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I did a PhD in pure math and now work for a big tech company. Having the PhD will get your foot in the door basically anywhere, so you'll at least make it to the screen, but ultimately you have to pass the same interview as anyone else. That means doing LeetCode and reading Yegge's stuff etc.

If your goal is to maximize lifetime earnings, a PhD is maybe not the right choice, but if you want to spend years studying something you love while financially breaking even then go for it. I definitely don't regret it, even though I would be worth a lot more if I had gone into tech straight out of college.

Btw, finance is also a common destination for pure math PhD's looking to leave academia.

Thank you. This is exactly what I wanted to hear. I’m more interested in studying math than maximizing my income, but post-graduation opportunities is a concern, since I’m not well off. Your reply gives me the encouragement I was looking for to pursue my passion. Thank you.

To add to the discussion. I did a CS PhD with a statistical bent. It's served me well. However, I would see if an MS provided you with equivalent benefits from a career standpoint. Very few companies do "research". And if you're in the US, unless you acquire funding with yourself as the PI its going to be impossible to find an academic position.

> I definitely don't regret it, even though I would be worth a lot more if I had gone into tech straight out of college.

My take is that life is ultimately about taking the chance to do interesting things when they crop up.

Personally I enjoyed my PhD, but I watched others get hurt, so I wanted to add some words of warning.

It's a risky choice, unless you're very good. You should go in with your eyes open, knowing that you'll be lucky to get an academic job afterwards, especially if you're in a 'pure' field without many applications. For industrial jobs, you'll probably have to re-train through self-study. After a maths phd, doing so may come easily, but it will also take effort.

You'll spend three to seven years (dependent on your location and ability) working on an extremely specialised topic. There is no guarantee that you'll finish: circumstances beyond your control like your relationship with your advisor can derail your progress regardless of your ability. There is also a 'point of no return' after a year or two where it becomes very painful to cut your losses and walk away with nothing.

Doing a maths PhD could open some interesting doors. It will improve your employability, but it's an inefficient way to do so. The only good reason to do one is that you really like your research topic and want to spend years immersing yourself in it.

Yes, I saw a lot of really good students enter an applied math program when I did. I left with a Ph.D., but nearly all the rest didn't. The flunk out rate was so high that Navy Seal training or Army Ranger training look like fuzzy, bunny play time.

The key to my getting my Ph.D. was research, research, and research. The first I did was on a little question that came up in a course. In two weeks I got a surprisingly good answer that was clearly publishable. Later I did publish, no problem, in JOTA. That work gave me a halo in the department and made the rest easier.

For my dissertation, I had identified the problem and made good, intuitive progress on it before I entered grad school. In my first summer I turned the intuitive stuff into math, theorems and proofs, wrote an 80 page manuscript, and that was the research for my dissertation. So, I found my own problem, found my own solution, did the work with no direction, and submitted the final work. So, in no meaningful sense did I have any dissertation advisors. So, I didn't have to depend on an advisor.

This is a good addition. Did you do a PhD in Math as well? My idea is to pursue a PhD in CS, but have a very theoretical bent. I was concerned since essentially I am studying pure math, under the CS department I'd have similar prospects as a Math PhD. But my aim is to set myself up for industry skills upon graduation, so I'll ensure I beef up my software and leetcode skills as Kevin recommended.

Mine was CS with a stats twist, yes. Fortunately the stats component put me in good stead for industry work.

I'd say TCS and pure math are about equivalent in terms of the career opportunties they offer.

Something I forgot to mention: under no circumstances should you self-fund a PhD. Make sure you have a stipend to keep food on the table. Self-funding magnifies the risks I've described tenfold.

This is a realistic perspective of what grad school is like in the average-to-bad case. I could identify with parts of it:

http://nautil.us/issue/56/perspective/what-does-any-of-this-...

> under no circumstances should you self-fund a PhD

Second this. I was told before starting "If you have to pay to do a PhD you're doing it wrong." This may not apply to fields like Literature, but it most certainly applies to Math and CS.

I am a maths PhD researcher in a CS department, just like you describe. In a few short words, my recommendation would be that you do the PhD for its own sake, not as a tool to get a higher-paying job or to learn for an industry job. If you want the latter, you're better off elsewhere, plus you will probably be miserable in a PhD. Be sure that you get into it for the sake of doing research in a field you like (even though it surely will net you numerous other benefits) because if you don't then you will not enjoy your time and also probably be at a disadvantage compared to not doing a PhD.

Myself I'm not particularly worried about maximising income or whatever. I like what I'm studying and researching, and I'm paid enough to live a comfortable life at least for now. I could honestly do this for the rest of my life (which is what an academia career is, I suppose), but if I ever get fed up with it I also know I have loads of doors open everywhere, which is certainly a comforting thought.

Agreed. I’d be doing the PhD for its own sake.

Also another thing other people have mentioned: do not go into debt to fund your PhD, you should be able to get a scholarship/stipend to pay for tuition and living expenses. By your username I infer you're an EU citizen. If this is the case then this gives you loads of opportunities throughout Europe on the same terms as nationals, which means that you have many excellent universities usually with good funding opportunities (though in 9 days that will be the UK out of that set, sadly; I myself got in last year still in time :p).

Best of luck!

> What are the career prospects for it?

I typed in a comment rejected as too long, clicked on the wrong icon, and lost it.

My view of the prospects is, in a word, poor.

Others have described the prospects for an academic math career. I would add, should include a lot of politics, friends, alliances, etc.

Outside of academics, long the main source of jobs in math was in US national security, with some of the major companies getting money for national security or just lots of smaller opportunities within 100 miles of the Washington Monument.

For Wall Street, I still have the letter back from Fisher Black at Goldman Sachs saying that he saw no opportunities for optimization on Wall Street. I sent lots of resume copies, went on a few interviews, had not yet heard of James Simons, and got nothing.

I've nearly never seen a business slot wanting a Ph.D. in math.

My experience in large organizations is that they want more people very much like the people they already have. What I saw doing math in business, e.g., FedEx, IBM, a staff slot at Georgetown U., is that for any good results there is a LOT of bitter resentment above, below, and from all sides. Math just isn't one of the job titles or descriptions.

My view is that mostly a job as an employee is too unstable to be financially responsible. For an exception, get a unionized slot in a monopoly, e.g., an electric utility. Generally it is necessary to start, own, and run a successful business.

My view is that computer science has run out of gas, e.g., can no longer extrapolate from what D. Knuth did and wrote about, and doesn't have good enough problems or tools for a good future. My view is that the best future of computer science is to be essentially a branch of applied math, complete with theorems and proofs, but not nearly enough of the computer science profs have sufficient math backgrounds.

My view is that practical computing is rapidly becoming routine, Web pages, database transactions, server farm and network system management.

My view is that automation is doing so well that we are in line for a huge amount of unemployment. E.g., I saw a lot of people on farms of 50 to 200 acres go very poor as only large operations with fewer people per acre and much more capital equipment did well. E.g., I put together a pizza recipe, a pizza for 1 in 10 minutes. The crust is the star of the show, and it has 9 cents of flour.

Some people are making money hiring illegal immigrants as common labor, having them sleep on the floor, a dozen or so to a room, and paying them in cash. After a few years of that, back home in Central America with the cash, they can live much better than before. US citizens can't play that game. That game is from currency exchange rates, and I'm still looking for the causes of such a valuable dollar.

My view is that computing and applied math are super tough ways to start a business but about the best there is. So, my startup, a Web site, has some applied math I derived, complete with theorems and proofs, based on some advanced pure math prerequisites; that math is the crucial enabling core of the startup, but users will not be aware of anything mathematical. The math is a secret sauce advantage, without the math, with results difficult to duplicate or equal. I don't know anyone else who has done such a thing. I don't know any one at all close who had done anything at all valuable with math outside of US national security.

In simple, first cut terms, I see no careers in math.

I've had my resume on Indeed for months with no responses at all. A few years ago I sent 1000+ resume copies with no meaningful responses. As far as I can tell, anyone over 40 years old with a good background in pure and applied math and computing is absolutely, positively, totally unemployable at anything, including minimum wage.

The industrialized countries are already so poor that the birth rates are so low they are rapidly going extinct.

My view is that, due to automation doing so well, so many people will be left with nothing to do that we are in for massive unemployment.

> The industrialized countries are already so poor that the birth rates are so low they are rapidly going extinct.

Country wealth and birth rates are not positively correlated, and due to immigration, countries can have positive population growth even as their birth rate is below replacement.

> For Wall Street, I still have the letter back from Fisher Black at Goldman Sachs saying that he saw no opportunities for optimization on Wall Street. I sent lots of resume copies, went on a few interviews, had not yet heard of James Simons, and got nothing.

To conclude from this, despite everything that has happened in the interim, that math is unemployable is an, uhm, mistake. As I recall, President Obama was lamenting the brain drain to Wall Street speaking precisely of the number of math PhDs lured there from more fruitful pursuits. Not to mention, as I recall there is an equation bearing Mr. Black's name, the accurate/efficient solution of which has had some importance in finance.

The industrialized countries are poor in a special, curious sense: The people are so eager to get financial security that motherhood is neglected. Or, when wives have to go to work for financial security, the country is still poor. In a sense, living in some of the tropical countries is better if only because can get by without heating oil in the winter or an expensive car.

Yes, Black-Scholes etc. have been important, were for a while via "covered call options", or as in the E. Thorpe, Beat the Street -- essentially the same as what Black-Scholes did the math for with a Brownian motion assumption, etc.

I got an interview at Morgan-Stanley, gave a little lecture on my recent work in anomaly detection, indicated that I wanted to work in developing applied math, algorithms, and software for automated trading, but was ignored. They just wanted people to hack code for back office record keeping. The money making was elsewhere in the company and was based on more traditional ideas, e.g., investment banking.

For automated trading, listen to a James Simons remark: Someone walks in and is just convinced that they should short GM and go long the German Mark or some such. Well, that's more traditional stock picking or hedge fund portfolio management, and Simons made clear that his group, no way, would ever do such a thing. Instead, each buy/sell decision was from some data, ideas, analysis, and software already thoroughly tested; when that software said buy/sell, there wasn't much doubt. Well, that's what Simons did. Don't expect many other people on Wall Street ever to have done such a thing -- it's a lot easier to have a gut feel to short GM and go long the Mark.

Lawyers have learned: A working lawyer reports only to another lawyer. Well, math guys need such a rule, but outside of academics and some national security shops, there are nearly no math guys to report to. So, my desire to do applied math, software, etc. for automated trading was just ignored. Once I was invited to lunch in lower Manhattan for a guy claiming to be recruiting for Goldman-Sachs .... There just is no respect for a mathematician on Wall Street, no matter what Obama said.

Other than James Simons, not clear that math made much money for anyone on Wall Street.

I understand your critique much better (and agree more), thanks for clarifying.