Was mathematics discovered or invented?

GQ. I think discovered, because it exists in nature in a lot of ways. The six sided honeycomb structure for one example. Maybe insects invented it? :) There’s also E=MC squared. There are a lot of fundamental principles based on mathematics. Nice question to make one think.

I have always thought that it was discovered also.

Neither, really.

Mathematical ‘stuff’ always existed, as it does today.

The question ought to be – “when was mathematics understood?”

You have people understanding what wheels could do (circles = geometry) a long time before there was an understanding of the mathematical reasons for them. Same with all of the astronomical stuff that Ancient tribes – Ancient Israel, Incans,Phoenician, ancient China – they all understood that there was a scientific/mathematical side to what they were doing, even if they didn’t have the formal terms and symbols to describe it.

@elbanditoroso A very interesting, and eye-opening answer, it puts a whole other spin on this.

I think discovered. It is like the trillionth digit of Pi. It exists and has a value even before we calculate what it is.

Invented. Mathematics is a language to describe physical reality, and all languages are invented. Mathematics is just more precise.

@ragingloli Imagine an alien race in a galaxy far away who also invent a language to describe physical reality. Could that language differ from mathematics?

Imagine an alien race in a galaxy far away who also invent a language to describe physical reality. Could that language differ from mathematics?

Imagine if aliens landed on Earth and handed you a math book. Could you read it?

@jaytkay – probably not at first, but my guess is that there would be some familiar looking diagrams and charts that would represent things like circles and lines, and by extension, concepts like Pi and radius and diameter…

Not to say that Science fiction is necessarily 100% accurate, but consider the satellite transmissions sent to earth in Carl Sagan’s book Contact. Or in Wylie and Balmer’s book, When Worlds Collide.

concepts like Pi and radius and diameter

OK, I guess I’m referring to mathematical notation which isn’t the math itself.

So yes, I’d agree we discovered mathematics and aliens who could travel in space would have discovered the same things.

Math is not invented, it is discovered. We give things we discover names like pi or e but these are not things we created to describe the world they are intertwined with it.

I am in the discovered camp much like astronomy and evolution; they existed before we recognized them for what they were.

I think it is a little of both. The underlying mathematical nature of the natural world has been discovered bit by bit over the last millennia or so. The symbolic notation used to describe this underlying nature, however, has been invented, starting with Sir Isaac Newton in England and Gottfried Leibnitz in Germany (or was it France?) beginning in the 18th century.

I like the idea of how it is both discovered and invented. Someone had to come up with the concept of zero so things made more sense. Zero always existed, but we needed a way to express it, like a language, like @ragingloli said. Also, I like to imagine a universe where Plancks constant can be slid on a scale for understanding vast differences of scale and time, from a real human perspective, but I’m weird like that.

@cazzie
I disagree.
Zero did not always exist.
Zero is a concept, invented as an analogue to the physical absence of something.
Or the sphere. A planet may look spherical, but it is not spherical because of the concept of the sphere, it is a sphere (not really a sphere, because of irregularities in the surface and its own spin) because of gravity. The same with orbits. Spheres, circles and ellipses are invented concepts to create models of reality.
An apple is an apple. Most languages have a word for apple. But the concept of “apple” within a language is an invention, not a discovery. There is no concept of apple outside of language, only the apple itself.

@cazzie your statement about the zero reminded me of a short film I saw either in Junior High or early High School called Why Man Creates. It has been about 45 years since I saw it and I still remember one of my favorite lines from the film. It begins at 2:53 in the attached video that your answer promped me to go find and goes:

First Scholar: “Allah be Praised! I’ve invented the zero!”

Second Scholar: “What?”

First Scholar: “Nothing. Nothing”

_There is another memorable scene at 4:14 I hope you will take the time to watch.

@ragingloli In a far away galaxy there may be no apples but they will still have pi.

the physical absence of something always existed. Of that, I am sure. At one time, I had no money. At one time, I had no husband. At one time, I had no children. At one time, we had no food. Physical absence needed a definition in relation to commerce. Therefore, it needed a definition. https://www.youtube.com/watch?v=gulApUKih2w

I disagree also, I think math is one of the only things in our universe that is actually real.

I watched a program produced by NOVA on PBS about mathematics and have to agree that aspects of it were discovered and others invented. The program offered the idea that mathematics has limitations because it only reflects the way we think and is dependent on its development it may not provide the whole explanation of the contents of our universe and how it evolved.

@Bill1939 I watched that NOVA episode too. The fibinachi sequence in nature was interesting.

I think there is an ambiguity in the question that leads to such different answers. The word “mathematics” could be taken to refer to the activities and products of mathematicians or to the relationships they use equations to describe. The relationships are already there to be discovered, but the method of uncovering them and the language used to illustrate them is an invention.

Relevant.

I know it’s 20 minutes long, but it’s an interesting listen.

I love this question! I was about to type the same one. I got into a GIANT debate with a mathematician over whether math was invented or discovered. I still feel quite strongly that it was discovered but I can see HIS point about them being invented. I tried to end the debate with, “then we are both right” but he was having none of it and said, “No I am” :P Bloody engineers :P :P

I’m not saying ‘Zero’ always existed. (I never revisited this question when I saw that @ragingloli misunderstood what I meant.) I’m saying that the concept was always there waiting for a definition and a name. I’m sure there are things on Earth and in the Universe that we haven’t yet named and discovered that very much do exist. That is what I meant about the concept of nothing.. or what we now call ‘Zero’.

When you look at patterns in the growth of leaves or flowers, there is math RIGHT THERE! The flowers have been growing for a much longer time than we had to the math to help express their patterns. https://www.sciencenews.org/article/mathematical-lives-plants

http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html

I think the answer really is both, but perhaps that is more of a philosophical answer than I usually give.

Some of these questions, like this one, I should take with me to my Science Friday group. They love this stuff and since the quality of the actual NPR program has dropped, we are thinking of creating one of our own.