I have not updated this in several months. I have been still thinking about math sometimes since then, but with a less focused obsession. But I still find it interesting and have not forgotten about it.
I started off with Leonard Wapner's book about the Banach-Tarski paradox, and thought it was very well-written, and that the paradox was pretty decently cool, and that set theory was very cool, and that I wanted to learn more about math.
I looked at some probably-interesting things but could not really understand them with my knowledge at the time, so I looked up what comes next in a typical upper-level math education in the Western world after calculus sequence and differential equations. I started learning about linear algebra by going through the textbook I had been assigned when I took the class for a week, years ago, before dropping out (the pdf is free online, and it seemed as good as any other). I started learning about proofs as well by going through the textbooks that AIM sugggests. The first one I tried did not work for me, but Richard Hammack's Book of Proof pulled me in and I went carefully through the first three chapters of background concepts and started the fourth, on direct proofs. Then I worked on other projects for a while and took a break from new math.
My goal is to continue going through linear algebra, although from the way I have been going through that curriculum so far, I will probably mostly do that when I am in the mood to work through algorithmic problem solving. The type of thinking involved in putting a matrix in row-reduced echelon form. Another goal is to keep going through proofs, and learn more there as a foundation for understanding the available resources on higher level topics. Additionally, through proofs, I am learning about other branches of math that Richard Hammack mentions or uses in examples. So this is a good way to keep the mathematical interest piqued.
Another area of interest is prime numbers. Related to this is the Goldbach conjecture and Riemann hypothesis. From what I have gathered, these and other such topics I find interesting fall under the umbrella of "Number Theory," so that is a third goal and interest.
Also of interest is pi. I am reading, slowly, A History of Pi by Petr Beckmann, and I find it, like The Pea and The Sun, to be conversationally well-written and rather interesting overall. So I am working my way through that, too, and using it to keep myself interested in mathematical concepts and the mechanisms of the universe (or perhaps more to the point, the mechanisms people use to understand the universe).
I find myself again wondering what the point of writing this all down is; or perhaps specifically posting it to a publicly available space. Who besides myself would care what my particular topics of interest are? There is something about accountability, I think. There is also the fact that I have read through a few other similar websites, blogs where people post their thoughts and learnings about math and life, and I find them interesting enough to read through and sometimes follow regularly. So there is something about community, too, I suppose.
Sometimes I find something to be so fascinatingly interesting, and then I found out that there are other people who think so, too; who know even more than me, who have been studying this fascinatingly interesting thing for years, and I am so excited and so full of hope. Or perhaps not hope (hope, too, to some extent), but even more so something else: energy and enthusiasm, relief that there is meaning. Sometimes I find the world to be such a complexly beautiful thing, and I want to shout from the rooftops, "Look! See how beautiful it is! Do you know about this? How could anyone ever want to leave when such complicated forces beyond our understanding form this universe we exist in and such intricate ways of thinking and perceiving have been developed to try to understand them?" Maybe that is why I write this, too. To try to keep this feeling so that I can find it again later, to try to send this feeling back out into the world.
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