In my first blog post I stated that I believed it would be the most important post; however, I would like to reiterate, for I have learned much more than I expected, and every post has some nugget of importance that I will try to expose here today—in this very blog post.

What I believe has manifested most to me over the course of my blog is the beauty of mathematics. Of course finding beauty in anything is a prerequisite to actually enjoying it, and so I talked about it in my first post. However, I talked mostly about the shallower beauties, such as the visual prettiness of a well-rendered fractal and the like, which I think most people can appreciate; but what manifests with some real effort and intrigue is this amazing sort of deeper beauty, which I think is a requirement to witness before one ever claims by their own volition that they “like math.”

Given that most people are forced to put in real effort into math for most of their young life by the school system, and yet so many claiming outright that they “hate math,” or simply write it off as something they can’t or will never do is a real failing of public education. The root of the problem is misplacement of emphasis.

I remember as early as first or second grade being given a large and dauntingly official looking sheet of paper crawling with countless little addition and subtraction problems to be graded based on how many were completed within the required time. It is this emphasis on a certain species of intelligence, of which it seems you are either gifted by some higher power or you aren’t, that turns off so many kids from the beginning. Math isn’t about being a meaty computer. You may recall the famous, “you won’t always have a calculator on you at all times,” that escapes the lips of most elementary teachers at some point or another, and they’re not wrong, being able to do arithmetic on paper is a useful skill for whenever you’re in the specific emergency of having to calculate a tip or count your sheep when your smartphone is dead, forgotten, or by some other extraordinary happenstance is not in your pocket; but beyond that the beauty of math must be introduced concurrently. This does not happen because math is taught in a very technical way. It is taught in the same way as lab procedure or car mechanics as if your are actually going to be out and requiring knowledge for these problems on the spot. But the other infamous question: “when are we actually going to use this?” still rings true. In most cases kids won’t use everything they learn in math class, but this comes back to the distinction of ‘knowing’ and *knowing* discussed a bit in the book from my last blog post.

*Knowing* is what is expected in schools today, understanding all details of a problem in order to be prepared to tackle it in any unexpected form on a test. Whereas ‘knowing’ is more like knowing about something, to know enough about something to see why it’s necessary, interesting, or beautiful; and to be able to *know* it quickly if ever necessary. *Knowing* is certainly a good thing if you’re a mathematician, where it’s important to not have to look things up when concentrating on work, or to have new insights from intuition; but it is this *knowing* that is turning so many kids off from becoming mathematicians in the first place, so let’s help them ‘know’ math enough to love it, for there’s so much more to math.

As someone who has already accomplished the last part there is yet a dilemma I face that has become apparent while doing this project, fueled by this bit of illustration: do I want to become a mathematician? Obviously the whole of human knowledge is so tremendously vast that any person hoping to acquire it all in one lifetime is beyond a dream, but do I really want to focus so much on *knowing* one small area of math so as to disregard all other areas of math and indeed human knowledge? For the tens of thousands of mathematicians internationally and throughout history there are so few famed greats whose work transcends the rest (but is of course supported and inspired by those in their field), yet I do not believe myself to be so special. I have no confidence in myself to be even a background mathematician, and the idea of fighting for tenure and constantly publishing papers to stay employed has no appeal to me. In fact, I have no desire for a specialty degree at all, and as someone who has gone to a “college preparatory school” their whole life, the notion might even seem blasphemous. But if it means not having a nice job, or house, or a lot of money (and, simultaneously, debt) it does not concern me; my only desire is to learn. I believe myself capable of following the canon of work from each field required to be a well-rounded man, and ‘knowing’ math is enough for me. But I digress. I hope to figure out the answers to my questions before my senior year is over.

I mentioned the “famed greats” and “the canon of work from each field.” Another thing I came to realize while self-teaching is what being educated in a subject really means. For every subject there is a history of prominent events: realizations leading to realizations, discussions to discoveries, etc. And I believe understanding the key questions behind the results, having a full context, is where the best learning takes place. I’m not talking about just history here. I don’t want to be a math historian either. I’m talking about full understanding; not just the loose but exclusive emphasis on computation, memorization, and rough guidelines that plagues general education.

Another section that goes hand-in-hand with full understanding of every subject is its meta-canon, or the philosophy of itself. I especially appreciate the philosophy of math. I believe the love for math lies tangled in its web of philosophic and meta thought, looking down on its surface beauty, and in the most important thing that I have learned: that math is metaphysical—and a full understanding of life requires knowledge of math.

I leave you with this nice video. Feel free to play some inspirational music over it, too.