Math Ph.D. does not know what to do with life? [closed]

Question

Background: I am a Math Ph.D. student in the U.S. (originally from a developing nation) in partial differential equations (PDEs) but on the theoretical side of PDEs (no simulation, no numerical). I am starting my 7th year, and my advisor is expecting me to graduate this year. I am on the job market now for a postdoc. I have 5 publications so far, 2 arxiv preprints, and 3 peer-reviewed in okay-ish journals (not high impact). I am an international student as well.

Summarize the problem Academic jobs are hard to find and I want to stay in the U.S. After a while of looking into the industry without any results, I am now losing both motivation and hope for academia as well as an industry job.

6 months ago when talking about jobs (we all know how hard it is for jobs in academia), my advisor has been very pessimistic. I am advised to apply to all countries, around the world, for any postdoc listing I find. Through the conversation, I did not feel I can make it, therefore I started to lose my motivation and hope. I want to stay in the U.S., for the following reasons:

• I could go back to be a lecturer in my home country with very low pay and a high teaching load. However, if it is the case, I think getting a postdoc, having more experience and connections for later collaborations when I am back is much better. I mentioned this to my advisor but I did not feel being supported.
• I can make more money going to the industry here (if I am lucky to find a job), at least for a couple of years. My family is dirt poor and as a Ph.D., I was not able to support them at all for the last 10 years (undergrad + Ph.D. salary).

What I have tried: So I started to look into the industry, as it is a natural thing to do. I first did a Bootcamp in Data Science and I bombed it hard, the pace was too fast and I fairly lost. I believe I can learn them, but not quickly enough in 3 weeks (the span of the Bootcamp).

I then tried Software Developer, taught myself using online courses and open sources projects. I have been trying to apply to some internships but have not been successful. I found myself panic every time looking at the job posting and see how under-qualified I am.

Back to Academia: I recently sort of having a verbal offer for a postdoc. However, after a couple of months of losing motivation in research and academia, I cannot seem to pick myself up again imaging I can be good at a postdoc. At the moment I just want to be out, but I am not sure if it is a good idea or I am just hate everything due to burnt out. I am extremely scared of making a big mistake and regret it later in life. I do not feel confident that I can land a TT position with this mindset and this level of motivation (assuming I can do 2 postdocs).

Somewhere inside me, I am still having fun doing some of the projects I have left unfinished, but I am not sure if it is just a comfort zone, doing something I am comfortable doing to avoid looking at real life. I want to comment that, I do not feel the work I do, while they are fun to me, are of interest or that helpful to many fellow mathematicians. I do not have a sense of fulfillment. However, I had a naive "dream" that given I have a permanent job, I can learn anything and make significant achievements in some related areas of Math. I realize this is a fantasy.

Resentments I hate being poor and lonely. I am approaching 30 without any relationship (even friendships). Throughout my life, I kept thinking about publishing and publishing, people will treat me better. I always have the sense of being worse than people, it really messes me up when trying to socialize and make friends. So, just like many other mathematicians I know, I followed them and isolate myself in the office, trying to write more and more papers, and thinking this is what defines me. I am sad.

Questions Do you have any advice for me to figure out what do I really want? Or just to lessen the tremendous stress I am having, which causes "analysis paralysis" to me?

Answer 1

I'm a current software engineer in the bay area, and have a similar background (without the phd) as you. I've wanted to do physics since I was 8, but after graduating with my bachelors I felt there isn't much future and definitely no money in academia. My friend's internship pay as an undergrad software engineer for 12 weeks is higher than my expected annual income fresh out of PhD. I then spent a few years working in different academic research labs while doing a masters in CS and preparing for and interviewing for jobs, before landing one.

First, I will not depend on what your professor says or recommends. The way I see it, the kind of person who will become a professor is not the kind who thinks about money, or a profitable career. Many academics are also dismissive towards money and folks earning a high salary. The fact that your prof allows you to do a 7 year phd program without a career plan suggests to me they don't give a shit about your career, or about what you want, since you raising this question suggests you don't want an academic career by this stage.

Second, you mis-interpret what a bootcamp is nowadays. A bootcamp is not only time for learning, 8 weeks don't make an app developer. A bootcamp, for the reputable ones, is an assessment centre, for someone who have spent 1-2+ years polishing their skills to have someone assess them so they can use that qualification to sell themselves, their ideas, and apply for jobs. The less reputable ones are not helpful, not because they don't teach you anything, but because the value of the bootcamp comes from their prestige and connections with potential employers. Hone your skills before spending your time and money going in, otherwise it's a waste of the latter and a stressful use of the former.

Third, as people have said, definitely finish your phd.

Fourth, in my opinion, there are 2 goals you can aim for. First, a generic software engineering ("swe") position. Your selling point will be your quantitative skills. I would keep this as a backup option. If you have only a bachelors in maths, sure, phd you can probably aim for something more relevant, especially since yours is pretty applied and relevant. But I have seen it work. Second, data or research scientist positions. Brush up on your software engineering skills, tech companies generally still want these roles to have decent coding skills, though the bar is definitely lower than for pure software engineering. Get a job similar to software engineering and then gradually transition there in your daily work if that's your inclination. I've seen maths or engin post-docs reach pretty high positions at a similar pace to what a computer science software engineer would have, so it is viable. I would advertise myself as a data scientist with very solid background in quantitative skills and problem solving and capable-if-untested engineering skills. Another path is to leverage more on the PDE work and apply to hedge funds as a "quant" (quantitative analyst), those will work out too and pay a lot better, if you can get it. It's definitely more competitive however, reach out to headhunters on linkedin or through career centre or friends, I would cold email and message and be aggressive, but it is do-able.

Next, to provide some context on salaries and career progression. To aid discussion, I'm going to use google's L3 (junior swe) to L5 (senior swe) levelling scale. It typically takes 2-3 years to go from L3 -> L4, and 3-5 years to go for L4 -> L5. As a post-doc, you'll join as L4+, meaning it should take 1/2 the amount of time from a L4->L5 jump for you to hit L5. So as compared to someone starting with a bachelors in CS, you have a lead of around 4 years. For pay, you're looking at (again google, check levels.fyi) ~300-350k starting, to hit around 400k in 2 years. So you'll be fine.

For the quant path, the variance is much higher, but I would expect 200-300k (base+bonus) for your first year, and you should expect to hit 500k in 3-5 years, and 1m+ if you manage to survive that long in 8-10+years. Look at some of the quant forums to see the salaries people are posting. Downgrade their values by a bit since only successful examples will post their inflated values there.

For your isolation. I felt exactly the same when I was grinding to get my current job too, and although my team back then is great, I hate the work since I don't feel it impacts anything, or pays well. I realize in retrospect that this has knock-on effects on my social life. Essentially, because I feel my current position in life is shit, I don't feel like going out that much or being socially active. I don't feel I deserve to be spending time out there, and that I should be grinding and doing something with my life instead. I'm not saying that life gets better when you get a high paying job. But that assuredness with my career and my life made me feel more confident going out and spending time trying to make new friends. That disposable income helps in subtle ways too, I can go out and spend without feeling guilty or indeed caring much for it, and that made me appear more outgoing and sociable. Maybe. So I will not think too much about the isolation part and focus on getting a decent job offer first.

Next, on what I would do if I were you now. First, I would create some application that leverages and advertises my strengths. Based on your bootcamp experience, I might do something like build a aws-hosted server that retrieves nyse stock data once every day automatically, derive some basic trading metrics, and post them on some website with some good-enough plots and graphics. Clean up the project, add a nice readme and some snapshots, and post on your github.

Second, interview prep. Leetcode, CTCI, elements of programming interviews, do all of them. Get good enough to confidently solve LC-medium questions you have never seen before, around 70% of the time. This should take around 3-6 months fulltime, but you can apply while preparing, since you only need to be ready come interview and not application time.

Third, get that interview. Clean up your resume, reach out to friends or folks currently in swe roles to ask them to review, get multiple data points since some opinions may be inaccurate. Reach out to career centre, I would take their resources and connections, but usually ignore their advice. Cold email and linkedin message amazon recruiters, apply to google/whatever's phd internships, for the last point you need to finish the internship before you graduate so do it early. Ask for referrals on teamblind or friend-of-friends or whoever you can find. Be aggressive and shameless in your search.

Finally, your situation is more common than what you might expect, so do reach out to other folks in potentially similar situations, for advice perhaps but more to have people to rant and talk to. It's a marathon, but like a marathon so long as you keep moving, you should be fine. Mentors are invaluable, have a few so you can diversify the rant load and get more considered opinions.

Caveat emptor.

Answer 2

Let me just comment on what you say towards the end, wich I believe is the root of your predicament.

I hate being poor and lonely. I am approaching 30 without any relationship (even friendships). Throughout my life, I kept thinking about publishing and publishing, people will treat me better. ... [I kept] thinking this is what defines me. I am sad.

People can thrive without a great job, but they wither in isolation. You're revealing an important insight here, which is: No amount of publication and hardwork has brought you closer to positive and nourishing relations (people who "treat you better"). Now is a good time to reconsider your actions and future "life decisions" in view of this insight. Your academic accolades (or perceived lack thereof) are not what defines you. Relationships are much more important in this regard for most people.

It can be hard to get a broader perspective on what matters for you from within the thicket of everyday academic bustle. When was the last time you got on a bike or swam in a river? When was the last time you talked the night away with someone who doesn't speak math? If these examples strike a chord with you, I encourage you to take care of these human needs first, because it sounds like you haven't in a while. Perhaps this is incompatible with your larger career plans and you may decide to put them aside for a while. But maybe not. The happier I am with my life, the more curious I get about my work. YMMV.

Answer 3

A lot of years ago I worked with man-in-the-loop and hardware-in-the-loop simulators as a real-time computer vendor helping customers make use of the platform and tools. Two hard problems which were unsolved at the time - flight near the ground (take off and landing, generally altitude below the wing-span of the aircraft) and pot-holes (specifically simulating anti-lock breaking systems). These both involve numerical heuristics derived from PDE because of a lot of features that are not solvable analytically. The arena of simulation has not contracted, just the computers and tools are no longer "special" and I've moved on to other modalities.

To my mind, having a theoretical understanding of PDEs might provide insights into providing better numerical estimates for simulations. Certainly there is a way to find a field of simulation that needs improved modelling. Anything involving turbulence in fluids comes to mind.

Most programming is aimed at the bottom of the math capabilities, but there are computing environments that work at a higher level, such as Mathematica. Don't do programming from the bottom-up, but from the top-down, where your experience and skills are more appropriate.

Answer 4

Maybe you could consider to look for a job that combines both math and social interaction, something like school teacher? you could stay some time there and go back to academia in the future, or switch to the industry later.

Answer 5

Consider applying for academic positions in your home country.

Generally, there's a rule of thumb that academics tend to work at institutions less prestigious than the institutions that they went to school at. As a result, you may want to consider applying for academic jobs in your home country, since you say that you're from a developing country. While there may be exceptions for specific institutions in specific fields, generally a university in a developing nation will have less prestige than one in a developed country.

Additionally, since it's your home country, you would presumably be a citizen, and not need to deal with visa issues, and your cultural familiarity may help you with the feelings of social anxiety and alienation you mention. While I expect that such a job would likely pay less than one in a developed nation, it's also likely that the cost of living would also be significantly lower; depending on the ratio of pay to cost of living, it might even be possible that you'd be relatively wealthier working in your home country, compared to getting an academic job in America.

Answer 6

Not sure if it helps, but where I live (Europe) just being able to do, and not being afraid of, high school math is already a selling point for software developers. So it's not like you have nothing special to offer, even if your field of specialization may have little overlap with the field a company works in.

Answer 7

You write:

I want to comment that, I do not feel the work I do, while they are fun to me, are of interest or that helpful to many fellow mathematicians. I do not have a sense of fulfillment.

When considering what you can contribute to mathematics and what others may value, try reading Terence Tao's article What is good mathematics?.

I can't do his article justice by merely summarizing it, but note that he lists problem-solving, technique, theory, insight, discovery, application, exposition, pedagogy, vision, taste, public relations, meta-mathematics, rigor, beauty, elegance, creativity, usefulness, strength, depth, intuition, definitiveness, etc. You may be able to contribute in at least one of the above areas and perhaps you have been focusing on just a few of them, not realizing that the others also have merit.

Answer 8

Just focus on getting your PhD submitted and successfully defended.

It's clearly high time you had a talk with your supervisor. He's allowed a 4 year program to advance to 7 years and that alone reflects very badly on him/her. If this supervisor doesn't display enough urgency about your situation, go straight to the Head of Department: this thing can't be allowed to drag on and on.

Your PhD must be your priority. But mosey on down to the campus careers office some day and have a conversation with the adviser for your department as they will know all the avenues for people with your type of experience.

EDIT

I incorrectly suggested USA PhD programs were typically 4 years long. In fact it is 4 - 6 years usually. But still and all, it's time to finish at year 7.