I think this will certainly be the most important post, as I answer the essential question, and the rest will be slightly more shallow progress reports.
Why did I choose math for this project?
Here’s a simple answer: I was already studying math and didn’t want this project to get in the way, as that would be counterproductive, if I do say so myself.
So here’s a better question, essential even.
To start I’d like to chart the progression of my own interest, starting from the early years and speeding all the way to the next heading.
In order to appear conceited I will say the I’ve always been pretty decent at math. Mrs. Grant even pulled me out of class to question my aptitude. However, my love for math remained aside for many years. It wasn’t until I stepped out of the world of arithmetic and saw that I knew nothing, and it was exciting. It was the realization that I believe many people failing to make is the reason that math remains esoteric and uninteresting. It’s that having the talent to add or subtract big numbers in your head isn’t what math is about at all.
What math is about
Early on it’s apparent that the reasons certain people love math are as subjective as their favorite piece of art, (Math With Bad Drawings: 39 Ways to Love Math, and I can recommend any post on that blog) but it’s not too difficult to generalize. Math isn’t just about numbers. Math is the love for patterns, being able to uncover the interesting and surprising using logic and your very own brain, beauty and truth, and minimalism and perfection.
Now, I’d like you to brace yourself for a few popular math things that get me excited about math, but going into detail on them won’t really add anything to this post. Ironically, statements like that are also one of the main reasons I started learning math. Blogs and articles with exciting math that is “too complex” to show a layman. I doubted that I couldn’t understand them eventually. I want to understand and get excited too! Even if out of spite, and I hope you do as well.
The go to for surprising and beautiful results. It shows how a bunch of unrelated, complicated ideas developed for thousands of years come together to produce something simple and elegant, showing how fundamental math is in nature. More
Fermat’s Last Theorem:
A simple expression that looks like Pythagoras’s theorem. After 358 years it was proven by one man’s 7-year-long dedication using a lot of complex and new mathematical ideas.
A E S T H E T I C
Godel’s Incompleteness Theorem:
“There is no formal (axiomatic) system of mathematics that can be both consistent and complete”
Beautiful because in a way it crushes mathematicians’ dreams of perfection, but is still amazing and in another way only reinforces mathematics’s perfection.
The Platonic Ideal
There is something common between every other branch of human knowledge, and that is uncertainty. No matter how clear or intuitive, or how much evidence we have about some fact, it is still impossible to know whether it is true, take gravity for example, if you like.
This is not so with math. Even if you’re a solipsist, you can still prove math to yourself. No matter where you are in this universe mathematical statements will still be true, math is universal. It is the very language reality is written.
So if you’re like me, you come to terms with the ambivalent, deterministic universe. You become depressed and search for meaning, find none, and turn to the only thing you have left, aestheticism. You find beauty in knowledge, truth, and once you see that math is all that is really true, you see that math is also the most beautiful.
Now that was somewhat pretentious, but what I am saying is that to me, math is the most important part of life. All I need is my health and math.
My self-teaching progress thus far
I really started to get serious about teaching myself math over winter break of this school year (2015-2016). I want to be able to understand complex ideas like Godel’s Incompleteness Theorem in all its beauty, but I must begin at where my knowledge ends.
First I picked up a couple of good looking books from the library. However, being the slow reader I am and with school getting in the way I’ve only finished one, The Information. And I have many more math books on my wishlist (buy me things).
I also have gone through a complete Calculus I course. Taught by my jacked math hero, Professor Leonard.
And I can confidently say that I can take a derivative.
Lastly, I began teaching myself Python using this guide, because I have not mentioned my equally large interest in programming and computer science (which is basically still just math), but more to the topic at hand: so that I can code pretty interactive math visualizations.
I plan on going through Calc II and III online, then on to the interesting stuff, probably while I’m still in Calc I in school.