Definition Of Mathematics: The Mathematical Concepts Of The Pythagoreans

Isara Suwansilp

October 22, 2015

Math 10

Mr. Enriquez

Research Task

What is math? The official definition of math is “the abstract science of number, quantity, and space.” However, while a definition as to what math is is given, we will have to dig a little deeper to see where the roots of math lie. Math is a very old concept that has been used since the dawn of humankind. The mathematical concepts of “number, magnitude, and form” were commonplace in the ancient hunter-gatherer societies.

“Do we discover the mathematical basis of the world or we impose mathematical structures onto the world?”, a debate spanning thousands of years, with the greatest minds ever each struggling to reach a consensus. This was similar to a conundrum proposed

The Pythagoreans of 500 B.C Greece. believed that numbers were universal principles. Plato, who Platonism was named after, similarly argued that mathematical concepts were concrete and as real as the universe itself, regardless of our knowledge of them. His belief was a century later than that of the Pythagoreans when established in 400 B.C. Euclid, who was acclaimed as the father of geometry, also believed that nature itself was the physical manifestation of mathematical laws. He did not believe that math came from nature, so it was a little different from the beliefs of other Platonists. So in a sense, he believed that the world was created because of math or to show mathematical

He saw it as a game, a deeply philosophical game, with rules like every other game. The fact that he believed that math was a game with human created rules proved that he saw math as a logical construct of the human mind, not one of nature, the universe, or a divine force. One of the most effective arguments provided by the non-Platonists deals with the definition of math. Math is defined as “the abstract science of number, quantity, and space”. The key word there was abstract. The meaning of abstract is “existing in thought or as an idea but not having a physical or concrete existence”, which helps the theory of the non-Platonists. They argue that mathematical statements definitely do not exist physically, hence the word abstract. Following the logic of the non-Platonists, math is therefore: an invented logic exercise with no existence outside of mankind’s conscious thought. The purpose of math, they argue, is to use patterns to discerned by brain, to create useful, but artificial order from