As an algebraic topologist who did not even touch anything less “pure” than PDE during my master’s degree, I would say the following: You have many possibilities, but you might have to rebrand yourself a little.

I went into a government job (DM me for details as I am already too identifiable). I was really unsure about going the PhD route or not, and ultimately opted for what I thought would make me the most happy. I am pretty sure it was right for me, though it is a little bittersweet in retrospect.

In my opinion the people matter more than the place, and with sufficient freedom and autonomy a mathematician can make any task interesting. Think about how you can make your skills useful for other things than pure maths (in a manner you could also enjoy) and sell yourself to an employer on that premise.

Quantitative finance. They want people with a math background to model the market.

You could also teach, either at the high school level or community college.

Bureau of labor stats is a good resource for seeing which careers require which degree, and where people with different credentials are getting hired.

https://www.bls.gov/ooh/field-of-degree/mathematics/mathematics-field-of-degree.htm

I have a friend that had an MS in math and he worked for an airline doing very long term forecasting to determine flight schedules to maximize efficiency. He found it a bit depressing though as what he would submit would never be done as it went to other groups who modified it as it got closer to now. In other words he made idealized plans that would be modified based on reality.

Does your university have a career center? Check them out because a lot of times they have good relationships with large companies and smaller local companies and know what the job market is like. Usually this just involves making an appointment with a career counselor and telling them exactly what kinds of things you like doing (math-related) and don’t like doing (programming, bureaucracy.) There are jobs that have titles with words like “Analyst” and “Design” that might be right for you; the career center will be able to point you in the right direction.

I utterly despise programming. I can not think of a more miserable, dreary existence than becoming a professional programmer

That’s hilarious to me because I feel the exact opposite way. Love programming except when it involves heavy math (e.g. lighting). Saps all the enthusiasm out of me. I hope you find the right career path for you because from reading your comments you seem super stressed and overworked!

All of them except the licensed trades. You can get any of those jobs by undergoing the proper training.

But basically go on indeed and browse the list of jobs. You can have any one of those jobs, in principle.

Do any of these suit your fancy? (For example)

You more than likely could find opportunities outside of the normal office, if you are willing to work outside of an office, possibly relocate.

I myself am pivoting from Offensive Infosec to rebuilding outboard motors (boating), installing marine electronics, Starlink, navigation etc etc, and I also repair laptops, swap out phone screens and general tech I could do 10/20/30 years ago. It does not pay nearly as much, but it’s fun, I’m outdoors, and I absolutely do not deal with Office Types or fucking HR.

Most importantly the people and clientele I deal with treat me as a seasoned professional and a whole human being, not some cog to be muscled around.

My last contract was a 6m remote position with Interpol (France) working in the Financial Crimes division, and if that could have turned into a FTE role I would have jumped on it. The French are a WONDERFUL people to work for & with.

Good luck my friend, keep positive.

I know a little about the academic system. it’s not an easy market to succeed in. but if you do it’s a wonderful life. you’re free to work on problems you find interesting, without worrying about whether or not they are profitable.

sounds like you genuinely love doing research in math, given that you put in a lot of time and voluntarily turned down a cushy job.

my suggestion is to put your nose to the grindstone and pass your quals. it’s not easy and not everyone makes it… but it sounds like the path to the career you want is this way.

I think generally speaking mathematicians are hired by insurance companies, the government, local administration. Random facilities that deal with studies and statistics… There is some overlap with computer science and there are a lot of technology companies out there, dealing with all kinds of domains, Analysis such as signal processing, statistics, more applied things that require maths for engineering, more abstract things like proofs that algorithms do the right thing. Optimization, robotics…

I mean if you dislike sitting in front of a computer in some office, all day… Teaching might be a good call.

Or see if you like electrical engineering. That includes some more at hands dynamics. And you also do a lot of calculations and integrals. I’m not sure how easy it is to get there without studying it. But some aspects of engineering might require formally trained mathematicians.

Your MS degree already puts you ahead of 95% of everyone else, all the PhD would do is add 4%. :)

I gotta be honest though, I don’t know what jobs require a math degree, maybe something in aerospace? Could be a good gig under a new Trump/Musk administration, lots of money going to SpaceForce I expect.

What about the public service? I don’t know about where you live, but in my country the public service doesn’t care what degree you have, just that you have one. Look into the graduate programs of your local/state/federal governments.

Do you want fries with that?

How broadly do you dislike programming? Data science kinda stuff could work for you if the main focus is on modleing and understading data, even if that means actually implementing the models and the algorthms by programming.

AI is currently all the rage. I know a guy who does neural networks training, and it’s the closest job to Pokemon trainer that you can have. He does not know any programming language, it’s all purely data processing, and it requires a heavy math background. It’s still an 8 hours per day job in a corporate environment, and a half of it is fixing his computing farm, because there’s no dedicated sysadmin for replacing burned videocards.

Another math-heavy option is signal processing. I’ve worked in a company which produces wireless communication hardware, it’s like 200 people, and there were two signal processing guys who patented an algorithm which increases data throughput by something like 0.5% in some specific high-noise scenarios, they are listed together with CEO on their website About page. That said, all the easier tasks for signal processing are already done, we’re already at the theoretical limit of Shannon theorem, so you’ll only be making gradual improvements.

I would also recommend cryptography research, but it requires a lot of coding knowledge, even if you’re not writing any actual code, and paranoia is pretty much a requirement.