(from an applied maths PhD perspective)

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.

AMD is hiring developers for the ROCm math and communication libraries [1]. If you're interested in developing open source mathematics code for GPUs, there are a number of open positions. Send me a message to discuss opportunities in more detail. My email is in my profile.

[1]: https://rocmdocs.amd.com/en/latest/ROCm_Libraries/ROCm_Libra...

PhD in math, US perspective, 20ish years working.

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.

I have a good friend, in the US, with a Ph.D. in math. It seems like there is no job he can _not_ do.

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!)

I had a similar situation with Physics PhD a few years ago. Now things have turned, I'm doing my startup and we urgently look for people like you.

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) :-)

You can find some pretty good responses on reddit.com/r/math. This gets asked quite often there.

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.

If you come from applied math, then numerics! For structural analysis, fluid dynamics, robotics, machine learning, etc. If you asked this question week ago, I'd probably hire you.

I think if you want to make good money, then your realistic options are finance, crypto or AI.

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.

Commenters are clearly trying to help. They can do better if you provide more context. What kind of math do you want to do? This does not have to be related to your dissertation area. And since you are asking on HN .. what kind of hacking/ development do you want to do? Coming from academia (I have a phd in game theory -- kind of useless in real world, other than ad auctions), it gets easier to find an industry job and develop idea of a good fit once you already have one! Don't be too picky to start with. Good luck!

I’d like to shed some pessimism on a lot of the optimistic comments. Unless you did your phd in quite an applied area you may find it tough to get a job without extensive study. I graduated with a phd in pure math and had a very hard time even getting applied positions as I didn’t have the domain knowledge. I ended up in software and still have the nagging feel the grass was probably greener on the other side.

Always seeking talented and curious mathematics PhD's in the defense sector (or 'defence' sector if your staying on that side of the pond). Autonomy, robotics, data analysis (for a variety of reasons) and even just basic research. Many of the applications worked have direct correlaries in the commercial sector if you'd rather work on that side. Plenty of work to be done.

Any kind of computational science? We need applied maths people to explain the maths to us <3 ^^

Any kind of data science/machine learning?

Not all "blockchain" is the same (case in point, there are firms that do Anti-Money Laundering/Fraud and Counter Terrorism Funding activities which use lots of big data/ML stuff).

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.

Maybe there's something interesting here: https://www.esa.int/About_Us/Careers_at_ESA/Professionals ?

Many Data Science/Data Analyst jobs would love to have someone with your credentials. Also, if you self-teach how to code and create software, a math PhD can be a huge boost for certain specializations (i.e. Machine Learning Engineer)

Not sure what your reasons are for not wanting to trade but there are other PHD maths roles in banks - quants, quant developers, structurers etc,

Economics doesn’t have to mean trading/crypto

Data science and/or ML? A mathematics PhD is a big advantage when applying for those positions.

post doc?

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