Is Mathematics Invented or Discovered?

The Queen of Sciences

Gauss referred to mathematics as "The Queen of Sciences". Mathematics is an universal language that uses logic as its own base for further predictions. We could define any physical object with the help of mathematics. But math isn't just about defining events or objects. Its dynamic, it is as though the language reveals further predictions from the logical assumptions we have taken from the nature. For mathematicians, they think of it as a game. A game which can be assigned, controlled or played with different rules. Rules which aren't compatible with reality. But why does a mathematician have to understand something which isn't compatible with reality? Isn't that just like a child dreaming about Sasquatch? The answer to this is mathematicians really don't care about what relates to the reality, their interests in math is exclusively for their own happiness or the pleasure they get. Mathematicians, can create their own mathematical world. All they needed to do is kick start a world with odd rules or rules of their own interest and play around with them, to find out the governing dynamics. Its beautiful, sometimes messy. The more messy it gets, the more unpredictable the world becomes.

"Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true." -Bertrand Russell

Our universe too is unpredictable but not too messy because of the symmetries and constants. The only reason our world is unpredictable is because of quantum mechanics. If rules of quantum mechanics didn't interfere with our universe then it would be easy to predict ones future with incredibly high accuracy.

The Uncertainty Principle

It states that if we know the velocity of the particle with high accuracy then it is impossible to find the position of the particle with high accuracy. This might sound bizarre, because it conflicts with our everyday experience. If we know the velocity of a car moving, then using Newtonian dynamics we can compute the position of the car to high accuracy. The only difference here is Newtons laws (Classical World)  are applicable only to classical objects i.e objects that are large. The rules of Quantum Mechanics (QM) are only applicable to tiny objects like electrons, protons. QM seems strange only because we weren't evolved to understand it. If you were to shrink yourself to the atomic level, your everyday experience will seem to conflict most of the rules of the classical world.

The uncertainty principle is a well defined mathematical model. Quantum physicists who study the world of QM find it extremely hard to grasp the concepts. In fact Feynman once said "If you think you understand QM, you don't understand QM" The only hope quantum physicists get is from mathematics. They put their theories for tests and gives the exactly the same result as what was predicted using the mathematics of quantum mechanics.

"The mathematical framework of quantum theory has passed countless successful tests and is now universally accepted as a consistent and accurate description of all atomic phenomena." -Erwin Schrodinger

Is Mathematics Invented or Discovered?

I'll be honest with you. No one actually knows the answer to that. But I think it is more likely to be discovered than to be invented. As a skeptic, I have no problem with mathematics being invented. If mathematics was invented then I would be astonished by the fact that the humans were so imaginative in inventing something that happens to work very well with the nature. Math is everywhere and the fact that we can relate/ define to at least some extent and predict its outcomes satisfies me. If mathematics was invented then there must be something or the other that cannot be fully explained by math. But we have no evidence to conclude that, since we still do not have all the mathematics needed for its explanation.

I haven't covered any of these topics in depth but I'll soon post a PDF on the nature of mathematics.