It feels like my understanding of "logic" as a "subject" is probably one big warm take: I think it is just a piece of maths and programming and maybe philosophy, because it exists in service of all the things that require similar rigor to maths. I'm too far removed from the 1920's to understand why "the birth of mathematical logic" in Hilberts search for metaMathematical Maths Proofs, Gödel, etc. is called that. (it's probably just a misleading name) Often it feels like people imply too big a distinction between maths and logic. Doing any maths, like solving a quadratic equation requires logic: Any of the common rewritings like adding to both sides are things where you know a logical implication from one equation to the next. Knowing an equation has two solutions means knowing a logical or between x = a and x = b. That makes me feel bad for early logicians as their ideas seemed to be boring for lack of applications.