I am wondering what jobs in the field of Mathematics are (seemingly) always in demand. I am also wondering what jobs there are that are (once again seemingly) greatly Mathematically demanding in regards to either deep specialisation or great generality in the application fields.
For the second criteria, I mean that a great amount of learning must be done to understand the career. Whether that be learning a lot of content from multiple fields, or significant investment in a specialization.
More specifically, what fields meet both of these criteria?
Thank you for your time.
Note: If you wish, give it in regards to any location you wish, I understand this can be (and likely is) location reliant.
With regard to your first criterion, Actuaries are often in demand. That's not to say that there aren't Actuaries who are out of work. The "problem" with being an Actuary is that you've got to pass their series of 9 (or 10) exams, where not all of them are mathematically oriented. You can be an Associate Actuary by passing 7 exams, but that wouldn't be as advantageous as passing all of them.
With regard to you second criterion, the work may or may not be mathematically challenging, depending upon what you wind up doing. There are definitely mathematical challenges, but one could still be a highly paid Actuary and spend more of your time in the business end of things than the highly technical end of things.