Doing Differential Equations For a Living

[Poopsilon]

So basically I am a pure math major intending on going to graduate school to get a phd in some area of pure mathematics (possibly something like algebra or functional analysis), and I want to be well prepared for the more than likely outcome that I won't be able to obtain a permanent job in academia.

So I'm curious if I can simply learn a lot about differential equations and techniques in applied analysis on the side and basically be paid by some company just to sit around all day solving differential and integral equations for them, do these types of jobs exist? or will there always be other large components of the job not directly related to doing the math? And by this I don't mean interpersonal relations and teamwork, which I'm fine with, but more like extensive programming and modeling or like having to learn a lot about the field from whence these differential and integral equations arise.

 

[f95toli]

I think it depends on what it means by "solving" differential equations. I assume you are aware that very few DEs that are important in the real world can be solved analytically (and then usually for some trivial geometry). So if this is what you mean by solving then no, I doubt it.
However, if you are good at solving PDEs using FEM etc then you might have a better chance, you will still be expected to know how to do some modelling but this is perhaps your best chance at being able to work on "only" math in industry.
Also, there are of course careers in finance etc, but just about all of them will require you how to solve things numerically.
Hence, my advice would be that you learn as much as you can about numerical methods and learn a couple of programming languages.