I really suck at math, especially when continuous functions are involved (ie non-CS-y math). Usually when mathy articles are posted on HN, I quickly give up, but I just ate this article up. I'm really impressed with the clear explanation, it's quite something! Thanks for writing this!

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.