[edflsafoiewq]

> The whole point of mathematics is that you come up with the definitions and theorems fall out.

That's just how it's presented in textbooks. It's obviously not math is actually done.

[ravi-delia]

It's presented that way in textbooks because it's way easier to learn it that way (or it's Stockholm syndrome, which I won't deny is possible). The motivated way would require way, way, way more background knowledge.