It depends what you want to do and what you're good at.
For example, if you're good in the academy thing and manage to get papers into top tier companies you will finish your PhD faster if you won't take breaks in the industry. If your PhD is on desrible topic (e.g., ML) there are plenty of academy and industry jobs waiting for you, regardless of your work experience.
Mathematics is closer to the least in-demand humanities than CS in terms of investment quality... actually, it's probably one of the worse fields in which to do a phd. History or Philosophy might be better... at least there you're free to live a life of the mind. If you sign up for a Math PhD in the USA, you're almost certainly just signing up to be a university College Algebra/Calc I teacher for like 1/2-1/3rd of what middle school teachers are making.
Seriously. Don't get a PhD in Math. It's a miserable field.
I disagree completely (my PhD is in maths). I don't know about the USA specifically, but this doesn't match my experience or that of anyone I know. Many maths PhDs don't go into academia, and those that do earn decent money (definitely more than our equivalent of middle school teachers). I don't know anyone who would describe the field as miserable, and I'm sorry to hear you have reached that conclusion (and confused, to be honest).
Seriously, if you're really interested in maths, look into a PhD in it. It's an exciting and fulfilling field. There are decent odds you won't end up in academia, so aim for an area with practical applications or that will teach you useful skills.
> Many maths PhDs don't go into academia, and those that do earn decent money (definitely more than our equivalent of middle school teachers).
I meant during the PhD. In the USA, it's very common for math folks to teach for most of their PhD. Teaching every semester + summers is not common at all in the rest of STEM. Between the higher salary and pension (!), middle school teachers are making a lot more than PhD students. It would be a weird apples-to-oranges comparison for most phd programs, but, unlike mot phd programs, math phds spend an enormous amount of their time TAing baby math classes.
> but this doesn't match my experience or that of anyone I know.
It matches the experience of almost everyone I know
> Seriously, if you're really interested in maths, look into a PhD in it.
But also consider PhDs in other fields.
Or just take an under-paying/low-time-commitment in industry and study math on the side; in a math phd program in the usa, your College Algebra/Calc I teaching load will be almost a full-time job anyways.
But, even more than that, if you're considering a PhD, choose a mathematically-adjacent field that isn't math and pick up a co-supervisor from the math department. The only parts of math that you can't do in other departments are exactly the areas that don't match the criteria of "area with practical applications or that will teach you useful skills".
That does sound quite different. In NZ TAing during a PhD is completely optional, something you do for extra money. It's definitely a good idea to do some, but in general you wouldn't be allowed to do more than ~10 hours per week.
For example, if you're good in the academy thing and manage to get papers into top tier companies you will finish your PhD faster if you won't take breaks in the industry. If your PhD is on desrible topic (e.g., ML) there are plenty of academy and industry jobs waiting for you, regardless of your work experience.