# Can I use my powers for good?

I hesitate to ask this question, but I read a lot of the career advice from mathOverflow and math.stackexchange, and I couldn't find anything similar.

Four years after the PhD, I am pretty sure that I am going to leave academia soon. I do enjoy teaching and research, but the alpha-maleness, massive egos and pressure to publish are really unappealing to me, and I have never felt that I had the mathematical power to prove interesting results. However, I am really having trouble thinking of anything else to do. Most people seem to think that the main careers open to mathematicians are in banking and finance. I really want to work in some field where I can use mathematics, but it is also important to me to feel like I am contributing something positive or at least not actively doing harm. For this reason, financial speculation is very unappealing to me, although I do find the underlying mathematics quite fascinating.

Here is my question: what careers which make a positive contribution to society might be open to academic mathematicians who want to change careers?

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@aengle: Ah, but is the NSA really a force for good? ($*$ducks away$*$) –  anon Oct 12 '11 at 3:07
If you are good at programming, how about working at a company that designs mathematical software? –  KCd Oct 12 '11 at 3:09
+1 just for the cool question title :D –  JoséNunoFerreira Oct 12 '11 at 11:23
"You either die a hero, or you live long enough to see yourself become the villain." - Batman The Dark Knight –  Peter Sheldrick Oct 12 '11 at 12:42
@PeterSheldrick: That wasn't Batman; that was Harvey Dent! –  jwodder Oct 12 '11 at 16:08
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If you are in the US, there are several thousand institutions of higher learning, and at many of them there is very little "pressure to publish". At others, the "pressure to publish" can be met by publishing a textbook or some work of scholarship that does not require proofs of interesting (original) results. High schools also need qualified Mathematics teachers. Consider staying in academia, just moving to a different part of it, as an option for using your powers to do good.

I suspect, but cannot be sure, that much of what I've written applies outside the US as well.

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Thanks for your answer. I did work for a year in a liberal arts college, but I wasn't an unqualified success. I would definitely consider a liberal arts career, but unfortunately we don't really have such colleges outside the US. High school has already been eliminated from my search. I do like the idea of writing a textbook, though; I am quite good at thinking up interesting examples, and that's something I would really like to do one day! –  Flounderer Oct 12 '11 at 3:30
I'm not sure why you are stating that high school is out of the equation. I had a math teacher in a similar situation as you were: he taught at a college, had more degrees than fingers, helped write SAT, ACT, AP tests, etc... He was one of the most popular teachers, and was a fantastic teacher. In 18 weeks he covered all but one chapter of what I ended up "learning" in Calc 1 & 2 in college -- and it never felt like we were moving too fast. You can do a lot of good by teaching in a high school, you just need the right situation. –  Scott Oct 12 '11 at 10:57
In the US, most people in the OP's position would, by technicality alone, be "unqualified" to teach at most K-12 schools because few people with PhDs in mathematics haven't gone through the unnecessary macaroni-art-making tedium that is an (American) university education course. As the old saying goes, Bill Gates is "not qualified" to teach computer science (or business, for that matter) to high-schoolers: forums.e-democracy.org/groups/mpls/messages/topic/… –  user5137 Oct 12 '11 at 18:44
@Scott - I didn't rule out high school teaching because I don't think it's a worthwhile career. On the contrary, I think it's one of the most important jobs in the world. However, I have enough experience to know that I personally am not good at it, and enough experience of bad teachers in high school to know that people who are not good at teaching should never become teachers! –  Flounderer Oct 12 '11 at 20:36
@JackManey: Many American high schools are in such need of qualified math/science teachers that they're willing to forgo the "teaching certificate" and accept other credentials. –  Ben Voigt Oct 13 '11 at 23:17
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Procedural world generation and AI in the field of games development needs people like You(!) to forward the state of the industry from the drivel we see today. It is as creative as it is technically challenging, and in my forays in this field (disclaimer: as someone generally mathematically inept), I have seen the use of a broad spectrum of mathematics and logic; to name just a few such applications:

• Diffusion equations for chemical detection in AI (such as simulating a sense of smell and pulling AI entities along the gradients created by these equations toward their goals)
• Radiosity algorithms using eg. Lambert's equations in realtime raycasting
• Fluid dynamics using cellular automata
• Graph theory for generating planar connected world graphs, including such aspects as finding and eliminating Kuratowski subgraphs
• Combinatorics in evaluating corner cases for constructive solid geometry applications
• Statistical modelling and analysis for game rules balancing
• Minkowski sums in opening sufficiently broad paths for navigation during world generation
• Spatial quantisation and subdivision as a general optimisation
• Quaternions to RK4 integration to Delaunay's triangulations in physics and geometry
• Combinatorics, probability theory and general statistics in projecting the emergent outcomes of complex systems
• Probability theory in random number generation eg. Mersenne Twister
• Formal grammars in narrative and physical object construction (eg. Lindemayer systems)
• And more mathematics applicable to broader field of computer programming, such as analysing and reducing computational complexity.

This is a very haphazard and sparse collection of applications, so forgive me but my knowledge of the very existence of many of these areas has come from a game designer/developer's perspective. In any case, this list goes on ad infinitum for all practical purposes, considering that modelling worlds draws from every known field, from demographics to hydrodynamics to geomorphology to psychology to genetics to narratology... with mathematics being what all of these have in common.

The spectrum in game development is vast, because you are modelling the mechanics of worlds / universes, according to the processing contraints of the system(s) you are developing for -- this latter part is where the real challenge comes in, and a broad, sound understanding of mathematics becomes even more necessary to apply new optimisation tricks.

A sprinkling of some of my favourite places on the www, which may give you some insight into the breadth I'm talking about:

• Infinity, generating galaxies from the top down.
• Miguel Cepero's blog about his as yet unnamed, procedurally generated voxel-based world.
• An interview with the author of Dwarf Fortress, describing how various aspects of the world were modelled (from history to geography to psychology).
• A collection of pages on procedural generation of mazes (graph theory).
• A video showing some emerging technologies in the virtual worlds arena.

I would speculate that it is far easier to be a trained mathematician and become a good programmer, than the reverse. In many ways I would rather be in your shoes, reading my post, than vice versa. Of course that's assuming that this is a convincing argument in terms of changing career direction!

If this does interest you even remotely, don't let what they say about games put you off. The line between games, traditional linear narratives, sandboxes for physical and AI experimentation, educational products ("serious games") and so on, is blurring at a rapidly accelerating rate. The vast majority of games, I would say all but less than 1%, are the same old rehashed tripe. But there is enormous potential for creativity, the more so for those with a strong mathematical background, as evidenced by some of the links above. I think there is something very positive in giving people new and inspiring spaces in which to play, relax and learn.

P.S. If my use of terms doesn't make sense, please correct me on every point, I joined this site to improve my mathematical knowledge and your criticism is welcome.

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That's a very interesting answer, thanks. I have written some interactive fiction in my spare time, but unfortunately I am not a skilled programmer. My brother kind of does this stuff - I think he works on light and shadows in games. –  Flounderer Oct 12 '11 at 20:52
I'm glad to offer some insight. Computational geometry (probably a large part what your brother does) is a fascinating field in and of itself, and a huge part of procedural world generation. BTW I added another link in the post, to a video showing some emerging techniques/technologies in virtual worlds. Best of luck on your path to better things. –  Nick Wiggill Oct 12 '11 at 22:06
This is one insanely cool answer. Though I know math is incredibly useful thing I sometimes feel whats its use. When I feel like that again I will come and read this. This gives me hope. –  Pratik Deoghare Apr 12 '12 at 21:13
@PratikDeoghare Your comment makes me glad that I put the time into writing this answer. It is the greatest honour to inspire even a single person. I think that our world is full of wonder, full of things yet-to-be-done, and I hope that will never change. –  Nick Wiggill Apr 12 '12 at 21:54
Making games is cool, and I can totally see how it would appeal to someone. But when a mathematician talks about working for "social good," I think of things like DNA sequencing to fight disease, or mitigating global warming. Improving computer gaming probably isn't exactly working on one of the world's big problems. –  DanB Oct 28 '12 at 16:02
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Have you read the book 'Surely you're joking, Mr. Feynman?' The great physicist suffers a similar problem to what you describe - having worked on the atomic bomb, he felt 'burned out' and unable to do further physics. Somehow, he wasn't able to interest himself, and work with the same vigour as before.

He then took the approach not to work to any reasonable gain, but to enjoy physics! To enjoy messing around with it, calculating things of no use to anyone. And he found that suddenly, he had his hunger back.

Think about why you went into this profession in the first place. Surely you love maths? Well, enjoy it now, as you enjoyed it when you were a small child. And you never know, your work may turn out to be useful (in Feynman's case, he won a noble prize for it).

And even if you choose to ignore everything else said, read the book. It's a great read.

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For example, here. –  Did Oct 12 '11 at 18:18
Thanks for the recommendation. It's one of those books that I've never read because everybody else reads it, a bit like the movie "Titanic". I'm not really burned out - I am still doing research. It's just that I am soon going to be out of a job and need to find something to do. –  Flounderer Oct 12 '11 at 20:59
+1 for this meaningful answer. Thanks! –  Cinco Sauces Jul 24 '13 at 11:28

You could go into operations research and work in the nonprofit/humanitarian sector. While OR has traditionally been applied to problems in business and industry, the nonprofit and humanitarian world has started to use it more and more in recent years. There are even interesting research problems being generated because the constraints and objectives in the nonprofit world don't always boil down to the same kinds of mathematics that constraints and objectives in the business world do.

INFORMS (the Institute for Operations Research and the Management Sciences) has been promoting this lately under the slogan "Doing Good with Good OR." A recent issue of the INFORMS journal Interfaces was devoted to humanitarian applications of OR; check it out to get some ideas for ways to use your powers for good. Or do a search on "Doing Good with Good OR" for more ideas.

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I found myself in a similar situation just over a decade ago: two years after PhD in mathematics, disenchanted with academia, and needing to make ends meet.

My own choice was to go into computing (specifically, I'm now a software engineer). A mathematician of any stripe will find this field easy to pick up, and some of the skills gained in completing the PhD -- in particular, meticulousness, precision, and tenacity -- are of monumental import.

I've worked on software in several different fields: mechanical engineering (aerospace), nuclear energy, finance, and Child Protection Services, among others. My job satisfaction is very high; I only wish I'd gone into it earlier.

A final, more general note: your options are vast and wide, much broader than you'd expect. I'd suggest looking into fields where the style of your mathematics is particularly applicable, and where you'd be both interested and happy. Software engineering has special attraction for me because (a) my area of math was combinatorics, and (b) I have a penchant for fixing problems and simplifying structural models.

Best of luck!

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Thanks! I like your answer. My problem is that whenever I ask people how they got into software engineering, it turns out that they already knew many programming languages before they applied for jobs, and I really struggle with programming. Could you perhaps give some more details of how you switched fields? –  Flounderer Oct 12 '11 at 20:56
A close friend who also had a PhD left academia for software engineering almost immediately after graduation; his STEM field required an enormous amount of FORTRAN programming, so it was an easy move for him. He began at once to persuade me to leave academia as well, and he finally succeeded. A few handshakes later, and I had a job waiting at the end of the semester. I took the time that semester which would normally have been devoted to research, and instead purchased two How To programming books and a compiler, and taught myself enough about the craft to get started in the new career. –  Paradox Oct 13 '11 at 14:17
may I ask which books you used? I have been learning some Python recently and using it to do a few calculations, but my knowledge is very basic and I'd like to develop my programming further. –  Flounderer Oct 13 '11 at 20:20
@Flounderer hey programming is easy, you will just find first programming language a little bit tough and then it will be easy, I will also suggest you python. So you want to know that which book is better? Any one, you are new comer , so I guess you get some thing from any book only thing require is don't stop once you start.Go to python.org and there are many resources, free tutorials and recommended books so hang with it. Or if want to do web programming then goto w3schools.com/php after installing xampp. Or for any other learning you can also check lynda.com –  Hafiz Oct 15 '11 at 9:07
W3Schools.com is filled with inaccurate information. See w3fools.com. I would instead recommend buying a book or codecademy.com / alternativeto.net/software/codecademy. –  Olivier Lalonde May 26 '13 at 5:23
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Don't write off the finance industry. If you are confident you can avoid your own self-corruption there is no need to think you can't have an amazing impact on the world by working in finance.

There are many areas of finance that add tremendous stability to society and are a good thing (for example, insurance). Mathematicians are able to provide the models and techniques that mean these things can be fair and sustainable as a business.

The finance industry will teach you what things are worth investing in and what things are a waste of time and money. Lots of firms and organisations are incredibly wasteful and stunted in potential because they do not know how best to organise their money. Someone smart like you can learn important skills to take elsewhere to solve these problems. As a mathematician you'll enter straight away into one of the more lucrative verticals of the banking sector. Give yourself ten years to make as much wealth as possible then leave. You'll have the experience and capital to set up a business/charity you believe in.

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Insurers like AIG..? –  Chris Taylor Oct 12 '11 at 13:53
It should be pointed out that the considerable majority of mathematicians hired in finance are "quants", who are pretty much used to generate money for their company, through things like statistical arbitrage if necessary. If you work for a financial firm, if you are asked to do something you can't refuse based on humanitarian grounds, and most of those companies will attempt to maximize their profits in any legal way they can. There might be exceptions of course, but creating fair and sustainable business is not their goal, and they admit this. –  Zarrax Oct 12 '11 at 14:58
@Rasmus - From wikipedia - "AIG is an American multinational insurance corporation" and was at the center of the 2008 financial crisis and needed to be bailed out as it presented systemic risk to the entire financial system (and then the bailout was directed to companies like Goldman that profited richly off the crisis). They employed many mathematicians/physicists/etc as "insurers" who did anything but provide stability to the financial system. Old-fashioned actuarial work is fine; but finance is for making the rich richer. –  dr jimbob Oct 12 '11 at 16:13
Insurance companies and investment banks don't use mathematicians to act more fairly, they use math in order to maximize their profits. Also the OP requested ways to find a job involving math that in some way helps the world. Your advice to sell out and then start a charity, in my opinion, does not respond to the OP appropriately. –  Matt Calhoun Oct 12 '11 at 20:25
Furthermore, I have a suspicion that the reason these firms hire so many ivy-league math/physics phds with little financial training (and pay so well) is largely a cover story (we have a 100 Ivy PhDs so thats why we were profitable). You have an algorithm that generates millions of trades that balance out to average market movement, so you can sprinkle some very profitable trades based on inside information without detection. Granted you have to work very hard to get your algorithm to balance out (its much easier to write losing algorithms), so its not stress free either. –  dr jimbob Oct 13 '11 at 5:54
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A lot of responses to this question are more upbeat than I think is warranted. Many answers give detailed lists of uses of mathematics in a way that suggests the writer has no experience actually hiring people out of academia to meet those needs. There is an awful lot of "fields X, Y, and Z need people to do math, so you can probably get a job doing that." The irony is that this attitude is most common within academia. Most people who will assume that a math PhD with no job experience outside of academia is good for something, to the point of paying them to work on an applied problem, are in academia--- in bioengineering, machine learning, and other fields that people have recommended. The point I would underline here is that these people work in universities and if you want to get into these areas, you will have to stay in academia, at least a little.

The experience of a researcher at a university in some applied area is very different from the experience of a professor of pure mathematics. For example there are often fewer teaching duties (e.g. lab supervision, instead of teaching large classes--- or no teaching duties at all). And there are more options for sources of outside funding--- unlike in most of math, where if you don't get a grant from a government agency that funds math, you aren't getting a grant. But there will still be publishing papers, and you will still spend the majority of your time with people who share their social characteristics more with other academics than they do with the general population.

Academia isn't the only culture with negative aspects. If you look for a private sector job, you will find that most people--- even in very technical companies--- are not open to hiring people with no private sector experience and no personal connections for non-entry-level jobs. And they aren't open to hiring PhDs for entry level jobs (you are "overqualified"). At many companies, it's not "we do a lot of mathy stuff, so math PhDs can help a lot," but "we do a lot of real world stuff here, and anybody who spends decades buried in textbooks won't know anything about that." For example, unless you have an easily documented and publicized history of programming (e.g. contributions to open source projects, or reasonably self-contained projects that you can make public and stick on a personal website), most companies will not give you a second look for any software engineering job. Even if you've done a ton of programming, you will never get a chance to show it, because most companies will not call a math PhD back on the off chance they can do something useful. Say what you will about academia, but if you apply to an academic research group whose work has some mathematical flavor, they are much more likely to actually give you a chance.

Someone linked a talk by Cathy O'Neil in another answer. It contains good advice, but recall that this was a talk given at MIT. Cathy O'Neil has a PhD from Harvard and research experience at MIT. Her first work post-academia was at D. E. Shaw. It is reasonable to assume that she does not have any experience with the obstacles that confront the average academic who wants to transition into something else. She writes: "being really [flipping] good at math is considered a superpower by the people outside. This is because you can do stuff with your math that they actually don’t know how to do, no matter how much time they spend trying." These are the words of someone who has had a very atypical experience in transitioning from academia to the private sector (granted, given the audience of the talk, it is reasonable to assume that most of the audience will be atypical also). People coming out of academia who are not coming from the absolute top schools, with the connections that often come from that, are generally not greeted as superheroes by the private sector. (I want to make clear: I'm not criticizing Cathy here, or suggesting that she hasn't worked hard to get where she is. It's just a lot harder to do what she has done than you might think, reading only her words and not considering the context.)

I would say: if you want to get a mathy job, unless you have a documented history of things that are of immediate relevance to the private sector, or professionally useful personal connections in the outside world--- stay in academia, but switch fields to an applied area (lots of good suggestions have been given here). After a few years, you may have connections that can help you transition to a mathy job outside of academia, or at least a broader resume that people might be more inclined to take seriously. I don't mean to be negative here--- you probably should be taken seriously as you are now. But outside of academia, in my view, the odds are that you won't.

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Thank you for giving a more downbeat answer. I have been looking for a job for quite a while (while doing teaching jobs, but with one eye on leaving academia) and I agree that some of the other answers are way too idealistic. –  Flounderer Oct 25 '11 at 2:52
I agree with the overall insights mentioned here. Connections are supremely important! –  fouryear Jan 16 '13 at 11:26
"And they aren't open to hiring PhDs for entry level jobs (you are "overqualified")." Do you have any evidence to back this claim? A maths PhD I know got 4 job offers in entry-level finance, probably the in the top 5% in terms of success. –  Jase May 24 '13 at 14:10
Also is worth mentioning that those "level entry" jobs can be really terrible jobs. It's important before taking the decision talk with sector workers, know the average times of advances in the chosen career path and be sure that worths the effort. –  bduran Jan 25 at 14:02

I've seen people in pure math who wanted to switch fields while saving the world get postdocs in biostatistics or bioinformatics. This was a few years ago when these fields were especially "hot" but I would guess it's still true. There were many expanding labs and research groups and they would often take people switching from other fields. If you go into these fields, epecially bioinformatics, you may end out doing a lot of programming, so be sure this is something you'd be comfortable with.

Another option would be to get a masters degree, or even go for a second PhD if you can stand it. But I don't think you should have to go this far.

If you are into programming you could try working for a company that does mathematical software, as KCd suggested.

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Wolfram Research for somebody who doesn't want to work for evil companies is the funniest suggestion I have heard in a while. –  Alex B. Oct 12 '11 at 4:51
I have no reason to think they're evil. Maybe you know something I don't. –  Zarrax Oct 12 '11 at 5:04
@Zarrax: You can get some sense perhaps from this review of Wolfram's book NKS, which is an interesting read regardless (at least I assume this is what Alex B. is referring to). The relevant paragraph is the one that begins "The real problem with this result, however, is that it is not Wolfram's." –  Zev Chonoles Oct 12 '11 at 6:32
Ack, I just realized my comment above could be interpreted as saying NKS is an interesting read; that was not my intention (I suppose I have no comment, not having read it myself). I meant the review is an interesting read, regardless of the fact that only a minor section of it reflects on what it would be like to work at Wolfram. –  Zev Chonoles Oct 12 '11 at 16:43
@mt_ It really was like that. People with math and programming backgrounds with no prior bioinformatics background were getting postdocs. Don't forget the field was quite new at the time and it didn't take long to get up to speed. Even professors in bioinformatics sometimes started in pure math such as combinatorics and switched pretty quickly. –  Zarrax Oct 12 '11 at 20:48
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The difficulty here is that "a positive contribution to society" turns out to be quite a subjective thing. So even if you feel other people might know what you mean, there's lots of space for confusion and disagreement.

I can tell you what I did with my maths (across the UK / NW Europe). I've tried to make a positive contribution to society, by my own standards. Your mileage may vary.

I've designed photovoltaic systems. I've been an urban transport planner and modeller. I've been an energy analyst, and created models for local, national and international clean-energy supply and demand. My work has cut across engineering, physics, politics, economics, sociology, psychology, urban design and architecture.

There are still plenty of gaps in all these fields; for example, for clean-energy modelling, it would be very useful to have a simulation package that could produce plausible patterns of insolation, rainfall and wind, at continental scale, and that which reproduced real-world temporal and spatial correlations, at the level of minutes to years.

Note that you're unlikely to use PhD-level maths in many places at all: there's a trade-off between depth of maths used, and number of options open to you.

Good luck.

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May I ask how you got your first job doing this type of work? It seems to me that these types of firms generally require a lot of prior experience. How would a fresh graduate get started? –  Antonio Vargas Mar 19 '12 at 7:38
@AntonioVargas I took a very very junior job in a photovoltaics firm. I used most of my spare time to read the technical literature. I networked continually - saving up my own money to go to the right conferences. And I was lucky. –  EnergyNumbers Mar 19 '12 at 8:12

Consider a career working for a publisher of technical books. Like Springer or Birkhauser. Be a force for good mathematics!

Years ago just after I finished my PhD I spent a week as a taxi driver (I don't recommend this career choice) -- technically I was helping with a conference and shuttling participants around. One of the people I met (the wife of the principal speaker) was a publisher working for Birkhauser. I mentioned that I still hadn't found "the job" and she suggested coming to work for her. They are always in need of someone with the ability to edit/correct/deal with mathematically technical texts. I didn't take her up on the offer, but have thought about it at times. The idea of sitting around reading and discussing math texts all day sounds...well...like goofing around on math.stackexchange.com :)

My second suggestion (this one's probably already been suggested) is join the Peace Corps for a few years. I met a "semi-retired" mathematician last year who joined the Peace Corps and went off to Africa (for an adventure). You would probably end up training math teachers in a foreign country.

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Do you have any idea what the job market is like in academic publishing right now? Just curious, as your experience was "years ago", and a lot of editing/correcting/dealing with mathematically technical texts these days is done at what residents of most Western countries would consider extremely low cost, by people who do not own property or pay rent in Western countries. I don't mean to criticize the career choice--- the OP should look into it--- but I think the OP will find it much harder to find a reasonable job offer than you apparently did. –  leslie townes Oct 24 '11 at 22:31

I am surprised no one has suggested you could start collaborating with the scientists working on the Azimuth Project. I was initiated by the renowed mathematical physicist John Baez. He recently stopped working on $n$-categories and their applications in physics to start "... help saving our beleaguered planet". He now works at the Centre for Quantum Technologies in Singapore (this is their website).

The azimuth project focusses on tackling the various environmental problems we are currently facing, including, but not limited to: global warming, extinction, deforestation, ocean acidification, dead zones, the water crisis and peak oil.

Everything is more elaborately and carefully explained in the links I provided you with and the links within the websites to which the links will direct you.

I believe this project is an overwhelmingly noble initiative and in my opinion, you would certainly use your powers for "good" if you started working on it.

Added on the seventh of April, 2014:

Recently, I discovered "The Ocean Cleanup" project. For a sustainability competition, Boyan Slat came up with a design for an ocean cleanup array that can help getting rid of a lot of plastic in the sea. The device consists of anchored network of floating booms and processing platforms that could be dispatched to garbage patches around the world. From inhabitat:

Instead of moving through the ocean, the array would span the radius of a garbage patch, acting as a giant funnel. The angle of the booms would force plastic in the direction of the platforms, where it would be separated from plankton, filtered and stored for recycling.

According to the organisation's (yup, the design is now being fleshed out by a whole organisation of students, postdocs and professors from the TU Delft, aided by volunteers) website, they're still looking for:

• Hydrodynamic/Fluid dynamics modellers
• Advanced Computational Modellers
• Physical Oceanographers
• Biologists and Remote Sensing experts

For more information: their website is over here. You can also view Boyan's TEDx Talk.

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there are a set of skills required for 'data scientists' that drawn mainly from math topics like graph theory and statistics. I'm not sure if this fits your ethos requirements though. You'll have to figure it out by yourself.

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I also hesitate to give this answer but here it goes.

You do not have to work in the most obvious jobs to help the society. As a mathematician you must be fully aware of the fact that many useless looking abstract mathematical tools turned out to be extremely useful in practice only later.

Besides how do you know that education is helping the society where we have an increasing evidence that our educational system is very wrong. So in reality, you might be doing the exact opposite what you wish initially i.e. making people love math and make them suffer by a pursuing a degree among those mean and arrogant alpha-males (Exaggeration police was here! But you can see this,this and especially this for the fun of it).

Moreover, you might do more good if you really love your subject and create a use of it. Many concepts like Street-Fighting Mathematics and Freakonomics showed that the academia is missing something that is truly crucial for its self-sustained dignity. The relevance.

By relevance, I don't mean that poem starting with math is pure, would you know that it is relevant from the start. I know what R&D departments do, because I worked for quite some time in one particular industry. Hence, I know how to measure how much of my work will be complete fun and useless (for the time being) and how much of it will spin-off to something that would be good for a product. Same holds for the academia, you can't expect every single person to publish and turn everything upside down with one 3-page article. Some people don't want to publish anyway. Some people love to get their hands dirty and work on applied math problems which most of them are not even publishable. Some even go into private companies and carry on their stuff applied to a special (and possibly boring but, hey who cares) practical problem (Not to mention the Google's PageRank).

Long story short, you would better off if you follow nobody's instincts but yours. Try to materialize your career plan with the given limited resources and surplus of happiness that it provides. Sounds cliché but it became a cliché, in the first place, for a reason. By itself, it is a damn hard problem. So you might work on it as a mathematician starting from the Lagrangian :P

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You may want to consider moving to a country where there is a lack of trained mathematicians. I'm sure that many of these countries have the problem of their best minds being drawn away by exciting overseas opportunties. The universities in these countries are probably less focused on research and more focused on the pragmatic task of upskilling their workers.

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Thanks, but I live in one of those countries. It's not that easy. –  Flounderer Oct 12 '11 at 21:00
But you didn't said you want to be easy... just to be good –  woliveirajr Oct 13 '11 at 18:53

Why not apply your math skills to Machine Learning or AI? The IT industry is starving for people like this. Check out www.ml-class.org as just one example Stanford is doing to help bring more ML to the industry. It's right up a mathmatics background alley!

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Your main assets are your ability to learn new topics and analyze complex problems quantitatively. These can be applied to any number of fields, some of which were mentioned above.

Try by searching for job openings as an algorithm developer and similar titles. Often requirements will include a Ph.D. in mathematics or a related field. Such jobs are often exploratory and include writing a prototype using either mathematical utilities such as Matlab, Mathematica or R, or programming languages such as Perl, Phyton, C. These prototypes either serve as an internal research tool or as a starting point for distributed software components.

Indeed, machine learning is often used and it would be a good idea to familiarize yourself with the approach and even gain some hands on experience, e.g, via the online course mentioned above by @Mech.

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Thanks for the search term! That was a helpful answer. –  Flounderer Oct 18 '11 at 23:59

I skimmed through the answers and didn't see this mentioned already, but have you considered working for an entity involved in making mathematical education resources available online? There's a huge gap between what current technology could allow us to do in mathematics education and what is currently being done. One could argue that mathematics education will likely be very, very different ten to twenty years from now. One site that has recieved a lot of attention and funding is Khan Academy, but I am sure there are lot more initiatives taking place around the world.

Imagine a world where the same group of mathematicians no longer spend each semester giving the same (often uninspired) lectures on college algebra and introductory calculus, because high quality lectures and supporting material are freely available online. Instead, classroom time is used to give individual attention to each student's current state of progress, and research mathematicians spend more of their teaching time supervising undergraduate research projects instead of explaining the perils of dividing by zero to students who are busily texting their friends their plans for Friday night. When you're done having this nice dream, go out and find a job where you can help make this a reality! :)

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The Khan academy is great! I actually watched a bunch of their finance videos and learned quite a lot. I also watched some of the calculus videos and gained some valuable insights into teaching ... I even almost got a job by copying some of the things that Khan did! –  Flounderer Jan 10 '12 at 4:27
In the US, there's Big Pharma, there's Big Tobacco, and there's also Big Education. This is a business of selling nicely wrapped hollow products to school districts -- little if anything has changed in 50 years since Feynman's chapter in Surely You're Joking. To feed this industry and give it a semblance of an academically solid one, there's a sister area of mathematics education. If you have observed a downward trend in math preparedness of your undergrads over the past 5-10-20 years, thank these guys. I doubt that you are welcome in their world. –  StasK Feb 12 at 4:37

You might want to look into holography related fields, which are mathematical complexity bound, but have the potential to change a great deal of how we interact with the world.

Beyond TV and Movies, computer generated holograms have uses in everything from medical imagery, geographic data representation and remote visualization. We are at our core visually driven creatures, and so having an enhanced way of visualizing data, whether real or artificially generated, has a huge impact on our ability to comprehend and react to the world around us. Dare I say it, but the ability to present data more dynamically is a world changer.

There are companies out there investing in the technology needed to make mass market holographic devices, and with good reason: We quite literally have all the technology required to do holography, and the only thing preventing holographic visualization from becoming the norm is the ability to do the math efficiently.

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I really appreciate that you are asking such a question. I suggest looking into non profits, and using an organization like Data Without Borders for guidence: http://datawithoutborders.cc/

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Use your skills to help improving cryptographic algorithms in projects such as Tor, BitTorrent and Bitcoin.

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how can we apply for this job? –  user42912 Apr 21 '13 at 10:09
Isn't it Bitcoin instead of BitCoin? –  Pacerier Dec 1 '13 at 7:14

Being an actuary is a good job, always ranked as one of the top jobs based on things such as salary and stress level. If you find the right company, you can work 40 hours a week and get paid a lot of money, while working on something that is necessary to culture (car insurance, for example). As someone who is good at math, you could pass 2 or 3 exams in a few months. You wouldn't want to do more than that until after you start a job, because companies don't want to pay someone with no experience a huge extra amount of money. If you have much experience with probability, you could probably pass the first one with very little study, possibly none at all depending on how much experience you have.

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Not to mention, according to a recent survey, the actuarial profession has a 0.0 percent unemployment rate (see collegiatestandard.com/?p=1736 for example). Seriously though, I have heard the actuarial job market recently is doing quite well. –  Zarrax Jan 5 '12 at 19:27
Thanks for taking the time to reply to such an old question! I've been looking into this one for a few months, although one actuary to whom I spoke did seem very surprised that a PhD would want to become an actuary. On the other hand, I have friends who have done it. Of the financial professions, this is definitely the one which attracts me the most. I am having a hard time finding entry-level positions, though. –  Flounderer Jan 10 '12 at 4:30

I am currently a PhD student in robotics and AI, and it seems to me that the field is thirsty for good mathematicians, to counterbalance the vast majority of heuristic-minded engineers (like myself). In fact, the main reason why I am a part of this community is because my work often leads to interesting mathematical systems that are beyond my ability to analyse (e.g. this one, why not use the opportunity to advertise my own question? :-)).

I find the field very appealing and I can see it being used as a force for good, such as in medicine and healthcare, personal care, search and rescue, and the like. Of course, there is always the argument that what you contribute to could eventually be used in military technology, but I guess that makes you as guilty as the person who invented the knife is for all the stabbings that happen. That being said, I have made a decision never to work directly on military applications.

In this way you could remain in academia, but I'm fairly sure that you would have an easier time publishing, because the mathematics involved will be simpler that what you are dealing with at the moment. At the same time, you will get to meet lots of interesting people of both genders (less alpha-maleness), as the field is probably one of the most inter-disciplinary around. Apart from the obvious engineers and computer scientists, you get psychologists, linguists, biologists, philosophers (for robot ethics), and people from pretty much every other science that you can think of.

I wish you the best of luck in whatever you decide to do!

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Cathy O'Neil gave a talk at MIT entitled "Math in Business" last week; she summarizes that talk in this blog post. There may be some ideas here.

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I'm not sure these areas have been mentioned already.

I would outline two areas that are beneficial for the society and interesting for mathematicians: cancer research and computer virus propagation. They are closer than one might think, applying tools from probability theory such as Markov chains, stochastic processes, limiting distributions, equilibrium states, optimization, etc.

You will be able to help a lot of people and maybe even save lives.

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