In my experience (undergraduate mathematical statistics, currently "quant financial engineer") this is exactly right. If you want to continue "doing" math in the sense you did in school, or in the sense we assume a "mathematician" does, it really is almost exclusively a consideration accompanying having a doctorate in the field. Mainly because as stated above, undergraduate mathematics really just scratches the surface of core competencies. That being said, while not many fields offer pure math tracks for undergrads it certainly doesn't make it irrelevant. In most "quant" fields mathematical literacy and the thought patterns accompanying having studied mathematics are far more valuable than actual proficiency. Outside of research few individuals are "paving new roads" mathematically, they are most often applying the results of cutting edge research or long standing industry standards in mathematics within the context of their job. This requires a high level of mathematical fluency and comfort with abstract formalisms, not theory expertise akin to that of a phd.

This was very informative, thanks. I am perusing postgraduate studies. I've been accepted into an Honours degree in Applied Mathematics so I am not hanging up my academic hat yet.

My reason for asking the question is two-fold: some badly needed reassurance that I have not rolled myself into a hole (I think it was a design flaw that we cannot re-roll characters in real life) and getting a broader perspective on potential places to keep in mind - in terms of extra-curricular skills that I need to gather along the way.

If it is reasonable for you to continue with postgraduate studies, I would recommend that you do that. The more math you can do or know the better. And it is going to be harder to gain those skills once you leave university.

You haven't mentioned any software skills. I would recommend develop whatever skills you have in that area. The ability to program is becoming as important as literacy and numeracy. Even more so for a mathematician.

My bias is that I have a PhD in math and have been a software engineer for the last 10+ years. I have worked in a lot of different areas and that has largely been because of the combination of math and software (and luck).

Oh. I can program. I've done two university courses using C++. I've taught myself haskell using Haskell Book and for my numerical analysis course I reimplemented all the matlab that we had to do in Julia and Python. A different poster mentioned C/C++ so I am currently considering going through the numerical analysis again and doing it in C++.

I didn't mention programming because I don't see myself being a developer, which I knew would get a lot of attention. I like solving problems with programming, but I don't see myself writing a webapp to collect information for someone to steal.

Computer Science is my secret lover. I initially studied that, but my university focused on producing java devs for industry and didn't do the "science" of computer science. I still work through books when I have time though. About half-way with TAOCP V1.

I think this really depends but yeah I generally agree with you - with respect to machine learning as an industry - but there is still fairly cutting edge ML being done at large companies which can use a lot of intense math - though as you mentioned that does generally require at least a graduate degree of some sort.

> climate science

Since you brought it up, I've had a hard time looking at positions for software engineers (not a single mention on this month's whos hiring for example). Any ideas?