Does Satanism agree that the nature of reality is mathematical, and that there is a rational and logical explanation for everything in existence?
Zevism, or Satyanism, does agree that reality is based on fundamental mathematical concepts.
There is no "1" in reality, for example. Everything is made up of smaller parts, so "1" is truly just a concept, which does have esoteric connotations.
Despite not being "real", 1 is the fundamental base for all numbers.
Same amazement can be had at infinitely complex numbers like Pi that basically can't be conceptualized fully in the material world (there isn't enough space in the Universe to write it all), but somehow this number is needed to work with real life circles, and works perfectly with them.
As for "everything is rational and logical", this is a matter of words and phrasing.
Can all of Existence be explained rationally by any human currently on Earth?
No.
Some things are mysteries and meant to be mysteries. They might have an explanation, or they might not. Debating this is just word salad to me, and I love philosophy, so that should say something.
ToZ is somewhat pragmatic, in the sense that we do agree that we should use reason to understand the world, but we also acknowledge limits, ignorance, and leave room for Mystery.
Zeus Himself, for example, is ineffable by definition.
If you could fully understand God, you'd just be God.
Rationalism vs Absurdism is always a fun debate, so I'd love to read more points about where reason can take us.
But besides the Ethics, which are deep enough to be studied and argued for days on end, these kinds of questions do not have clear "doctrine" in ToZ. Live life and answer for yourself, maybe you'll contribute something big to the Temple.