What is math?

To me, math is the foundation of many other disciplines of study.  Math is the earliest type of science.  Math is a complex system of numbers, algorithms, and proofs.  Using math, many things can be done.  Math allows for its user to be able to study circumstances that they encounter.  The reason that I call math a "science" is because without math, no scientific studies would be able to be quantified, all studies would have to be qualitative and therefore much less precise.  Math is the building block onto which all other forms of number systems and theories can be and have been built.  For instance, the theory of gravity is only a theory because it can be quantified as a velocity of 9.8 meters per second.  Before the mathematical calculations, only the thought of gravity could be used, there was no precision as to how gravity affected all the things on the Earth.

There have been many discoveries in math.  I have ranked the top 5 in the order of importance that I find them for math below.

1. Algebra
2. Geometry
3. Pythagorean Theorem
4. Calculus
5. The Fibonacci Sequence

I have ranked algebra as number one because without the discovery of algebra then no other mathematical processes would be possible to do.  Algebra allows for variables in math to exist and for us to know what those variables represent and how to use them.  I have ranked Geometry as number two for two reasons.  The first reason is that it is a very visual representation of mathematics.  Geometry allows for the user to visualize what they are doing which is very helpful in other fields that incorporate math.  The other reason I have it ranked number two is because if I remember correctly, I had heard that through the discovery of Non-Euclidean Geometry mathematics became its own subject instead of just being used in conjunction with the sciences.  The Pythagorean Theorem and Calculus come in at three and four respectively because they are pivotal to the advancement of math.  While I do not know a whole lot about the discovery of the Pythagorean Theorem, I do know the importance of this discovery.  Calculus is also a very wide subject to be put at fourth.  The discovery of Calculus helped many other fields of study because they could/can use Calculus to solve for certain variables, an example, through derivatives and integrals, if given the formula for acceleration, velocity, or position, we can find the others.  I put the Fibonacci Sequence as fifth because I know that its discovery is very important, but I do not know much at all about the Fibonacci Sequence or its discovery.