What is math? Part 1

So this article should have been the first one, because it begins to answer the question of “What is math?”.
Before we start that exploration, let’s have a thought experiment. It is not new that the school system is broken. Students are absorbing facts but not actually learning anything, meanwhile racking massive amounts of debt and harming themselves. Suppose that we get rid of the current school system and decided to democratically chose what subjects get taught in schools. We go through the basic subjects and add some new ones, but we eventually have to address whether or not mathematics is going to be kept and at what level. Of course people who want to be engineers or doctors or computer scientists or mathematicians should have to take math, as it is the foundation of what they will do for the rest of their lives.
However, what about the people who won’t use math? The marketers, the artists, the athletes, the average person who just wants to live their life. Beyond the simple arithmetic and algebra why would those people need to learn how to find the vertex of a parabola?
To answer this question we must first answer the question of what is math. Depending on your answer to this question will determine whether or not there is value to be found in mathematics. There are three main philosophical points of view that we are going to look at.
1). Platonism
2). Formalism
3). Socio-Humanism

All of these have fairly simple definitions but their implications have massive impact when it comes to math education, for both the student and the teacher.

So the first perspective is known as Platonism which are the teachings of the ancient Greek mathematician and philosopher. The part of those things we are going to look at are his metaphysics. His idea was that the world around us isn’t entirely accurate. If you try to describe a cat you describe properties but not its essence, its cat-ness. The essence of things or the perfect version of things, including abstract properties such as goodness and justice, resided in a world of forms. Mathematical ideas also resided there, and some how mathematicians have the ability to receive those ideas and relate them to everyone else.
Like I said, it is a simple idea, and historically this idea has stuck.
There was a mathematician by the name of Pythagoras, most people have heard of the name from the Pythagorean Theorem ( he did not come up with the theorem, it was used by the Egyptians long before the Greeks. )
Pythagoras had somewhat of a cult following, where all of his followers lived together and followed his teachings, and alot of those were that of Plato which included the world of forms. To Pythagoras and his people, numbers were thought to be real, and assigned abstract ideas to numbers. For example marriage was the number five, because it was the union of 2 and 3 which were numbers for masculinity and femininity.
To us this may seem ridiculous but numbers were thought to be somewhat magical, which isn’t all that absurd. Numbers have amazing properties and capabilities, and when mathematics was still developing these properties could be thought of as magical.

But part of their idea that numbers were real, was that numbers had to be even or odd, and had to be rational ( can be written as a fraction ). If they discovered a number that was irrational (cannot be written as a fraction ), they were able to get very good approximations, but still thought that the number had a decimal end point. However one of the followers of Pythagoras discovered a proof that the square root of 2 was irrational. This knowledge would have disrupted the entire system that Pythagoras had set up. So like any other cult leader, he killed ( or banished the history is uncertain on this ) this student of his and then threw a feast to celebrate.

Now nobody today who follows the ideas of Plato, in a mathematical sense, is going to kill someone for disagree with their concepts of numbers. We have enough knowledge in the branch of number theory so that won’t happen. But there are still potential consequences for having this thought process.

Suppose you are a math teacher, high school or college, and you accept this idea of a world of forms. Why bother teaching your students? Or going the extra mile that teachers are so often applauded for? If mathematics is presented itself to mathematicians, then what about everyone else? There seems like there is little motivation to be a teacher of mathematics with this point of view.

Now suppose you are a student of a teacher who has this point of view. Why should you bother actually trying to learn the material at all? If you don’t get it, then all that means is that you aren’t meant to be a mathematician, so extra effort is not necessary. This just feeds more into the idea, or myth, of a math gene. Effort in mathematics ends up not mattering because you are genetically predisposed to be good or bad in math.

This question is not yet fully answered, next time we will discuss the next point of view, formalism and have a story on the birth of calculus. Let me know what you think below.