Aristotle and Math

So the other day before class I read some Aristotle (thinking about what courses to take next year, decided to do some pre-reading) and as I grappled with the first two paragraphs of his book on politics, I got the feeling of turning over a concept in your mind. A feeling that is almost pain, and almost pleasure for me. It's when you are beginning to understand something but cannot even begin to grasp or appreciate it's magnitude and importance in it's entirety.
Because of my reading Aristotle, I was able to grasp concepts with much more ease than I could before--because my brain was already working in a mathematical way (more on how philosophy is essentially math later). A few things occurred to me that I found very interesting that I'd like to share with all of you:
1. At a very young age we already understand complicated and trigonometric principles: we understand what one is. We understand having one which to us seems very simple, however in that we also understand trigonometric principles and functions without even realizing it:
sin^2(alpha) + cos^2(alpha) = 1. Inherent in one, is the fundamental identity of trig, the Pythagorean Theorem, angle measurements, radians, degrees, minutes, seconds, an entire world of trig all inherent in the simple number which we grasp at a very young age... One.
2. Math is essentially philosophy. Just look to the great philosophers, Aristotle wrote entire books on what he called, "logic." And "logic" is a common word used to refer to mathematics. Many great philosophers were also mathematicians who discovered groundbreaking theorems and proofs, such as Pythagoras. Also, what is math other than the pursuit of knowledge to better understand the world we live in? And what is philosophy other than this? Why do we seek knowledge other than to know what to do with our lives, and how the world around us works? Philosophy is essentially the same thing: figuring out what's ethical and what is not, how states should run, how people should live, free will or predetermination, the meaning of life even. Also, I was talking to Cullen a teacher here at Paideia who teaches philosophy, and he said that when he was studying philosophy he had to take a class that was all proofs, and that inherent in algebra and in such things as proofs is philosophy in the case that they make an argument for something or other...

Anyways, just food for thought...

-Luke