[hnfong]

What are mathematical proofs but mere 'thoughts'?

(I'm only being half rhetorical. I've been thinking about this deeply lately.)

[hibbelig]

The relationship between thoughts and proofs is analogous to the relationship between noise and music.

It’s a subset kind of relationship.

There is also the social aspect: people have to agree on it. Noise becomes music, and thoughts become proofs, only if several people agree.