“The question “is math real?” is answered in the epilog of this book. Cheng tells us that math is real because it is an idea and ideas are real.”
Alright great lol
Alright great lol
> CHENG: I'm not trying to answer whether math is real or not. I'm trying to show that considering the question at all leads us to interesting thoughts. And in the end, what I say is that, with all these questions, I don't think there are yes-or-no answers, and we shouldn't claim that there are. What we should do instead is say there is a sense in which - you know, what is the sense in which math is real, and what is the sense in which math isn't real?
> And the thing is, I think a lot of people who say math isn't real are using that to say, oh, so it's irrelevant and stupid. Why should we study it? It's made up. And what I want to say is that just because it is made up doesn't mean that it's irrelevant. And actually, the fact that it's kind of made up makes it really powerful because - well, it makes it really, in a way, more accessible because you don't need a lot of money to get it. All you need is an imagination. And I think that's a really amazing thing about it. And just like fiction isn't real, but fiction can give us insights about the world around us to highlight much more, specifically, things about society. And that's what I think is powerful about abstract math as well - because we're not constrained by reality.
I haven't read the book, but it seems like the title may be a throwaway question meant to pique the reader's interest and say "let's get philosophical about math".
---
Think of a triangle. Now draw that triangle on paper. If you look closely enough, you'll see "imperfections" in the triangle you just drew. Now ask yourself: "how do I know this thing I just drew is imperfect? Where did the idea of a perfect triangle come from?"
Plato would say the perfect triangle comes from the realm of "forms". This mystical place which is "more real" than "reality" because everything there is perfect and everything here is just a flawed approximation. Plato also said that this is the place where our souls go when we die, and we engage in "congress" with the forms and then return to earth, reincarnated. When we learn things, we aren't learning something new but actually recalling memories of the forms. This is why everyone knows what a perfect triangle is but no one has ever seen one in the physical world.