0 and 1 are interesting as integers in the same way that a blank canvas is interesting as a painting. Very foundational, very useful but also very plain.
In my limited math experience, I really found an appreciation of the number one. My favorite part of high school algebra was realizing that "solving for x" was often just a repeated exercise of multiplying each side of the equation by a "clever form of one."
Solving for x often entails multiplying both sides by the same number, not necessarily one. Perhaps you're referring to simplifying fractions where you do often multiply by a clever form of one?
Ah, yes, you are absolutely correct. The _clever form of one_ trick did not apply as often as I recalled!
Pretty interesting if you work in an industry where you use them to represent every other number.