For pure math, by far, essentially the only, "force" in education is being able to work the exercises. That's ugrad school. For more, be able to do new, correct, and significant original research in math. And that's all Folks!
Nothing but nothing, nichts, nil, nada, zip, zilch, zero, not social skills, not presentation of self, not frequency of bathing, not haircut or hair style, not clothes, not politics, not race, not gender, not country of origin matters at all.
Example: For positive integer n and the set of real number R, show that, on any finite intersection of closed half spaces C in R^n, any linear function that is bounded above on C achieves its least upper bound on C.
Example: In a separable metric space, each closed set is the union of a perfect and a set that is at most countable.
Example: Prove that there are no countably infinite sigma algebras.
Example: For positive integer n and the set R of real numbers, for any closed set C in R^n, there exists a function f: R^n --> R so that f(x) = 0 for all x in C, f(x) > 0 otherwise, and f is infinitely differentiable.
Examle: For positive integer n and the set of real numbers R, show that convex f: R^n --> R is continuous.
Example: For triangle ABC, by Euclidean construction, find D on AB and E on BC so that the lengths AD = DE = EC.