I can’t seem to wrap my head around the fact that math is invented? Maybe he came up with the symbols of integration and derivation, but these are phenomena, no? We’re just representing it in a “language” that makes sense. I’ve also heard people say that we may need “new math” to discover/explain new phenomena. What does that mean?
Edit: Thank you for all the responses. Making so much more sense now!
In: Mathematics
Whether math is “invented” or “discovered” is largely a matter of semantics and a topic of the philosophy of mathematics.
It is easy to take mathematics as some sort of thing that exists outside of people and embedded in the cosmos. However if you think about some of the symbols, they don’t really correspond to anything universally meaningful that isn’t defined by humans.
In the statement “2+2” what does “+” mean? Does it just mean that you’re taking 2 things and putting them physically closer to 2 other things? Does it mean you’re just manipulating symbols on a sheet of paper? It’s kind of just an abstract idea that corresponds to a vague and poorly defined pattern.
That brings us to the issue. When we really want to be rigorous, we need to have precise definitions. There are times where it makes sense to define “+” such that 6+7=13, but there are also (literally) times where it makes sense to define “+” such that 6+7=1 (like a clock).
You could probably get more precise and state Newton “invented” some of calculus (some of the symbols and definitions are uniquely his creation) and some of calculus was “discovered” by Newton (that Newton figured out some interesting facts that follow as consequence of reasonable base rules known as “axioms”).
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