Did we invent math,or did we discover it?

God invented it.

Math is a language we created to describe patterns that already exist.

Invented.
It is a description of reality, not reality. The universe does not do math to function, it just functions.

We discovered the facts that we invented math to describe.

I love this question!
It is a way of describing processes that already exist.
Two apples and two apples made 4 apples before humans walked the earth.

So math does not exist for animals other than ourselves?
Intriguing.

This is a classical question in philosophy. Look at numbers, which are just one part of mathematics. Why is our universe numerically describable in so many ways? Length, mass, time and magnetism are different aspects of our world, but all are measurable. The physicist Eugene Wegner spoke of “the unreasonable effectiveness of mathematics”.

The geometry used to describe general relativity was developed before relativity was thought of. Can there exist a universe not describable by mathematics? Max Tegmark has floated the idea that mathematics is the ultimate reality.

Both really. Our systems of numbers and equations are an invented nomenclature. We have created many forms but the fundamentals behind them are intrinsic to the universe.

We conceived it.

Mathematics is a part of reality that can be explored and discovered like any other part.

Everyone here discovered math when adults told us about math. But math is a kind of symbolic language for a class of concepts and a way of thinking. The language is invented, and the ideas are in a way discovered.

I agree with @raum. Math is a language. And for the record, language did not exist until we invented it. It’s not like the trees were verbally speaking before humans arrived.

Also what I just thought of: Counting your fingers.
There are no fingers. Not in reality. You just virtually and arbitrarily divide your body into parts, or descrete groups. But in reality, they are not separate. You could deform your body into a sphere (like this cow), without intersections, divisions or additions.

The hardest question a child ever asked me led to the answer I consider my best.

I was asked what is the difference between letters and numbers.
My answer…
Letters get arranged together to make words, and ell stories. Stories about people, animals, places, all come from sorting letters.
Numbers also tell a story. They tell how big, how small, how new, how old.

With this in mind, my answer to this question is we invented language, symbols, measuring tools to share knowledge. We invented the symbols found on a calculator to better understand what exists, and what we can do with what exists.

A light-year is something which existed before humans, but we calculated it and use those calculations. Math is a language we use to share what we know, and to learn what we don’t know yet.

@Patty_Melt, Using a language presumes that the speaker and the listener know what the words mean. You can’t talk about houses, trees or numbers without some understanding of what they are. Houses and trees can be defined in simpler terms, but how do you define what numbers are? The best you can do is to give examples and hope that the person catches on. We are not born with the concept of number. There are tribes in the world with no words for numbers greater than 3.

That’s where education comes in @LostInParadise, whether it’s from school or home.

I said they tell stories. I did not say anyone has ever been born understanding a language.
Literacy was not the topic.

Who are you talking to @Patty_Melt?

@Patty_Melt, You are missing the point. Stories have words and those words must be understood. If you point to trees and keep calling them trees, a child will figure out what you are talking about. It does not work that way for numbers. First you teach about one or two objects. Then you have to explain the counting process. It is more than just telling a story.

The point is, did we invent math. The sizes, events, areas exist. We invented the language which tells the story. Boom. That is all. Learning is associated with everything in our lives. Learning is not the topic. Pre exist, or manufactured is the subject. The learning curve is not part of the topic.

Math was invented to describe our world better and define it.

So math didn’t exist until we discovered it @ruiamsoru?

@Dutchess_III Many of the facts that math engages with and describes existed long before we discovered and described them. But math itself is a formal science that we invented as a tool to investigate the world in a particular way.

It has to be said, that math as it exists today, is very different from what it was before.
It used to be pure geometry:
https://www.youtube.com/watch?v=cUzklzVXJwo

That is a great video about complex numbers. It took a while to accept negative numbers. And then square roots of negative numbers? It just seemed absurd. And yet, as the video shows, complex numbers are at the heart of quantum theory.

I taught kids to understand negative numbers by envisioning a post being sunk in the ground.

@Dutchess_III That’s similar to how subtraction gets taught at the elementary level in some educational apps.

Obviously it would be taught at the elementary level.

Of course. I just thought it was interesting that you had come up with the same solution as some thoroughly researched and rigorously tested educational tools. It speaks well of you as a teacher.

I keep telling my husband I’m a genius. Now I have proof!

I like the idea of using a balance scale to teach addition and subtraction. Link
One thing that it shows is that, for addition and subtraction, the rules are the same for positive and negative numbers. It is completely arbitrary which pan is used for positive values and which is used for negative values.

If you take any equation that uses only addition and subtraction, you can reverse the signs of the numbers and get a correct result. For example, start with 7 – 1 = 6. Change signs to get -7 – ( -1)= -6. This is kind of a fun thing that never gets taught.

Extending to multiplication, i and -i are indistinguishable. Take any equation involving complex numbers and change the signs of the i coefficient and you get a correct result.
(a+bi)(c+di)= (ac-bd) + (ad+bc)i. (a-bi)(c-di)= (ac-bd) – (ad+bc)i This is taught by saying that the complement of z1 x z2 = complement of z1 x complement of z2.