There an interesting paper about how doing science is basically about coping with feeling stupid.

No matter whether you do research in math or whether you do research in biology, you have to come to terms with tackling problems that aren't easily solved.

One of the huge problems with Reddit style New Atheists is that they don't like to feel stupid. They want their science education to be in easily digestible form.

As well as having had plenty of instruction in actually breaking down big problems into smaller pieces.

I agree, that's an important skill and probably undertaught.

The ability to tackle complex unencountered problems that you have no idea of how to solve is definitely important, but I would still prioritize giving them a maximally strong understanding of the existing mathematics first.

Nobody understands all math. For practical purposes it's often more important to know which mathematical tools exist and having an ability to learn to use those tools.

I don't need to be able to solve integrals. It's enough to know that integrals exists and that Wolfram Alpha will solve them for me.

And even those research mathematicians will primarily need a good and thorough understanding of the more basic mathematics that they're building on.

I'm not saying that one shouldn't spend any time on easy exercises. Spending a third of the time on problems that are really hard might be a ratio that's okay.

A thorough understanding of basic statistics and probability would seem much more important.

Statistics are important, but it's not clear that math statistics classes help. Students that take them often think that real world problems follow a normal distribution.