I'd be thankful for any idea thrown my way (be it actual companies, domains or just vague career plans).
Cheers
I'd argue that you can distinguish between career paths that
- make use of and are related to your broader specialisation within maths (e.g. fluid dynamics, actuarial sciences, cryptography, derivative pricing, specialised ML research...). For these, it's hard to give recommendations without addition details. They can still be open to folks from unrelated maths backgrounds, but it depends on other experience and circumstances.
- are highly quantitative and tend to value PhDs from quantitative disciplines (e.g. "Data Science" & data consulting companies, banks, (Re)insurance companies with internal training, quant trading, applied ML research and startups, possibly sports betting...). For these, PhDs in physics and EEE will probably be similarly appropriate.
- value smart people with academic titles regardless of discipline and might require separate skills and qualifications (e.g. strategy consulting, IT consulting, patent attorney, software development ...? ).
I would start by assessing where your interests and qualifications sit within that range. It can help to start by focusing on a specific industry that you find interesting and then find out what kind of maths-adjacent roles there are. In my experience, this tends to be very different for purer vs more applied maths PhDs.
[1]: https://rocmdocs.amd.com/en/latest/ROCm_Libraries/ROCm_Libra...
GPU coding sounds very technical! But I'll read up on it :)
Members from my class (including +/- a couple of years) went to startups, think tanks, SEC, NSA, trading, hedge funds, digital media, academia, postdocs, consulting, and commercial research labs that are incubators within larger corporations.
You didn't indicate your specialty, but it probably does not matter. Many current DS and related jobs list PhD in a STEM field as baseline or preferred requirement. I know logicians who got non-academic work (this is not a dig at logic, they were really worried about this).
If you want to go the software developer route, at this point you do know how to study for leetcode type puzzles. But you are in direct competition with many others who specialize in that, and a PhD in math will not carry much extra weight in the hiring decision.
Watching my own and my peers careers evolve over time, the impact of one's network should not be underestimated.
Finally, assume you will never be asked about your dissertation. Ever.
Consulting for oil/gas/drilling as they always need analysis.
Financials.
Data analytics (of any kind).
Physics labs/research labs.
Manufacturing (optimization problems, efficiency problems, actual problems <snicker>)
Have you thought completely outside the enclosure?
Sitcoms (look at the people on Futurama or Big Bang for example)
Porn (how _would_ you figure out the volume of that thing??)
Entertainment (Bill Nye the science guy, rosetremiere the math is near!)
Since I don't want to tamper my anonymity here, let me tell you a few tips:
First, find out for yourself whether you want to work in enterprises or startups. Whether you want to apply scientific methods/conduct private research or not.
I had a clear idea for myself: startup+research. Once you know this, you can basically let yourself "go with the flow": Look up interesting people and topics (at TED(x) conferences, at youtube, at fairs or conferences) and ask if you can work with them. Works best if they are CTO/CSO at their startup (such as I am) :-)
The short story is: software development. Sure, there are more quantitative jobs like data science and ML and other mysterious math/scientist jobs that are quite hard to find and secure, but software development of any kind is the quickest way to a job. You'll need to convince people you're not a pie in the sky thinker, and so I'd recommend building up some side projects. Functional programming languages will probably suit you better, and those jobs can sometimes be more technical. Also, universities and research institutions, at least in the U.S., are hiring more and more software developers.
Regarding trading and blockchain, having some principles is fine, but you also need to eat. There's nothing wrong with taking a job for a couple of years to get your feet into industry and then moving on from there.
As someone who made the move to software from math many years ago, it feels like it was a good short-term decision, but I don’t know if I can make a life-long career of it. Sometimes I wish I’d chosen something that played to my strengths more.
Thanks! Indeed, software development seems like one of the most probable course (my bachelor was in CS, so that's not too far either) but I'd be worried to end up too deep in software development, with no "input" from what I learned studying maths. Ideally, I'd still put this background to good use.
BadCookie: isn't it possible to choose that as a short-term solution, and then slowly navigate to something closer to your strengths?
I’ve mostly enjoyed my career and can’t complain about the money, so take my half-hearted regrets with a grain of salt. I’d probably be questioning my career choices no matter what path I had taken! And with your CS degree, you can probably avoid some of the imposter syndrome that I have experienced.
I would pick AI, because it's a growth industry with on-going innovation. You would also be able to work in many different kinds of applications. It seems like it would be fulfilling work.
You didn't mention why you're uncomfortable with trading. Finance used to be a great choice, but it's not a growth industry now, innovation stopped after the Financial Crisis in 2008, and the industry has been saturated with PhDs for over a decade. Meaning math PhDs not in demand very much anymore in finance and most of the work is not very interesting anyway.
Personally, I wouldn't pick crypto ("blockchain") as a lifetime career.
Note that any of these career would require significant effort and learning on your part. You didn't mention what your PhD in mathematics is in. You would be competing with PhDs who have done their thesis in something highly relevant to AI or finance and/or have done a great deal of research on the topic before applying for jobs in their target field.
If you don't care about how much money you'll make, and enjoyed your PhD work, then I suppose postdoc would make sense. If you don't care about money and didn't like the academic environment, then you could go into teaching relatively easily with your qualifications. Perhaps teaching / lecturing at a private school or college, if not a university. I would suggest that you do care about money though, because it is an important factor in determining your quality of life.
Re. uncomfortable with finance: I guess it's a mostly "intuitive" ethical concern. I don't feel like finance is very much part of a society I'd like to live in or contribute to. I have heard arguments that e.g. trading is a big part of making the economy fluid and optimizing throughput or something, but it sort of rings wrong to me. Maybe it's just preconceptions and I should learn more about it!
Re. significant learning: Indeed, and that's part of the problem: since I'm not entirely sure where I want to go, I don't really have the mind to invest too much time learning about fields I probably won't work in, which makes my profile less attractive I guess. I originally had hopes that I could learn on the job: you often hear people tell you that a math PhD is proof that you can learn efficiently and have the capacity to work any technical field, or something. But I see now that it's probably not how it works: hirers still want some proof you're competent in their specific field.
Re. postdoc: the problem here is that the competition is rather fierce and the work conditions not always optimal.
Your intuition about ethical dilemmas in finance is not entirely misplaced. I know all the arguments about finance and trading being useful because it is the process by which capital is "efficiently" allocated in the real economy, but that's academic fantasy which ignores how the real world works. The truth is, in order thrive in finance (and, by extension, crypto) you need to be someone who is perfectly happy being "ethically flexible."
By the time you start running into these ethical dilemmas, you're typically in too deep and it's too late to get out. You justify it to yourself because you're just a small cog in a big machine who can't change anything and you need to earn a living (and have gotten too dependent to a certain level of income that you can't earn anywhere else at that point). You can relatively easily make as much as a doctor or lawyer, but I can assure you that in a successful finance career you will need to "ethically flexible" whether you like it or not. A doctor can go home knowing that they saved lives, in finance you'll feel the pretty much the exact opposite.
You said the competition for postdoc is rather fierce, the competition for other jobs (e.g. AI and finance jobs) is just as fierce if not more. Basing your decision on fear of competition is not a good idea because every career or job is highly competitive.
You need to pick a track and work on it. Significant learning is part of it, but I should also mention that your network is equally important if not more. You need to build your network. One way to do this is to stay in touch with people you went to school with, not least because some of them will get jobs in your target field, and they might be able to help bring you onboard. Another way to network is to ask out people you don't know (e.g. that you find on LinkedIn, or profs or whatever) for "coffee" to learn about their industry - this is known as an "informational interview," you can Google the term to learn more. Good luck!
* Bachelor in CS, and I kept an interest in computing/programming languages, although I don't have much to show for it. I do have some scientific julia code, but it's closer to the hackish academic-type dump of code than a well architected endeavour.
* I'm coming from pure maths, and I have very little experience with computational aspects of analysis/geometry. I also have pretty much no knowledge of probability/statistics.
* I _do_ feel like it wouldn't be too hard learning the prerequisites for the above, given a few months and a good textbook.
* Re what kind of maths/development I'd like to do: I guess pretty much anything where there is a relatively strong "research" component. Not necessarily meaning pure research, but where it's not just about applying methods, but also about developing them and understanding the problem and solution space before "rote application", if that makes sense. If I was super sold on the end goal of the company, then I guess I'd naturally put less weight on those "requirements".
* Typically, I've been interested in compilers/PLT for quite a long time, but that's typically the kind of thing relatively far from my field. There would probably be quite a steep learning curve, and I'd be in competition with people that actually studied that, hence little chances of success there.
* My university was a small European local university, with a small maths department (third tier, as some might say). I don't feel like I was a particularly bright student, and I also figured that PhD students weren't necessarily as intelligent/productive/creative as one might believe from outside.
Re game theory: I would have guessed it wouldn't be kind of useless! Doesn't it at least provide you with a good perspective/insight into plenty of real life problems?
Any kind of data science/machine learning?
Disclosure: I work for one of those firms (CipherTrace) so I may have some bias, but really, this is the portion of the Fintech/Crypto spectrum I find acceptable.
BTW I love what you guys are doing over there.
Interesting, I didn't know about this side of blockchain.