You're right! Here is some more context:
* 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?