Comment by dataflow

Probably the best example of this I can think of (for me at least) from mathematics is calculating combinations. I have it burned into my memory that (n choose r) = (n permute r) / (r permute r), and (n permute r) = n! / (n - r)!

Can I derive these from first principles? Sure, but after not seeing it for years, it might take me 10+ minutes to think through everything and correct any mistakes I make in the derivation.

But if I start with the formula? Takes me 5 seconds to sanity check the combination formula, and maybe 20 to sanity check the permutation formula. Just reading it to myself in English slowly is enough because the justification kind of just falls right out of the formula and definition.

So, yeah, they go hand in hand. You want to understand it but you sure as heck want to memorize the important stuff instead of relying on your ability to prove everything from ZFC...