I only spend one hour a week in my office for my office hour.

Looking at my calendar from this past semester I was in 3 courses, which each met for 3 hours had 8-10 hours of homework each week. I attended 4 weekly seminars (1 of which I was helping organize; two of which I presented in some weeks). I taught one course which met for 4 hours, double that for class prep. I had 5 hours regularly scheduled in the tutoring center, plus an office hour. I’m slow at grading, so it often took me 4-6 hours per week. Plus an hour a week for my advising meeting, and we’re at 60 hours before I even begin talking about when I’m doing my own research - I typically try to devote my weekends and also Thursday afternoons in their entirety to either reading math books of interest to me or papers of interest to me (I do the rest of that stuff MTWF).

So it’s not quite 90 hours a week every week. There are weeks when the tutoring lab was shortstaffed so I needed to pick up an extra three hours there. There were times when I would proctor a 3-hour exam. There were lots of severe injuries in my department this semester so I’ve covered people’s classes too. So there were a lot of 90 hour work weeks just due to the structure of everything, but I guess saying that every week is a 90 hour week is an exaggeration. I don’t think I’ve worked fewer than 75-80 hours a week all semester though.

Paul Erdos got his PhD in mathematics when he was 20 years old. If you wanted to name a famous academic without a PhD, you should have gone with Freeman Dyson.

But yes, I need to not starve to death in case I need to leave my program. That’s why I mentioned jobs.

How broadly do you dislike programming?

After undergrad, it seemed like I had two career paths. I could either apply for PhDs in mathematics, work 90 hours a week for 19k/year in a state a thousand km away from anyone I’ve ever known; or I could have tried for a cushy entry-level coding job making 6 figures starting salary in an area close to all my friends from undergrad, and working something normal like 40 hours a week. I chose the former.

I am currently doing what little coding I currently am in an effort to get it over and done with ASAP. My plan is to never write another line of code again once I’m done with my numerical analysis courses.

Again, I don’t think I can personally work for military contractor companies like Boeing, Northrup, etc.

In undergrad I did a project on harmonic analysis and wavelets, with some attention having been paid to the signal processing applications. (And by that I mean I learned enough to say ‘this has applications in the fields of signal processing and image compression’ in the abstract). But at this point it’s years ago and I don’t remember too much.

I took seven computer science courses as an undergraduate, including three that were programming courses designed for people who would go on to be professional programmers (intro, intermediate, advanced programming). I also took other CS courses that included programming components. Every single task that was just, “please program tetris” or something of that sort, I loathed every second of it.

I will not like programming.

Introductory QM is for undergrads, who also know next to nothing about QM, and I’d bet there are plenty of profs who’d like to unload that job and get back to their desks

Yes, so the job would be given to physics grad students. Which I do not know enough physics to apply to be.

If I’m in a position where I’m being thrown out of my grad program with just a masters, I’m not then going to turn around and say, “well, time to do it all over again, this time with a field I’m less passionate about!”

I will never work for an insurance company. And just saying “the government” is so vague and nebulous as to be meaningless; at least in the US where I am I think it’s mostly either military/‘defense’ stuff, or essentially spying on people. Neither of which I’m comfortable doing.

I’ve never heard of random facilities, but it warrants looking into given all of the things that you’ve mentioned. I’m not interested in all of these things, but it definitely sounds like it has a lot more to offer than most other “mathy” jobs. You also say “more abstract things like proofs”, but proofs are the entirety of what math is if you have a math degree.

Electrical engineering is its own discipline, separate from math. Unless I go back to undergrad and study EE from scratch, I will never be competitive in that job market against people who have specialized degrees in it.

I don’t know quantum physics though. It involves a lot of math, but it also involves a lot of physics which I don’t know. It’s something that I’d like to learn at some point, but right now I just don’t have the available bandwidth to learn it - and I definitely can’t teach something I don’t know.

Maybe? With the recent DOGE stuff I’m not convinced that the NASA budget will do anything but shrink, and if I were to do aerospace I would probably want to do it under NASA. (I’m a pacifist, and don’t think I can work for the militarized SpaceForce nor contractors like Boeing while still maintaining my personal code of ethics).

But, I will definitely look into it as a possibility.

I don’t know much about how to enter into a relationship online; I know people who have done it, but it’s never been something that I’ve been interested in. However, many of my strongest friendships were made online.

The trick to making friends online is to not set out with the intention of making friends. It’s paradoxical, I know. What you should do is just find something that you’re interested in, find places online you can talk about them, and try talking about them. Personally I like math, so I met some friends on internet math chatrooms and forums. I like Star Wars, and I made some good friends through talking about Star Wars online.

Many such places also have a casual conversation place attached. In niche communities where you (a) are already engaging with people with a common interest and (b) there’s few enough people that you will see names and faces regularly, but enough people that the conversation never dies down, eventually you’ll become a known quantity and make friends.