I want to see the point of view of people who think math is discovered while I personally think math was invented. I think math was invented because it is a tool people use to solve problems. You don't discover tools you create them.
Math is used to solve problems that people have in life. These can be simple or complicated. An example would be if you added 3 apples to a cart with only 4 oranges in it then how many fruits are in the cart? This is simple addition and the equation is 3+4=7. The equation was created by humans in order to find out how to use this equation with other problems. To discover something means you find something that pre-existed. The equations used in math were created by people. If math was never created and was discovered then how was it discovered?
You are somewhat correct in your definition of math but you fails to capture the differences between a invention and a discovery. A invention is the creation of a tool that had previously not existed to solve a problem or fulfill a need. A discovery is the finding of something already within nature. Math has always existed whether we were ignorant of it or not. For instance if you had 3 apples and 4 oranges their would always be 7 fruit in the basket whether some figured out how to use a numerical system to discover it. Also inventions to not have laws that are irrefutable. For instance a triangle always has a interior measure of 180 degrees. This fact remains constant no mater what. This is similar to the laws of physics which were also discovered not invented. Also your argument for the equation being created by humans is incorrect for 4 plus 3 will always equal 7. The only thing that was invented by humans in your example is the Arabic numeral system which helps clarify mathematical contents better than previous systems. However just because humans have a different way of seeing things does not mean we discovered it. For instance we did not invent infrared light but rather discovered how to harness it in thermal goggles. Thus the mathematics that we know of to day is not a invention but a profound discovery with our best conveyor of math being the Arabic numeral system.
I will admit you are right about your argument against what I said. About how the numeric system was invented to use math however math is still invented. Like time which is man-made it is used to see a better understanding of how things work. The foundations were discovered but it by itself was not. The teaching of physics are man made just like the teachings of math are man made. Before math was invented people would have said there are just some apples and oranges due to the numeric system not being invented. The notions or problems that math solves are discovered naturally. Math like I said before is a tool used to solve these problems. The use of equations were invented, but the fact the problems that are solved happen on there own. However the problems are not math because math is a tool used to solve problems.
You once again are failing to see that math was slowly discovered. A triangle will always have a inner angle measure of 180 degrees whether we knew it or not just as the laws of physics will always be true whether we knew them or not. The equations that you speak of that we "invented" were not inventions but profound discovers that changed our view of mathematics. You also fail to realize that the numerical system is our method of interpreting math not actually math. It doesn't matter how I express mathematics its fundamental nature remains the same. For instance in physics if the unit Newton was not named a newton it would not fundamentally change physics it would just change how it was written. The same is true of the numerical system which merely facilitates math just as money facilitates trade. Also just because somethings solves problems does not make it a invention it must have not existed previously. To continue with the apple orange analogy their will always be those 7 fruit and that fact is irrefutable this number was not invented it just is and that is the nature of a discovery not a invention no matter how much interpretation we use to make mathematical discovery's.