What is Math

Let's discover the meaning of mathematics.

What is mathematics?

Many people in general, and those coming from high school especially don't take math seriously. Generally it's well understood what a physicists, a chemist, or a biologist does by general population.

Math is a bit harder though. Because it spans all these fields. It abstracts the general concepts from the intuition of a particular application. And replaces that intuition with intuition of abstract relations.

As a basic example, consider the concept of natural numbers: 1, 2, 3, ... They can be used to count some specific things. But this structure is independent from these things. In some sense it's us that impose this abstract structure in an intelligent attempt to categorize and interpret information around us.

Study of this kind of "structure" is generally all mathematics is about. Number theoriest would no longer care whether these numebers represent cows or chicken. But they would notice that there is some additional structure that is hard to see when thinking in specifics.

For example, one would notice that not all natural numbers are the same. Some divide the others, while others do not. And some are only trivially devisible by 1. This then gives rise to the concept of prime numbers. Which is both interesting in itself, and is also useful for applications in other areas, for instance, by providing an intuition for desigh of hash functions. Also cryptography lol.