Math: Discovery or Invention?

[nofx]

Debate!
I say that math is both, but I am more leaned to invention. Aren't words, letters, number just a conglomeration of symbols and wicked lines. Dictionary.com says an invention is the act of finding... but I am more in line with invention... just look at Calculus, finding arc length, and applications to physics the possibilities are quite endless.

 

[DEATHMASTER]

Well the fact remains that there are things we still don't know yet still exist and are waiting to be discovered.
I see where invention plays a role since the discoverer has to be a freakin genius and actually come up with it. It's like when I think of stuff that I could really use and it turns out someone has already made it.

 

[Qonfused]

Well, inventions are discoveries in themselves. Kinda.

 

[nofx]

But are not feats in engineering (a branch of math) such as the highway system, bridges, air planes; inventions based off of physics, chemistry, and ultimately math... surely things not yet seen cannot be discovered, but invented (besides god of course? or is that an invention )

 

[nofx]

Well, inventions are discoveries in themselves. Kinda.

That is what dictionary.com said, but the premise is
discovering:
dis?cov?er (dĭ-skŭv'ər) Pronunciation Key
tr.v. dis?cov?ered, dis?cov?er?ing, dis?cov?ers

1. To notice or learn, especially by making an effort: got home and discovered that the furnace wasn't working.
2.
1. To be the first, or the first of one's group or kind, to find, learn of, or observe.
2. To learn about for the first time in one's experience: discovered a new restaurant on the west side.
3. To learn something about: discovered him to be an impostor; discovered the brake to be defective.
4. To identify (a person) as a potentially prominent performer: a movie star who was discovered in a drugstore by a producer.
5. Archaic To reveal or expose.

inventing:
in?vent (ĭn-věnt') Pronunciation Key
tr.v. in?vent?ed, in?vent?ing, in?vents

1. To produce or contrive (something previously unknown) by the use of ingenuity or imagination.
2. To make up; fabricate: invent a likely excuse.

 

[Qonfused]

Yeah. I realize that the definitions are different. But theoretically if you invent (to make up) something, you are discovering it (to be the first, etc.). It doesn't matter what the difference is, and I didn't mean to derail your thread. I think math was invented.

 

[tehsolace]

You can discover mathematical theories and concepts, and you can invent proofs/methods for showing or proving those concepts.

For example, someone (presumably named DeMorgan) discovered the mathematical concept in discrete mathematics and then invented what is now known as the DeMorgan's law, which is a method of showing/proving his concept is valid and true.

 

[nofx]

No you didn't derail anything . I am on the invention fence too. Some portions of math are more like inventions in the purely math sense.. i.e. antiderivates... but when applied to physics and deriving the amount of work done when lifting a bag of sand 5m... then concepts become interesting.

 

[Adabiviak]

I'd say math is an invention, as it is itself a description of things that are actually happening as well as a tool for predicting things. You can describe, say, the trajectory of a ball several ways using different types of math. The language of this description is an invention, the tools allow you to predict where the ball will go, what you find with these two things may be considered discoveries.

 

[DEATHMASTER]

what he said ^

 

[Qhartb]

A discovery is, most generally, the learning of something that was already true. Since all true statements in math are already true, in this sense all of math is discovery. In another sense, though, it seems silly to call certain things "discoveries".

For example, if you specifically design a contrived example in order to be able to prove something about it, the specific thing you prove isn't much of a discovery. Like, if I explicitly define a weird function so that I can prove that it's continuous but nowhere differentiable, then the fact that that function is, in fact, what I tried to make it isn't a discovery. If I didn't know that there were any continuous but nowhere differentiable functions, then the fact that one exists is a discovery.

Because it was specifically and arbitrarily designed, the function that I described in the previous example would be an invention. There's nothing fundamentally special about it, but it was useful for doing what I was trying to do. Things like that would be reasonably called inventions. Certain mathematical techniques, like Cantor diagonalization or Godel numbering, could likewise be considered inventions, too. Most (maybe all) notations would be considered inventions, too, since they are just arbitrarily chosen symbols to represent ideas.

So, I guess my answer would be that math is fundamentally about discovery, but because of the way we have to go about discovering it, we come up with inventions to help us think about it.

 

[Viperidae]

Invention. The concept of mathematical relations is the invented part. I won't dispute relations found in nature aren't invented, but the system as a whole, yes.

 

[Jerry_111]

the symbols we use in math are invention, but the principles are discovery.

 

[The Monkey]

It's a discovery, as math has existedin the universe long before humans appeared. We just wrote down the formulas.

 

[CrazyHarij]

it depends on your perception, it's pretty much a way of counting things and theorising around that, but technically, on a molecular level it doesn't even exist, singularity is rarely constant

 

[Jintor]

I would say discovery, given that invention is merely a process of discovering how to dismantle the universe and rearrange it so it does this.

 

[Tyguy]

Discovery, you cant invent 1+1=2. You discover that it works

 

[<RJMC>]

is a nightmare in school

 

[Solaris]

I've been discussing this with a friend for quite some time now actually.

I think we discover mathmatics, we discover properties of numbers, patterns in which they appear. We can prove very interesting things with mathematics. But the problem is, the fundamental axioms of mathematics, did we create these, or are they fundamentally true?

 

[Dog--]

People are just saying it was an invention/discovery because it has always been, since humans could speak, and we don't know any different. It's kind of hard to explain.

It's just an illusion invented by man-kind, like time. Think in an "oogie-boogie" mindstate. It only exists because we say it exists.. Y'know?

If I had to choose one it'd be discovery, because of what Tyguy said.

 

[Asuka]

Invention to understand and measure things we dont understand and cant measure.

 

[dream431ca]

It's both. Invention was first. People probably started to experiment with objects, or try to find out the area of a field they wanted to harvest..but that would imply they knew what square meters were, so they would have to know math first. Anyway, next came the discovery of something they could use to calculate various things.

The Egyptians were the very first to use the Pythagorean theorem. Not Pythagoras, as many people think. They used it to measure the area of their harvest fields by the Nile river.

 

[ailevation]

Math is a projection of your mental reasoning and logic through symbols. It's both a discovery and invention.

 

[Robbo]

It's Invention. Before humans maths did not exist, yes the principles that it describes did but MATH did not. We invented numbers and from that came other inventions.
I can see now how the line is blurred but remember that math is not the universe it only describes it.

 

[Solaris]

It's Invention. Before humans maths did not exist, yes the principles that it describes did but MATH did not. We invented numbers and from that came other inventions.
I can see now how the line is blurred but remember that math is not the universe it only describes it.

Maths does not describe the universe, that is physics.

Maths is pure, and discoverable. If we were to meet an alien civilization, it is very likely that they would have made the same discoveries as we have, therefore, mathematics is discoverable.

 

[dream431ca]

Maths does not describe the universe, that is physics.

Maths is pure, and discoverable. If we were to meet an alien civilization, it is very likely that they would have made the same discoveries as we have, therefore, mathematics is discoverable.

But math and physics go hand in hand. You take one of them away and you have nothing.

 

[Muffin Man]

The system of numbers and equations is invention, what the numbers and equations represent is discovery. That's my stance.

 

[Solaris]

But math and physics go hand in hand. You take one of them away and you have nothing.

Physics is effectively a mathematical model, mathematics is in no way reliant on physics for it's existence.

To be able to partake in this discussion in a meaningful way, it's important to be aware of the difference between applied mathematics (things like physics and statistics) and Pure Mathematics (Number Theory, Topology ect.).

Number Theory has very little if no connection to the physical world, it is mathematics at is most beautiful, the study of the patterns and rules to which numbers behave and the best discoveries are usually absolutely useless in the sense you cannot apply them to the physical world. Pure mathematics is discovering things for the sake of discovering them, all the best mathematics is pure.