Why not just use calculators?

*To the extent that you have a perfect black box
 which solves a problem for you,
 --you don't need to understand the insides--*
EG, don't need to know how car or computer works to drive or write.

However, to the extent that:
- maker: you must build your own models
- user:  the black boxes are imperfect
...you need -intuition-.
Good EG is FX trading, say: Black-Sholes is imperfect.

Math for non-math people is largely about -intuition for
underlying models- (and so that you can solve exercises
to understand the models / theories better).

A subtler issue for model-builders:
- if you can build a perfect black box, go for it
- ...but if not, there's a trade-off between -accuracy-
  and -understandability-:
  users build their own adjustments / model -to a tool-:
  if a model is inaccurate but understandable,
  it's often easier to build a -useful- mental model
  than if a model is "quite accurate but not good enough"
  and -opaque-:
  *** you can't tell what adjustments to make!

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A small note:
suppose you have a model that depends on a parameter.
(EG, the price of a car depends on the price of steel)
Then, presuming the model is monotone or homogeneous in that
parameter,
you can -compare- instances:
- either order (if monotone)
- ...or find relative sizes (if (close enough to) homogeneous)