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
Fields of Mathematics require certain assumptions to be made, called axioms. When we’re modeling things in the real world, we might choose axioms that give us a system that is similar enough to our reality as we understand it to make it useful for modeling, but that need not be the case.
Newton (and separately, Leibniz) came up with some axioms that allow us to have the field of Calculus. Newton also developed a set of symbols and norms that, along with already-accepted mathematical symbols and norms, allowed Newton to convey these ideas and perform useful operations for modeling things within this field he developed. He then practiced and studied this new field in order to find useful conclusions upon which more complicated ideas can be modeled and explored, and wrote about these extensively in ways that other mathematicians could use them as a foundation.
One could say that fields of mathematics are more discovered, rather than invented, as the math sort of naturally flows from a starting point of axioms, and everything else is just finding a good way to communicate it and write it down. Regardless of whether you view it as an invention or discovery, though, Newton certainly paved the way for very much of what we still use in Calculus today.
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