three key goals of teaching math:
- mathematical understanding
  useful for mathematicians,
  useful for applications,
    (but they think only somewhat useful)
  beautiful for everyone
- facility with computations
  somewhat useful for math,
  useful for applications,
  kinda fun (or useless) for everyone
- transfer
  that is, transfer of skills (esp. logical) to other domains
  ("math as a liberal art/way of thought")
  useful for everyone

How to maximize -transfer- is a rather difficult skill;
this is true -for all topics-: it's hard to bring wisdom/skills from a
different domain to bear, but this is the source of much progress.
