I recently started watching this lecture series on Category Theory by Bartosz Milewski and he delves into some mind-boggling existential questions in the first video.
To paraphrase, mathematicians believe that they are in "a field of discovery" with the implication of "discovery" being that mathematicians are discovering something that already exists.
He gives an example of how mathematicians believe that lambda calculus and other systems like set theory and graph theory are actually all the same thing as category theory. In a metaphoric way we have discovered the abstraction (category theory) and recognize that lambda calculus "implements the trait/interface"
The dilemma is: did we truly invent a theory of a pre-existing phenomenon? Or do we somehow map physics of the universe to a what a brain is capable of parsing?
To paraphrase, mathematicians believe that they are in "a field of discovery" with the implication of "discovery" being that mathematicians are discovering something that already exists.
He gives an example of how mathematicians believe that lambda calculus and other systems like set theory and graph theory are actually all the same thing as category theory. In a metaphoric way we have discovered the abstraction (category theory) and recognize that lambda calculus "implements the trait/interface"
The dilemma is: did we truly invent a theory of a pre-existing phenomenon? Or do we somehow map physics of the universe to a what a brain is capable of parsing?
https://www.youtube.com/watch?v=I8LbkfSSR58&list=PLbgaMIhjbm...