Here's a long essay because I was in your shoes once and it took me a while to find myself.

Well, I'm currently in between roles but I'll give you a basic summary of my resume. It's a lot of weird director roles mostly in eCommerce and design. I explain this a lot as well, math is the same everywhere. Jumping has its risk but overtime it's stabilized decent growth in my salary and I'm constantly picking up new skills.

I have a BS in Math. I think my minor was in applied? Not sure. I was lucky enough to take grad classes for all the requirements for quantitative finance MS under my scholarship but wasn't eligible to graduate because my scholarship didn't cover that school technically. I could've figured it out but honestly nobody even asks if I have a degree or not. Basic lesson I learned is that the easiest opportunities out of applied math all involve learning some Python. I find R in the wild less unless its for research, but I still use it.

Out of school I did two things, I worked at a number of teaching opportunities which paid okay sometimes and I slowly began the process of building out a data science startup.

I definitely entered tutoring and teaching with a sense of humility, I was not going to be making much money anytime soon. These kids needed my help, not my attitude. Traditional roles for math are far and few. But there's a lot of really nice tutoring and substitute teacher roles if you know the right people. I suggest starting out at an agency which contracts you out to build out a client network. At least in the Bay, this is a good way to meet a lot of smart rich people. I don't know if I'd recommend this role now with COVID. I prefer at least pen/paper/chalkboard one-on-one sessions for teaching and find it cumbersome to do online. Programming is better online since you have to deal with different environments and hardware anyways, good practice.

For the data science startup, I knew immediately that my biggest flaws out of school was that I did not network enough, did not pursue research more seriously and overall sucked at socializing. It was an incredibly awkward and humiliating period of my life. Being smart means absolutely nothing if you're not a stable, professional and confident person that people are comfortable working with you. Especially if you are handling sensitive, complex information. So I spent the next 5 years working on that.

I did some questionable practices, such as cold starting my professional network by setting up an AngelList browser script which applied to like 22,000+ jobs and left a little personalized message for them to contact me directly. Not a very cool thing to do, but I was desperate and scrappy. Being somewhat familiar with Python, I found a lot of lowhanging fruit from modernizing Python 2 repos for data science and machine learning into Python 3 which involved adding parentheses here and there basically. That encouraged me to be more confident that I can actually contribute to research and develop my own projects. Last, I purposely seek out more directorial and managerial roles that involve more face-time and meetings than actual programming. Socializing does not come naturally to me and I have to practice it every day or I fall out of my rhythm. I'd have to say, I do not spend as much time doing or studying math as I'd like to in any role, but the benefit of what I know comes handy almost all the time because I'm at least aware of a solution or technique that applies to almost any given situation. Anyways the moral of this story is that, as a student of mathematics, you cannot reasonably apply the rules of normality or societal expectations to naturally shape your career. By and large, most of us do very poorly in making a decent living, and it behooves you to be pragmatic about your thinking and work towards decisive changes.

Takeaways: In order to succeed in math, I had to drop my attitude that anything about math mattered at all. I don't even bring it up these days. It's kind of a liability, because it reeks of "esotericism". It bears unfaithfulness unfortunately, but there's nothing you can do to change people's stereotypes. Most of my success these days comes from learning how to function as a human being and not a coffee algorithm machine. Take on whatever work you can find, it will invariably lead to a better recommendation even if you're just cleaning up Excel spreadsheets or teaching kids. People in math are generally very good at being lost for a long time and it helps to keep up with where they're going, sometimes they introduce you to things that are once-in-a-lifetime.

From a more practical standpoint. Here are some things you can do to build out a professional presence, that in my opinion are a good idea even if you're not focusing on getting a PhD.

Start a math blog. Wordpress, GitHub pages, doesn't matter. As long as it supports basic LaTeX and Markdown, you should be good. Find something you're interested in to write about. Learn how to market your ideas. If you need help setting one up, I'm more than happy to help you find something you like.

Treat research as a lifestyle, not a career. Find preprints you like. Experiment with repo's that are cool. Build projects for yourself. Share your ideas on Twitter, talk about papers, meetup with interesting people in your field or industry. You're already on Hacker News, that's great! Contribute to open source, publish tutorials. Golden rule, if you are generous with your time and space, the universe will kindly return the favor to you.

If you're deadset on FAANG or prestige startups, that's actually a fairly attainable goal. Learn the ins and outs of an interview process. If you've taken basic algorithms courses, understand data structures, and are generally good at problem solving theory or metaheuristic approaches, you're in good shape. Generally I have found that the higher bidders tend to appreciate people who understand numbers a lot more since they have a generally higher incentive to focus on endeavors that actively make money. Polya has been incredibly helpful to me in this regard.

My most successful roles have been almost always completely made up. Standing at frontier of research or science opens up a tremendous number of opportunities, simply because you can see them. The best jobs don't exist yet. If you want a place in this world, there's a lot less competition when nobody does what you do, and you get more credit for doing it because you're the first to do it. Treat the world like you would treat yourself.

To conclude, be open. You are a mathematician. What you do is incredibly noble, demands creativity and its essence is freedom. The vast, vast majority of people will never have the opportunity to study what we have, and that gives us a tremendous advantage even in tech and computer science. I have been hired for roles for reasons that had nothing to do with being smart or writing good code but mostly because I was interested in ethics and taking on hard choices and problems. Your career will invariably be nonlinear, like almost all money is. Focus on maintaining a discipline in yourself outside of school. Learn to specialize, learn to generalize, learn to do balance both while practicing moderation in moderation. Keep doing math for yourself and only for yourself.