Can I use my powers for good? [closed]

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.

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.

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.

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.