Logic is a formalisation of grammar — Banno

do you have proof for this?

Logic is part of language — Banno

are you sure? is it not logic upon which language is founded? i would assume before humans could communicate as well as they do now, they could still put 2 and 2 together. logic may very well be very intuitive in some instances as well, which i find hard to believe is based on language. i would also assume that language does not sprout from itself, rather something else.

Probably came from algebra x2 + y2 = z2
32 + 42 = 52 — EnPassant

yes but that needs a proof to show that x^2 + y^2 = z^2. it needs a reason. however it could have been an observation, but not all x, y and z can satisfy this property for natural numbers. so most likely it was an observation, then the proof/reason came about for any x, y and z that satisfy. and there are many proofs for pythagoras, some are visual and some more algebraic or concrete and some are even just bi-products or specific cases of different ideas. a good example of that is ptolemy's theorem. ptolemy's theorem is more general than pythagoras theorem. it is the general case for any cyclic quadrilateral and pythagoras is just one of the infinitely many cases.