Is Math an invention or a discovery?

Every person who loves math would , at some point of time come across this question. If it is a discovery, what are the reasons? Providing examples from history does not prove the point! Was counting created by humans or was it borrowed from other creatures on this planet? If it was an invention, what made the man transform from counting numbers orally to give a structure to it?

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

It all depends on what exactly is an invention and what is a discovery.

To me it's clear cut:

Mathematics is the the theory behind the workings of the world. It's the structure of the world, the order that the world follows.

Mathematics would still exist without humans or animals. The world wouldn't spin into chaos, the structure would remain. Mathematics just IS. It CAN'T be an invention.

We humans have a gift of being able to discover the structures that exist. The only thing we invented are the words to descibe it.

Even Peano's Axiom's are just a means to descibe what is there!

Ton de Moree - 7 years, 7 months ago

I'd say the theory behind the workings of the world to be physics instead of mathematics. Mathematics generalize and abstract the world further than physics; these generalizations must certainly be inventions, since there's no rigorous reason of why we should generalize them in this way.

Regarding definitions, I'd say a "discovery" to be something that can be rigorously reasoned (although it might take a fantastic leap of logic to think of that discovery before starting to reason it), and an "invention" to be something that can't be rigorously reasoned. "Rigorously reasoned" simply means following the rules of logic, just like all proofs must be rigorous.

Ivan Koswara - 7 years, 7 months ago

My personal opinion is that physics is applied mathematics ;)

Ton de Moree - 7 years, 7 months ago

While nature can't be an invention, but counting numbers which is fundamental is an invention. I mean, numbers aren't invented but counting is!

Varun Ramaprasad - 7 years, 7 months ago

To me Math is a discovery, just like magic squares and many other fascinating aspects of Math in our world. We discover Math because even if humans have not known of Math, Math still exists in our world, in nature. So how can we say we invented Math when we just got the knowledge of it from our world?

Happy Melodies - 7 years, 7 months ago

Just my opinion :)

Happy Melodies - 7 years, 7 months ago

There is absolutely nothing wrong in ur opinion! The main idea behind this post is to know how people think! There is no one correct answer to this question!

Varun Ramaprasad - 7 years, 7 months ago

@Varun Ramaprasad – haha alright :)

Happy Melodies - 7 years, 7 months ago

firstly natural numbers existed in the sense that they occurred naturally .. !! for eg.. a shepherd who could guarantee that the number of sheep he took for grazing are exactly the same as he had before ; by having an account of the stones (he took originally the same number as sheep he had before). One stone in the pocket means that one sheep is in .. and as soon as all the stones are in his pocket he will be sure that the sheep are well in .. !! this accounts for thee counting you just mentioned .. and later on the man transformed it to a subject which had many applications .

Ramesh Goenka - 7 years, 7 months ago

Yes, but what made man transform these simple techniques to a set of rules? is it inquisitiveness or simplicity?

Varun Ramaprasad - 7 years, 7 months ago

Math is both invention and discovery. We just define axioms "arbitrarily" (Peano's axioms generate the natural numbers, for example). But we find that they mesh together beautifully, and we start actively discovering things that can be derived from them. It's invention that makes math to exist, but discovery that makes math an active subject.

Ivan Koswara - 7 years, 7 months ago

Is it the invention that preceeded the discovery or vice-versa? This leads to a situation like "Egg first or hen first?"

Varun Ramaprasad - 7 years, 7 months ago

Huh. That one is interesting. I'd say invention goes first; they invented an "infinite number of axioms" called the natural numbers (that $1$ is a "single object", whatever that means, $2$ follows $1$ , $3$ follows $2$ , and so on), and then they discover the rules of addition perhaps, and perhaps the concepts of fractions and real numbers and elementary functions and calculus and more, until finally Peano makes this natural numbers more succinct by his axioms thus rigorously completing the base.

Invention (of natural numbers) goes first, but they expand both ways quickly; math is continuously invented while also being discovered.

Ivan Koswara - 7 years, 7 months ago

well actually we have invented mathematics as in mathematics sometimes we can make some axiom and then find other deductions from it and these axioms can be anything.like as we study plane geometry,but actually there is nothing like a plane we just imagine it,in actual sense we use spherical geometry and its laws are very different from plane geometry.this is the difference between physics and mathematics

Aditya Kumar - 7 years, 7 months ago

I think its is an invention at its base. As in creation of the mathematical "Universe". Once the basic rules are set, the rest becomes a discovery.

Extending the analogy, I say natural numbers map to our home, the place which we start "discovering" as kids. Rational numbers to our city and Real numbers to our country... And the higher concepts map to other planets and systems and galaxies..

Srinivas Gunti - 7 years, 7 months ago

math was basically a necisstity for humans...just try to take out math from daily life and you will know it's importance.it was indeed an invention.

Saad Hassan - 7 years, 7 months ago

Each and everything has it's own importance! We cannot live without physics and neither chemistry! But, how do u support your claim?

Varun Ramaprasad - 7 years, 7 months ago

it is an discovery

S rohith - 6 years, 10 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$