Are you familiar with the work of Haldane, Kimura, and many other population geneticists?
Somewhat. The mathematics that they use is ordinary mathematical probability theory. Is that what you mean by "mathematics of evolution"?
So why doesn't it take 10 or 100 replications for each evolutionary step?
I puzzled as to why you would think that.
Evolution isn't a mechanical system to grind out a sequence of steps leading to a particular result. Rather, evolution is a system of keeping the population well adapted to a changing environment.
Don't you find this surprising that drug-resistant bacteria would appear in bacterial populations that were never exposed to the antibiotics and there was resistance to many different antibiotics?
No, that is not at all surprising.
Evolution is a system of trial and error, in order to see what works well. If you are using trial and error methods, then you are going to try out things that turn out to not work. So the bacteria population tries mutations that turn out to not be currently helpful. That's what we should expect.
If they could not produce occasional antibiotic resistant variants when not useful, then they also could not produce them when would be useful.
Fundamentalism - the anti-American, anti-Christian branch of American Christianity