Fermat’s last Theorem: There is no positive integers x, y, z, and n > 2 such that x^n+ y^n = z^n.
Important, yes. But it took three centuries and far more than a single line of algebra to prove the idea. An idea can be succinct, whereas a proof (whether formal or casual) is generally going to be far more complex. Ideas without proof are only useful when you’re willing to trust an appeal to authority, or you’ve already verified the proof to sufficient confidence for the task at hand.
Fermat’s last Theorem: There is no positive integers x, y, z, and n > 2 such that x^n+ y^n = z^n.
Important, yes. But it took three centuries and far more than a single line of algebra to prove the idea. An idea can be succinct, whereas a proof (whether formal or casual) is generally going to be far more complex. Ideas without proof are only useful when you’re willing to trust an appeal to authority, or you’ve already verified the proof to sufficient confidence for the task at hand.