In (pure?) mathematics, author order on papers is alphabetical, based on the assumption that all authors contribute equally (e.g. as discussed here and explained in this statement from the AMS). Moreover, single author papers are quite common, even from students. Many math PhD students will have few (or no) papers coauthored with their advisor, and when people from the same research group collaborate, the usual practice of alphabetic authorship is followed.
As an outsider from a "related" field (theoretical physics), I'm wondering how this works in practice and what the experience of a PhD student in mathematics is like. The description of "joint work" from the AMS statement makes sense in describing collaboration between colleagues, but not advisor-student collaborations.
In physics, typically a professor will suggest an idea, and the student(s) will explore the idea, do some calculations, etc. Then they'll have some discussions, the student(s) will present their results, the professor offers some suggestions, the student(s) do more calculations, and eventually they write a paper.
How does it work in mathematics? Is it similar to physics, where the advisor offers ideas and direction, but with the convention that the student typically writes up the results as a single-author paper? Or is it the case that mathematics PhD students really are expected to be highly independent, and receive much less help from their advisors compared to graduate students in other fields?
A related question of mine is whether there is any "grunt work", so to speak, in mathematics research. There are no experiments to do or simulations/computations to run, but is there still a certain amount of calculations or proofs that merely require "routine" work?
For example, I imagine that mathematical research, conducted "physics-style" might look like this: Professor thinks of some theorem to prove, problem to solve, etc, and introduces it to a student. The student works on it for while, and then brings their results to the professor, who then offers their interpretation and new ideas, and so on. Over time, they "jointly" work on the project, but the student does the vast majority of the pencil-on-paper work. Is this style of research (or rather, of advising students) not common in mathematics?