Is mathematics discovered or invented?

[subscribefornoreason]

Mathematics is a discovery.
Our way of expressing it is invented.

[LuisAlbertoRodriguezGoff]

Discovered, the symbols and operations to describe are invented.

[BlahBlahBlah]

I was actually having a heated conversation about this with a few friends a month or two ago. I'm no expert, although think this ultimately comes down to what 'mathematics' actually is. Is mathematics the study of the patterns we observe in the natural world or is it those actual patterns? After some quick research, the definition of mathematics seems debatable and subjective, so I think the answer to this question is the same. 

If it is the actual study and description of the patterns and relationships in the physical world - the medium in which we explain these patterns - then it would be invented. Although, if mathematics is those actual observable patterns, then it is discovered. Eddie raised an interesting point about how something's discovery implies it is independent of human measurement and observation, and I agree. 

Personally, I think that mathematics actually IS those relationships that we explore and explain through the language of mathematics. Hence, it is discovered, but I totally understand why someone would be inclined to think the opposite. 

Very interesting. I wish I was in this class. 

[sirtthetea]

In my opinion, universe is as it is.
Mathematics is a tool we invented to describe it.

[DeJay]

Mathematics really is both a discovery and an invention.
We Invented symbols to describe things we discovered.
We discovered the speed at which objects fall due to gravity, and because of that we had to invent a way of describing it.

[ragerecords]

the basic fundamental concepts(such as lines, points, integers) are invented and discoveries are based on those concepts

[ChauTu]

Nice lesson.  Can I say both?  We invent  mathematical tools in order to make new discoveries.

[SocksWithSandals]

Mathematics is based on axioms: Arbitrary laws and definitions from which we all agree whether or not they are true. From these, logical investigations follow.
Occasionally we stumble upon a mathematical relationship that describes the physical world, but there's no reason why any given phenomenon should follow any given equation. Just sometimes it does.

[inlandviews]

Always thought of it as a language used to describe reality.

[Veins]

um... where's the rest of the video? or better, where the results of this question?

[verstengenericks]

The passion that comes through in the posing of this question--is wonderful, even beautiful...

[raj-]

Mathematics is a way to quantify the physical nature around us.
<it is like a universal language>

[bm]

In my opinion mathematics are a ''human model'' of making sense and translating the behaviour of natural patterns. I'll say mathematics it's us, it's the way we interpret the world around us based strongly on the interconnection between our senses, structure of our brain and surrounding environment.
I'd rather say that mathematics is like a 'print on our lenses' that is changing accordingly to our evolution. Maybe one day we'll see mathematics as a primitive tool but very efficient one in its time, day in which the new model of making sense of the natural laws will be different from what we know as mathematics(for that we need to wait).

Let's say that on an alien planet, fungi, trees and many other plants exist, but no animals. The fungi and trees evolved a conscious mind. The first environment of the fungi to deal with in its early evolution would be one of 'electricity, chemistry and quantum phenomena'. Same with trees, no manipulative members, no eyes, no ears etc. but still evolving a spherical vision in an environment where there is not much physical movement apart from the movement at the chemical and quantum level. I bet they will have a different model to make sense of the patterns of their natural world, but in some sense their models would be similar to our mathematics according that the laws of nature are the same, and not continuously evolving, as new conscious species 'add' new undiscovered laws in the universe. As a sphere of influence in the local universe around them, by the act of observing(with a different mentality) the quest for discovery :))

So, contradicting myself, my ''today' opinion about either mathematics is discovered or invented, I'll say neither. I'll say it's evolved and very specific to our own way of 'absorbing reality'.

[thisnamegoeseveronandonove]

Invented, based on discoveries, I guess. (e.g. *one* twig is fundamentally different from *two* - an observation.)

[rollingdownfalling]

I think the notations, numbers, operation are invented. Then the axioms are discovered, like the associative, reflexive, the existence of dimension etc. And then you put them together you discover more law or more weird things happening and then you invent more ways to group certain things together and to label certain things and such.

[jagatchaitanyaprabhala]

Basic high school and applied engineering mathematics is discovered but higher mathematics like abstract algebra is invented but yes the invention was triggered by observable patterns

[nvvam]

I am not proficient in math and the level of my knowledge in math does not extend beyond simple algebra, which is to say very little. From a philosophical point of view, because I can't explain in it scientific terms, I am inclined to believe the laws of math are innate within our physical universe. These laws were discovered by mathematicians. The mathematical symbols that perhaps represent a specific law were invented in order to explain said law, and apply it accordingly in the real world. I believe if we were to go back in time and begin all over again, the equations, theories, symbols would be fairly similar to the ones we have today. For example I conclude that E=mc2, would be repeated nearly identically if not verbatim . Because this theory is a scientific law, a smart person like Einstein, or ever someone else, would come up with this equation to explain the law. I contend mathematical law has always existed, there for it is discovered more than it is randomly invented..
Could someone please comment on what I postulate and tell me if I make or don't make sense..

[majid__jafari]

I think it is discovery. Because we dont get to choose how many apples we would have if we add up 2 apples with 3 apples. It will always be 5. There are lots of math problems that are yet to be solved. If math was invention we could just set an answer for these problems. Just like a puzzle that needs to be solved. Its all about rules and you cant just change them. But the symbols are just invented to help us talk about these rules.

[stankyman]

Literally all human knowledge is discovered and then the language used to describe it is invented. The trick is to get the invention to match the discovery.

[starofdc]

Although laws of nature are inherent, mathematics was invented as a means to describe these laws. Mathematics is a philosophy that humans have formulated from man-made definitions based off observations. This is to say that fundamental postulates such as 1+1=2 were invented as a means of communicating quantitatively.

To discover is to come across new information such finding new planets. We may discover new approaches to calculate or model concepts, however these discoveries are found by utilising the invented tool of mathematics. For Newton's Second Law of Motion, we may state that an object will speed up if a force is applied to it from mere observation or 'discovery'. However, we equivalently use the mathematical description F=ma (using units that humans arbitrarily invented) to describe this discovery. 

Mathematics is the language in which we use to describe these conditions. Just like every other language, it is an invention, not a discovery.