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
Was the game of Monopoly discovered or invented? It’s a list of rules, that someone made up. The *consequences* of those rules follow from the application of logic.
Mathematics is the same way. Someone says “hey, these are the rules I would like to study” and then we follow those rules to their inevitable consequences. We *want, desperately* for the rules we come up with to reflect **something** about reality, and we do a pretty good job of that, but ultimately the harsh truth in that reality is reality, and math is a language. At some point, someone must make a decision about HOW to translate between these two realms, and there is no Right or Wrong way about it. How well a rule actually reflects reality is simply a matter of opinion from person to person. A famous joke in mathematics is “**The Axiom of Choice is obviously true, the Well–ordering theorem is obviously false; and who can tell about Zorn’s Lemma?**” But all three of these things are equivalent to each other!
There’s a saying in science circles: all models are wrong, some models are useful. We choose the rules that give us useful results. Newton and Leibniz were able to codify the rules that lead to really, really, useful results. Their rules didn’t come from on high. Their rules did not grow on trees. They made them up. If that’s not inventing, then I don’t know what is.
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