>>7
Well... it depends on where you are, what year you're in, and what you're trying to do. Obviously the answer will be different if advising a math major trying to sell out of undergrad vs. one intending to go grad school --> postdoc --> R1 TT.

Since the latter is so difficult, I think the worst thing you can do to yourself is graduate with 0 marketable skills apart from LaTeX, being able to use a web browser, etc. You are literally worse off than the biz majors you probably look down upon for being brutish apes who don't do any work; really, you'll be no different than some Africana Studies major, but at least they can go to some policy nonprofit lol.

Take a class or two on numerical methods/ computational statistics/ machine learning and *definitely* at least take intro computer science. If anything, that should also "unlock" your TCS classes and so on. I feel that is a very interesting, promising area.

>analyism - fight against everyone else

I am not sure what "analyism" is.

> education

Yeah, don't. Maybe after freshman year... it does not exactly help you for grad school, but you're hired to be researching *and* teaching as a professor. Teaching is annoying, but it pays. I think TA'ships during the academic year are more interesting/ compelling/ notable than something over the summer. But, this does not really give you much to write about in your statement of purpose.

> research

Talk to your professors. Talk to any postdocs at your uni. Talk to your advisor. Take hard classes, figure out what you want to do, and just start cold emailing the people who do things even just vaguely related to that. Younger academics/ postdocs are much more likely to have things to dump onto you/ be willing to take you on than will tenured faculty; I think it is literally a matter of "they have not gotten tired of it yet" + it helps them to have "advised XYZ and they are now successful" brownie points on their CV -- student success is a huge part of promotion considerations!

The national labs have a number of opportunities, as do a number of privately funded places and companies' research divisions. Lo and behold, none of these places are really going to have undergrads come in and do pure math. REUs or something at your university are really your only recourse on that front. If you demonstrably know some serious physics/ engineering/ computer science, you have a great shot at the national labs. I would look at JHU APL, NASA JPL, Flatiron Institute, DE Shaw Research (DESRES), Lincoln Lab... etc. these are mostly east coast (because I am on the east coast), but there are certainly plenty of others.

Basically all that goes on at the companies is engineering "research" and machine learning shit...

> fight against the top 45 unis

You're doing this for literally anything you apply to btw.

> actuarial

Yeah, soul-killing I think.

Quant finance is the biggest sham on the planet. Don't do it unless you are really interested in that for its own sake. Especially don't do it if you're not seriously interested in computer science, low latency programming/ computing, and to a lesser extent probability theory.

> anything else - lack domain-specific knowledge

I think it is worth applying to most of these still. Again, you should apply for software engineering things to just give yourself the option and because it will come in handy at some point/ you're doing some work future you would have needed to figure out anyways (like how the fuck bash/ zsh work and what a compiler is).