change is extremely challenging.