Here’s a message I sent to a math/programming-genius friend of mine who’s helping me stay motivated while I study math/programming:
I’ve been procrastinating about sending you an update, so this’ll be a partial list of things I’ve been thinking about:
1. If you find YouTube ads annoying, Google “adblockplus”. It installs in 1 click for Chrome and disables ALL ads. It’s amazing, and I can’t believe I’ve been dealing with ads for years when they’re so easy to get rid of.
2. Check out “Dimmer” for dimming your screen, if that’s annoying and you don’t already have a solution.
3. Check out AutoHotkey for Windows (it lets you move the mouse around, click, press key combinations). It’s great as a way of creating a macro that works across different programs, eg you want to copy something from Excel, switch to Chrome, and paste it in Google Search.
4. I started working on a Venn Diagram Teacher for my LSAT students but lost interest when it came time to make a menu:
5. I found these cool explanations of how you can use linear algebra to analyze Chutes & Ladders and Candyland:
6. I’ve started a serious effort to try to be active in the AoPS community, use their free Alcumus service, and do a page from the AoPS Vol. 1 book every day. I’ve started with the topics I found most interesting (probability, counting, proofs), and I’m doing the practice problems at the end of each chapter every 2-3 days so that I get spaced-out practice.
6a. I helped Richard Rusczyk solve a problem he was having by using AutoHotkey, he responded “Wow; thanks. You really crushed that.”:http://www.artofproblemsolving.com/Forum/viewtopic.php?f=133&t=542039
7. I spent a lot of time learning about AoPS, MATHCOUNTS, the AMCs, USAMO, and the IMO. I honestly had only the vaguest conception of what any of those things were when you would talk about them during high school. I watched the documentary “Hard Problems” on YouTube:
8. I’ve continued to make slow-and-steady progress studying for a perfect score on the SAT. I’m going through “Dr. John Chung’s SAT Math”, making flashcards of every problem that I i) get wrong, ii) find hard, or iii) solved in a different way than the solution given in the book. I can tell that I’m slowly getting better.
9. I highly, highly recommend that you check out Anki. It has really been amazing at helping me learn Spanish, Russian, German, American Sign Language, math, programming, people’s names, the main ideas from books, etc. I know you said that you found spaced repetition to not be efficient without understanding WHY some mathematical thing was true (eg constantly rereading books), but I think that you can incorporate your idea of picking-stuff-apart into Anki. For example, you can add a card that says “This theorem says that these two things are necessary. Why is the first thing necessary? What happens if you don’t have it?” and then on the back of the card it can be the lesson that you learned from working it out. Here’s a useful reference of how to make effective cards:http://www.supermemo.com/articles/20rules.htm
10. I’ve been slowly making Anki flashcards for Teach Yourself Mathematical Groups, Introductory Graph Theory, and some other things. My goal is to make the cards work so well that a person can learn the material without reading the book. I’m starting to suspect that books are going to become outdated technology once people figure out how to use computers to help people learn faster. You can find my flashcards here: https://github.com/NathanWailes/Math-Flashcards
11. The more math I do, the more I’m enjoying it for its own sake.
12. I highly, highly recommend that you learn about the mathematicians Ed Thorp and Jim Simons if you don’t already know about them.
Jim Simons talking about his career:
Very, very interesting articles/chapters (re: Jim Thorp, Michael Dell, etc.):
13. After I took the LSAT I wrote up a lengthy guide on how I did it, which is now considered by many to be one of the best out there:http://www.top-law-schools.com/forums/viewtopic.php?f=6&t=120471
Would you consider writing up a short guide on how you got to where you are? I remember asking you about this in the past but I still only have a vague idea of what your path was (all I remember is you saying something like, “I was doing math on my own when I was like 4”). I’d be interested in things like, Did your parents read to you when you were growing up? Did you participate in MATHCOUNTS? What books did you use when you were in elementary / middle school? Were you in math clubs in elementary / middle school? What was the exact chronology of your learning to program? Was there a club at your elementary/middle school for programming? Did you start learning once you got to BCA, or did you know how to do it beforehand? Basically, I’m interested in having a very nitty-gritty understanding of how you got to be so good.