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Re:With Category Theory, Mathematics Escapes from Equality (... by galaxyLogic on Sunday March 27, 2022 @12:11AM (#30817642)
Programs and logical proofs are "isomorphic" according to Curry-Howard. So logical theories like math in general are "programs". Two programs can be "equal" in the sense that same inputs produce the same outputs, yet their source-code can be very different.

Therefore to explain a theory to a layman or anybody consider that your theory is a program, and therefore there can be any number of equal/equivalent but different programs, i.e. representations of that theory that are "equivalent" but have a different representation.

Therefore, and this is the point I'm trying to make, (and maybe I'm wrong) any good explanation of a theory could also be presented in some other way, and possibly in a simpler way. Programmers know this intuitively: You can write the same program in a complicated way or in a much simpler way, sometimes. Therefore the fact that some math is difficult to understand may in fact not be the fault of the student, but of that "math" itself.

And therefore it is useful that people come up with questions about what they find difficult to understand about a given theory. The "stupid" questions reveal something about the theory, they reveal what is difficult about it, what kind of mistakes people make when trying to understand it.

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