Is mathematics invented or discovered ?

[Majed]

Is mathematics invented or discovered ? 
Mathematics is a language. And like all other languages the goal is to develop fluency in it, through massive experience. Just like with English, a very good English speaker will speak English in the best way possible intuitively not through reasoning or consciousness of all the grammar rules. A good mathematician solves mathematical problems intuitively because he has internalized its rules and know how to use them. Now to the issue of mathematics being invented or discovered, the answer is mathematics is invented. This isn't a mathematical problem but a philosophical one. Because reality is imagination, all language are artificial dissections of the same unity which can be very useful for manipulating reality,  however it shouldn't be confused for reality itself. Which is an infinite unity otherwise called God. Which is indivisible oneness. Now since reality is imagination, hence truth is imagination. Therefore mathematics is true as imagination because there's nothing but imagination. In this sense mathematics is discovered but in a deeper sense, mathematics is invented.

Edited November 13 by Majed

[Ramasta9]

Vibration > Geometry > Math 

[UnbornTao]

It's a language - invented.

Sorry, no elaboration.

[Ishanga]

Discovered, as a certain Potential that was waiting to be discovered to help explain Reality!!

 

[Hojo]

Invented by God discovered by humans.

[Roots]

Mathematics itself is more fundamental than the language used to describe it.

[zurew]

1 minute ago, Roots said:

Mathematics itself is more fundamental than the language used to describe it.

What do you mean by "more fundamental" there?

[AerisVahnEphelia]

Self generated by you 

[Bjorn K Holmstrom]

This is an interesting discussion. I’ve been thinking about the "invented or discovered" question, and I’d like to offer a viewpoint that bridges both sides.

I believe the fundamental principle of mathematics is discovered.

It starts with the most basic duality we can conceive: existence and non-existence, something and nothing. You can represent this as 1 and 0. From this single, discovered relationship, an entire logical structure inevitably unfolds. The concepts of quantity, relations, and even infinity follow naturally from this core. This structure exists whether we are here to see it or not.

However, the language of mathematics; the symbols, notations, and formal systems we create to describe this structure, is invented.

We invent the numeral "2," the plus sign "+," and the rules of calculus to navigate and communicate the relationships we have discovered. This is similar to how we discover the natural phenomenon of a mountain, but invent the word "mountain" and the techniques of climbing to interact with it.

So, in short:
- The logical structure (based on 0/1, being/non-being) is discovered.
- The human language and formalism we build around it is invented.

We are discovering a profound truth about reality and then inventing tools to understand and use it.

From the absolute, nondual point of view though, it is all the Self looking at itself though.

[Elliott]

It's invented, and incorrect in the sense that 'something counter to it is incorrect'. The double-slit experiment has proven infinity, not that there was ever any logical way infinity could be false.

Take 1+1=2

There are no two identical objects in the universe, nor is there true separation between anything for there to be 2, nor the combining of anything. This befuddles all math. The patterns you're discovering are purely conceptual.

Edited Tuesday at 07:50 PM by Elliott

[UnbornTao]

12 hours ago, Elliott said:

It's invented, and incorrect in the sense that something counter to it is incorrect. The double-slit experiment has proven infinity, not that there was ever any logical way infinity could be false.

Take 1+1=2

There are no two identical objects in the universe, nor is there true separation between anything for there to be 2, nor the combining of anything. This befuddles all math. The patterns you're discovering are purely conceptual.

This is roughly the way I'd argue for it being a language - and therefore something "invented." Without the possibility of language itself (not only a particular language), where would math even be found? Not even symbolism (etc.) woild be possible. You couldn't use one thing to represent another thing.

For example, words point to distinctions, to your experience of some thing. Without language, or without a word for something, it isn't experienced. In many ways, the distinctions that show up within that particular language couldn't arise without the linguistic framework itself.

In the process…

Edited Tuesday at 10:31 PM by UnbornTao

[Salvijus]

Music and geometry is basicly math. Those things are discovered. 

There are autistic or savant people who see the world in numbers and formulas and complex geometric patterns. 

Some people see the world like this. 

Edited Tuesday at 07:57 PM by Salvijus

[UnbornTao]

1 minute ago, Salvijus said:

Music and geometry is basicly math. Those things are discovered. 

There are autistic or savant people who see the world in numbers and formulas and complex geometric patterns. 

Do you discover that your hand has five fingers, or do you invent it?

In other words, we can see that the division itself is something we do - or interpret. If we remove every form of concept from reality... (okay, that's a massive meditation.)

It's interesting. This topic may very well require an inquiry into language itself. Still, I think I'm conflating two claims. The main one is that math is a language. The other - whether language is invented or discovered - I'm not so clear on.

[Salvijus]

Google Jason Padgett. The guy is the proof that math is existencial.