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I graduated in December 2018 with a double degree in math and electrical engineering and have applied to various graduate schools in pure math and electrical engineering and have been offered admission to phd programs in pure math and electrical engineering.

During my undergraduate studies, I have heard many academic mathematicians say that a math degree opens many opportunities for you and mathematicians can get any job, ...

On the other hand, I have also heard people saying that a math degree is useless financially and you can not get a decent job with a math degree; you either need to become a school teacher or work at a bank, ...

Now that I am about to start my phd program, although I enjoy math a lot, I do not want to get a phd in math and after four years find that it did not worth it financially and I have to do a not well-paid job. I can not also hope that I will end up in academia as I have heard academic jobs are very hard to get.

So that leaves me to think that if I want to get a well-paid job, I should do a phd in electrical engineering and not math.

I am so confused and I do not know which paths am I supposed to take? do a phd in math or electrical engineering?

Just a personal anecdote, not really an answer, too long for a comment.

I have a master degree in mathematics and now I'm doing physics simulations for visual effects in Hollywood blockbusters. I believe that a math degree gives you a massive upper hand in any field with reasonable amount mathematics in it. However, you have to be interested in that field and study it in your spare time. I studied computer graphics in my spare time and my math background allowed me to comprehend things in computer graphics orders of magnitudes faster and deeper compared to fellow computer science students.

Take it with a grain of salt, master degree is completely different kind of a beast compared to a PhD degree.

This can depend on more than just the mathematics. You don't say where you are, nor anything about the nature of the educational system. But, for the US, at least, a BS in mathematics is a great basis for many careers, both in and out of academia. But that is because the baccalaureate is, in the US, a very general degree. One studies more than just mathematics, which amounts to only about a third of the courses taken.

But mathematics is about thinking and you can apply that thinking, especially thinking in a formal and disciplined way to other things. But if you don't really know anything except mathematics, then you aren't in such a good place, except to do more mathematics.

But any company that needs analysis of things, such as products or strategies or, well, anything, can use people that have a disciplined way of organizing and presenting information. Mathematics helps with that, as long as you also have the more specific knowledge that the job requires. But that knowledge is easier to obtain, in most cases, with the discipline of thought that mathematics brings you.

A degree in EE would teach you to think in a different way, whether that is better for you is up to you, however.

But, to give some perspective here, I also think that a degree in Philosophy is also a good launching point for a career, and for much the same reason that mathematics is. It teaches discipline of thought that can be generally applied.

However, you are starting a doctoral program. Such programs prepare you to do research and they are very specialized. They are not general education in any sense. Most, or at least, many, PhD holders (guessing a bit here) stay in academia since the doctorate is a good preparation for that. There are other opportunities, of course, but like the degree itself, those opportunities are very specialized. But mathematics is, even at the highest levels, still good mental training that can be applied in other domains.

Where I live, a lot of math degree holders work in software development and are generally doing quite well ... especially since many computer science degree holders are not really good at maths. Other opportunities for mathematicians are simulations (i.e. in engineering) or insurance companies.

In fact, maths teacher is also a quite decent occupation where I live, but that is of course subject to supply and demand.

Were the people who told you you might not find a good job also math degree holders? I have found that non-mathematicians sometimes do not really know what mathematicians work aa.