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
Maybe it’s more that he discovered it?
What is a ‘phenomena’ to you? Math is used to describe other stuff (when useful at least). And it has rules that let you transform things into equivalent other things. Sometimes those other things are clearer or answer something for you.
Do you know what Calculus is, or is used for? And what happens with/in it? It’s not just 1 + 1 = 2. It’s about getting the area under a curve from the formula, and precisely. Or finding how much change is happening at a specific point (where a curve changes direction for instance). Or what happens between 0 and infinity along a curve. Or at least that’s what I can recall from my long ago Calculus classes.
They’re useful if you have questions they answer, and they’re not obvious unless you already know them (to most people at least).
That’s how a new math would be useful. It means we’d have a new way of answering something that stumps us today using symbols and numbers, maybe with new operations like sin/cos/tan did for triangles. It’s the hope that some new way of looking at a problem will be much faster than existing methods, or answer new unknowns.
And as far as “Newton invented calculus” it’s that he’s credited with publishing the ideas first. Maybe he did, maybe he didn’t… but it’s not a big deal to me who specifically did something in a well known/public way. He worked out the rules and results of it, and shared it with other people. Who looked at it, and tried to see if it made sense to them or answered anything useful.
In math and science, some people use the word “invented” but scientists usually say “discovered” Newton didn’t invent the fact increasing force increases acceleration, he discovered the correlation. Same thing for calculus or any type of math; they didn’t invent the phenomena, but they used they tested the phenomena and recorded results until they came up with the terms, variables, correlations, equations, etc.
Does one invent a martial art, or discover it?
Did someone invent fishing, or discover it?
Did someone invent metalworking, or discover it?
Did someone invent the wheel? Or discover how to make a wheel?
Did someone invent the table, or discover how to make a table?
Even take a motor, or a lightbulb. Did someone invent those, or did they just discover a process by which to make them? The thing is, the process to create one would have worked before whoever first did it carried out or described that process. A lightbulb, or a table, or a blender are all amongst possible configurations of atoms. Was the inventor not just the first person to perform the process and represent it in “language” as you say?
not really, calculus is their way of manipulating numbers and representing phenomena; you can come up with your own way to do the same and name it whatever you want. But until then, it’ll still remain that Newton is one of the people who invented calculus
Can you see a continuum?
If you tell someone directions to go to the store, are you actually going to the store? No, you’re just explaining how to get to the store.
Math is the same. Math is how we explain how the universe works. It is not how the universe works, just an explanation. When someone invents something in math, they are inventing a new way of explaining how the universe works.
Now imagine you’re used to giving directions in lefts and rights. In fact, you’re very good at it, you even know all the angles down to the degree. This always worked when someone needed to get to the store. But suddenly you realize, helicopters exist. You discover this when a helicopter pilot comes up to you and asks you for directions to the store. The current way you tell directions no longer works. The helicopter can go straight there, but there’s a mountain range in between, so altitude is very important. What do you do? You invent a new way of giving directions that makes sense in the context of helicopters.
That’s new math, it’s a new method that works within a context where the current math does not. It shares a lot of the same principles and, at its core, a lot will be the same. But you need new methods to explain problems that current math does not solve.
Imagine a chessboard. No one invents a piece or how a piece can move. You can’t invent a rook, it just is a rook and it moves how it moves. But you can invent a sequence of things to get a result you want, like the scholars mate. The person who figured out how to do a scholars mate invented it, even though the pieces could have moved like that at any time.
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.
Some people might say that they invented it… like some people say someone ‘invented’ gravity — no they just figured out how things can be better described, or how numbers and mathematics can be used in new ways.
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