Math Educations: who needs it, how much and when?

[pocaracas]

I once had a Quantum physics professor, at Uni, who wouldn't consider anything simpler than an integral to be a "calculation".
He could fill an entire blackboard with sums and multiplications and divisions, but none of it was "calculating" anything.
Eventually, the integral was in just the right format and then he'd "calculate" it.
The week after, we learned Dirac's notation and all the integrals got hidden.