This is one that is way out in left field: being a quant (aka rocket scientist), aka financial analyst in a heavy weight math setting. Most found in investment houses calculation financial option prices.
Why? Because it seemed fun. I was working in Tokyo for a US bank when I realize there is such an occupation for math grads.
It would be fun putting my interest and skills in math and programming together. The closest I've got since was to write a bunch of bond price-to-yield calculations which involve solving a bunch of degree N polynomials. It is really high school math then it is "advanced" math.
The saving grace these days is me having the ability to talk intelligently about financial instruments in general how it is modelled in the application.
The other side effect is to be able to argue with accountants and implementation folks about what kind of accounting entries need to be created for the financial instruments we model. Yea, amortization and interest accrual, debt expenses and stuff are *really* sophiscated math. :-)