I believe that math was invented by humans to better understand there place on earth i feel like we only see patterns in geometric shapes and our environment due to the fact we created it to be like that there are many mathematical equations that explain a lot of phenomena and are able to exist even if we didn't just like schrodinger's cat theory whether the cat is dead or alive can only be determined by opening the box or leaving it closed due to the fact that that it is a paradox mathematics is its self a paradox due to fact that math is the cat and it is simultaneously dead and alive because of us not knowing that mathematics is both simultaneously existing and not existing with this we can only be more than definite that we are the only beings that follow the principles of math and without the existence of us math would probably as a entity that defines our universe end explains how life works would not exist
Math is completely relied on how the viewer sees the world. It was not sitting there waiting to be discovered. Actions in our world, and the things we do in it, are measured by the scales that we apply to it. If math were not invented, myself and the person next to me would not see a tree standing directly in front of us as the same distance. But with math, both me and that person understand that we identify that tree as 50 yards away because we were told to use a meter stick and we concluded the measurements ourselves. We can manipulate math to anything that we want it to be, but it's not practical. For example, a cave man could have 14 rocks. Math has been invented, but he does not know that he has 14 rocks. Now if someone comes up to him and takes one of his rocks and says, "you had 14 rocks, now you have 11" now he understands that he had 14, and now has 11. He then creates a system of measurements and values to determine the world around him, but now, instead of losing a rock and thinking he only lost that one, he thinks he has lost three. Not only that, but he changes subtraction to gain value adding numbers, and he coins the term adding to mean lose value. If he can make sense of the world this way, no matter how ridiculous it is, you cannot tell him that he is wrong because he can still achieve taking away one of your rocks like you did his, and he can tell you how much you have added to your total, which to him means losing value. It is entirely a perspective, therefore it must be an invention.
Being close to mathematics, I see the following. There are natural parts of mathematics: positive integers, and basic operations: division (and thus multipliciation), addition (and thus subtraction). But more advanced ones are there, as well: for example, calculus, was 'discovered' for physics. However, the current mathematics includes mostly abstract parts: primes (even more: twin primes), graphs, topology, etc. While some (primes, for example) come from previously existing parts, it is not a discovery. In the nature, there is no such thing as a prime, thus we can not even discover it. On a side not: numerous theorems were later used in physics. Still, they are invented: we discovered their use later.
Math is a human construct. The only reason mathematics is admirably suited describing the physical world is that we invented it to do just that. It is a product of the human mind and we make mathematics up as we go along to suit our purposes. If the universe disappeared, there would be no mathematics in the same way that there would be no football, tennis, chess or any other set of rules with relational structures that we contrived. Mathematics is not discovered, it is invented. This is the way I see it anyway.
Math is a language of numbers. We use equations and numbers as symbols to make sense of naturally occurring phenomena. One example that I would like to bring up to address the confusion is the idea of proportions. When you measure the length of a vertical stick to the length of the shadow it creates; you can use that proportion to measure the shadow of almost any object and determine its height. While it might sound reasonable to say is that the rule the shadow proportions existed before humans, math isn't the length of the shadows to the objects, it is the symbols we use to explain the two things.
While common sciences, like biology, study a certain aspect of the world, like life, math is the study of math. It is extended logic used by humans after years of manufacturing it. Before math, people would use their fingers or stones to show numerical value. Math's invention just made the process of showing and calculating numerical value easier.
...Axioms are self-evident concepts. If something is self-evident, it need not be invented.
Here are other concepts that are axiomatic. (They require discovery, not invention):
Water is wet. Wind Blows. A day without sunshine is night. On the other hand, you have different fingers. I started out with nothing, and I still have most of it. (etc.)
In my opinion it's: Could it have been done differently, it was invented, and if not, it was discovered. America couldn't have been found somewhere else, no matter how hard someone would've tried. Thus, it was discovered. Cars can be built differently, with two wheels or with only one door (if we liked), thus, they're invented.
'Two' plus 'two' makes 'four', and even if we decided to change that, it will never equal 'five'. Therefore, math was discovered.
In my opinion, math is the universal language. One cannot communicate with another without math. Verbal and non verbal, the rules of communication and reality itself are regulated by math. Whether we as humans are able to interpret the math or not, the rules still stand. Just because one does not know the equation for gravity (F = Gm1m2/r2) does that mean gravity does not apply to them? I think not. The philosophic idea of solipsism comes into play here when ones states "Math is a product of the bicameral mind and conscious thought." This is simply a cop out for the inexplicable way mathematics was in one moment, incomprehensible, and in the very next, comprehensible. "Since math exists in the first place, and is comprehended, it must be a product of the mind and for all we know, doesn't exist outside my own mind." This is a false statement from a fool. Lastly, it is in my opinion that mathematics is a challenge for species to take on to display their intelligence. In today's world, we study quantum physics, calculus, geometry, algebra, etc. But all of those had to have originated from man finally being able to comprehend 1+1= 2. Now this is a reach, but if there are indeed extra terrestrials, and in fact they have mastered interstellar travel, wouldn't they have had to begin somewhere also? Wouldn't the alien species have to originate from 1+1= 2 to that point? Thus proving math isn't an invention of man. Also, it is to my knowledge that because of how big the universe is, there would be different theoretical alien species who either aren't as skilled mathematically and more mathematically skilled than the theoretical species I used as an example, also proving that math is a journey and a challenge for different species. Some are more advanced than others, just as we are to less intelligent species on our planet. Just something to think about.
While its true that math is a language that allows us to predict our universe with more accuracy, things existed before they were discovered. 1+1=2. The '2' is a number and a way of expressing a value that is expressed differently in our brains but is technically the same thing. We could replace 2 and 3 and say 3 is 2 and 1+1 is 3, but no matter what we do it will remain the same. Things are added and subtracted in nature all the time. And we must define our parameters of what we mean by discovered before we ask this question. Did Pluto existed before it was "discovered" in 1930. Even if we change the value of units in math the same things will occur in nature.
My personal opinion on this is that the CONCEPT of math was invented by humans. However, the actual systems in place already were already there, so that would be a discovery. Humans have been shown to have an innate sense of math since they're infants, so this shows that math is a discovery. The universe cannot have worked without math, so we just discovered the concepts, equation, formulae, and whatnot and made it into something we can understand with more ease.
Math has always been around the language for math however has been invented. A cave man can have 14 rock in a pile he doesn't know that it is "14" per say but if someone were to take some he'd notice he had less. Therefore the actions of adding and subtracting did exist without the language. That is like someone finding a plant that plant already existed before a name was given to it by the discoverer but the name is what is made familiar to us. The language of math is what is made familiar to us.