Ehh, it’s really your opinion.
Since discovery means “the act of discovering something that already exists”, I;d have to say invention because we made up the numbers and the rules, although they do fit.
@JONESGH Nothing in Mathematics was our own creation. Theorems are conjectures made by observing natural order and proven using the rules and limitations imposed by nature. We didn’t bend the composition of the universe to come up with things like the Fundamental Theorem of Calculus or Set Theory. These are things that, while seemingly based on human construction, are just abstract ways of thinking about natural occurrences.
Yes, the things that math seeks to explain are already there. If humans did not create math, this language, to explain those things, however, math would not exist. Math is a human creation, a human invention we use to explain natural phenomena that we discover.
Contrast this with the work of scientists. Like that radio show that @Rarebear posted pointed out, a discovery can be made by many people at the same time or by no one at all, but it exists regardless independent of humanity. Indeed, Darwin rushed to publish his Theory of Evolution because he was afraid someone else would beat him to it. *
What math seeks to explain exists regardless of humanity, but math is a tool created by man that would not have existed without man.
Then you get to the level of math, beyond what I am capable of fully comprehending, where you start to discover things that can exist within the man-made framework of the language itself that do not yet exist – to the knowledge of mankind – in reality.
Math is an iterative process, leading mankind beyond the cutting edge and yet owing its birth to man. It would seem math is both an invention and a discovery…kind of like Hal.
* As a side note, this logic is why I think genes should not be allowed to be patented as they are discoveries, not inventions. We cannot know with any certainty that the genes created in lab do not already exist in the world somewhere – where we have not yet thought to look. What they have “invented” may have already existed in the world but has yet to be discovered. After all, they have discovered that it is possible for that gene to exist in the world, which is kind of like the pathway to proof that their discovery is not an invention.
It is both. The underlying principles surely were a discovery, but math itself, the symbols, the structure and the rules on how to conduct it, like the rule that you do multiplication before addition, were all devised by humans, thus, invented.
It is an expression of partial understanding. Which probably falls in the discovery camp, but doesn’t eliminate the fact that while we can definitively label gravity we still don’t know why it happens.
Perhaps they can. We’ll never know in our lifetime. That you can count, I think is a discovery…that you assign symbols to account for quantities is a system you have invented.
If you look back over ancient civilizations, they had different symbols and different systems (base 2, 5, 6…) for counting. They all discovered they could count but had invented different methods for doing so.
The question assumes that we have two choices. The premise is false. Math is a way of describing or defining natural phenomena, no different than words do. Without math, certain relationships in nature could not be integrated or described for analysis. With math, this scrutiny is possible. Math is not an invention, nor is it a discovery. It is a product of the human mind at that mind’s attempt to put in concrete form the abstract observations of reality.
People have been working, studying, passing the idea of “Math” for a long time and it is still being worked with.
So its impossible to invent something when a number of different people at different times all contributed to “Math”. Nor is it a Discovery because someone didn’t wake up and say, “Hey, look, its “Math”!
Yes, many things we observe about the universe are amenable to description using math. That may be the best way humans have to express what we observe.
The notion that these phenomena in any way suggest that math preexists human thought is not reasonable.
We use Base 10 numbers most frequently mainly because we have ten digits on our two hands and feet. Math is a tool that is a function of how the human brain has developed to function. Math as we know it has certain fundamental properties arising from how we defined it and its operations.
It is possible that other species on other planets may independently develop systems of numbers and numerical operations than have properties both similar and different in any number of ways.
We developed machines that use mathematical rules. Initially these machines could accept only Base 2 (Binary) numbers. Later we developed machines that could accept and use Base 16 ) Hexadecimal numbers.
We don’t use numbers with fractional Bases but we could. We use a system that can represent the notion of zero. Earlier number systems could not.
We invented the math we use and machines that can do it faster than we can. We chose components of those machines that could represent those numerical properties we could use and understand.
Math wasn’t just sitting somewhere waiting for humans to discover it and find a way to use it!
That is like saying modern English always existed, even millennia ago when people spoke entirely different languages.
@Dr_Lawrence Yes, thank you. I was thinking along the exact same line, and then twisted my mind up at the end. Math is a human invention. What we discover by using math are discoveries. The phenomena that can be explained using math may have always existed unnoticed, and we may have discovered them by using math, but math itself is a creation of humankind and would not exist without man. I completely agree with you.
@Dr_Lawrence, I think it depends on what you mean by “math.” As a purely semantic language, then obviously if that’s what you mean by “math” then we “invented” it.
But some people mean the signified, not the signifier. So it’s not comparable to English, so much as the things “out there” that words described. We invented the word “tree,” and the syntax to understand the word… but trees obviously pre-exist humans. The function of language is to filter and categorize what is “out there.”
Math is a language tool. And all language tools are used for describing observable or theoretical phenomenon. The phenomenon was discovered through observation. The math was invented to help describe it better.
Math is an invention. It always describes something other than itself, just like every language tool does.
I can describe a sunset with Math or Poetry. The Math tool allows me to describe it with great accuracy and how it relates to other phenomenon. But Math can never tell me or anyone else how I actually feel about that sunset. Only Poetry will suffice for that.
Language is a description tool. And all descriptions are authored, not discovered. Only the phenomenon is discovered.
Both. I think the abstract concept of a cube is a discovery. It’s out there with or without humans. The minimum polynomial extrapolation as a sequence transformation in numerical analysis requires a human invention.
Me thinks…you can’t “invent” something that was already there, whether you know about it, or it’s attributes, or not. When the first Indians crossed the Bering Land bridge, they discovered the North American continent. They didn’t “invent” it.
@mattbrowne Any any analysis that you can do requires rules that are natural, not a human fabrication. A disciplined approach to doing something is not an invention, it’s just a formalization of what was already there.
@XOIIO What do you mean? What you are saying is that math is sane. Who does math and expects a different result? I guess maybe with complex problems, when we are unsure how to solve something, we might try different calculations for the same variables, but then that still is trying something different so still sane.