# Is Mathematics Invention or Discovery?

Tso William 12B

Is Mathematics Invention or Discovery?

The question on mathematics being invention or discovery has long been debated. In the ancient Greeks, Pythagoras and his school of thinking, Pythagoreans, considered number in mathematics to be a representation of reality. Plato, one of the most important Greek philosophers in the Western Philosophy, reasoned mathematics being the only way to understand the true reality of the world or the form. Thus they both suggested math being the ultimate reality that must be discovered by human.

On the other hand, there are three fundamental questions about the nature of mathematics itself. First, we must know where mathematics exists and where it is operating. Secondly, we are not sure how we discover the so-called reality of math. We must take a closer look on the system we are using to find the mathematics laws that represents the reality. Finally, since mathematics laws must correspond with the reality if it’s discovered. Therefore we will find how and why the real world will obey the mathematical laws.

The most reasonable answer might be mathematics being operating and existed in our mind. We processed the abstract idea, such as numbers and logarithm, in our mind. This is an obvious answer but it suggested mathematics being invented by humans themselves. We use our reason and logic to arrive a conclusion to describe what we know and the idea we have. This is similar with using our sensory perception to create an image of the physical world in our mind. A bat‘s perception will be very different from ours because they have different sensory organs. Similarly, an alien from the other planet might have a different reasoning to describe their world.

A scrutiny on the mathematics system could help us to understand. We derive our mathematical laws by having axioms first. These are certain assumption and definition in which there are no questions about them. Then we use the rule of logics to solve the problem and find the result. This is known as the theorem. Euclid, the most famous Greek mathematician on geometry, based on the axiom of two points can be joined by a straight line to derive his theorem in his geometry.

In the processing stage from axiom and theorem, we use deductive logic. Thus ...