mathematics discovered or invented?

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Was mathematics discovered or invented? I personally think it was discovered.

Mathamatics?

Well sorta both really. I think the entire universe is subject to mathamatics, but we 'invented' a language which we can understand Pure mathamatics. The maths we learn is Natrual in our language. why else is it so beautifully fluid? Even the maths in quatum physics (where you will have your common sense ripped apart before your very eyes) is fluid.

Discovered in my opinion. Mathematics is just calculating and measuring the things around us, the principal of math would exist even if humans did not.

both

There is a huge world of mathematical facts out there, like an enormous landscape. When we advance mathematical knowledge, we are simply revealing more of the landscape. However, there is "invention" involved in another sense - only a tiny fraction of the landscape is relevant for our purposes, and so we have to use intuition and cleverness in order to decide where to explore.

I agree that it was discovered rather than invented. I tend to think that all ideas are discovered, and that "invention" is merely an illusion.

Consider a situation in which someone "invents" something. Their invention already existed as an undiscovered possibility, and they are just one of the first people to have discovered a new way of doing something. The implications this has for well-known creative people is that they are creative because they *seek* new ways of doing things, or new ways of thinking. Isaac Newton, for instance, didn't just pull equations out of his ass; he continually thought about physical phenomena while referring to things he already knew, and there was a fair amount of trial and error involved as well. Eventually, after thinking about physics continually, his mind finally made the right connections, and out came the theory of gravity. He discovered the way gravity works, and then had to express the law in terms of mathematical symbols on paper. And that was hardly the whole story; he just laid the foundations upon which later physicists built.

Newton is actually an interesting case for the topic of invention vs. discovery. Consider the well-known quarrel he had with Leibniz about the so-called "invention" of the Calculus. It is most likely the case that they had both discovered the calculus within the same time period. They both read the same academic papers, were in the same academic community, so it is very possible that they both just happened upon the idea of calculus independently. This implies that the theorem of calculus already existed as a possibility that had yet to be discovered by a human being and expressed in human language.

One could also say that the terms "invention" and "discovery" are synonymous, in which case ideas would be both invented and discovered.

I'll have to go all David Hume on this one and say that without having discrete items and wanting to group them together and count them, math would never have occurred to anyone. Despite being a dyed-in-the-wool Platonist, I don't go along with Plato's theory of recollections. So the basic concept of math, which is grouping discrete items together and then counting them, is discovered. Without things to count, we'd never come up with math. I am a Platonist, and think that concepts of math are built into our universe, and would exist whether we were here doing math or not. However, our models of how we do math come from the real world we are trying to model. So there's nothing innate in us that gives us the ability to do math. We had to build all that from scratch. Some models we create match the real world better than others, and it's been a long process of trial and error.

Indeed. I am also a Platonist who doesn't go along with the theory of recollections. I agree with Kant's theory of categories of the mind, which I believe are how we organize and eventually come to know mathematical objects and relations among them. A proponent of the theory of recollections will argue that these categories of the mind are what are responsible for our "recollections." However, I believe that these categories have evolved as an inherent feature of our cognitive apparatus because the external world requires us to have them. In other words, throughout human history, the evolutionary process gradually developed these categories out of environmental necessity. This of course is based on the theory that evolution is a gradual process that proceeds by means of natural selection and random mutation -- but that's an entirely different topic. So I agree that the models of how we do math indeed originate in the real world, but that the real world is what is primarily responsible for our gradual and necessary development of innate mental structures (categories).

I agree that the answer is "both." Like, in the instance of calculus, Newton and Leibniz and others really did invent calculus, as it was never used or understood before. But calculus's principles and role in nature and the rules of the universe always were inherently there. So mystifying!

Any platonists who are not truth-value realists here?

I agree with others, both. The principles inherently exist as they are - it's up to us to figure them out, explain them and/or duplicate them.

This question is like asking if physics was discovered or invented.
I find it fascinating that the physical universe has an intellectual dimention to it - that dimention we describe as mathematics.
My question is, how can there be logic - expressed as mathematics - in the natural world, without that logic being a natural element?
I know you cannot find logic on the periodic table, but could the universe have been created without it?

Ancient. Aliens. Lolololololololololol.

Things always moved. People saw things moving. But Newton had to -invent- calculus (he called it the theory of fluxions) in order to understand motion.

ruveyn

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