Relearning Math at 38

(with a little help)

I’ve always thought I was good at math, in fact being good at math was part of my mental self-image! But I recently found out I wasn’t as good as I thought, as at the very least my math education was woefully incomplete and lacked certain fundamentals.

Enter Math Academy. I discovered the site through Kris Abdelmessih’s writing on it (and I highly recommend Kris’ writing, I feel anxious even writing about MathAcademy because Kris has already done some great writeups on it). Math Academy is a paid math education site that uses AI and principles of adaptive/accelerated learning to teach math mastery. Underpinning the site are some strong values/opinions are how math learning should be structured. I love the writing from Justin Skycak (chief quant at MathAcademy) on the theories of learning which the site is centered around. Even after many years of education, I was not familiar with several of these ideas! And did not find all of them intuitive (see here on challenge problems and their value). 

In a nutshell the site figures out where you are on a broad set of topics, and aims to give you bite sized amounts of material - along with problems you need to solve, at the edge of your comfort/knowledge zone. Additionally it throws in systemic reviews of past concepts to reinforce the material (prevent forgetting). There is an incredible amount of detail in Justin’s writing as well as an entire free book! on the principles behind the site. I’ve spent 40+ hours on the math exercises part of the site and another handful of hours reading the educational theory which I find fascinating.

Here’s a screenshot where I can brag about my excellent XP gain this week (1 XP ~= 1 minute of effort - I am recovering from a full Achilles tendon tear and doing a lot of sitting :( which is one reason for the high score)

My experience

I began by taking the evaluation test to see where I was. Now I like math, I’m pretty good at it, I crushed exams like SAT Math and BC Calc in high school, and using math as a tool was central to my career. However this evaluation showed my current knowledge frontier was jagged. A few topics I used recently are fine, but I had forgotten most details of topics like trig and geometry, even at a high school level.

Ok so I finished the diagnostic and began the material. Most of it came back very quickly and is served in small chunks. But I found two curious things as I went along, one - my mental foundations were becoming sturdier… concepts that I vaguely remembered became snappy, I could feel the neurons firing differently. Second - some of these (foundational) math topics I had never learned! Maybe I had been out that day in high school and I didn’t need it to pass the test. But this didn’t happen once, I was finding several new basic math concepts (law of cosines for example I guess I could derive but never explicitly learned), that I didn’t know I didn’t know!

[It’s easy to spot inconsistent thinking and decision biases in others. Shaking your head at the conspiracy theorist, mystical thinker etc. But I’ve often wondered “what in my own mind is faulty? What do I believe that just isn’t so?”. Maybe a friend who deeply knows me could tell me, but it’s almost impossible to see for myself. Going through these exercises and realizing there were simple things I didn’t know, in an area I thought I was great in, was a small dose of the feeling of filling holes in my brain. In some ways this can be terrifying (if one day you wake up and realize your religious practice was in reality a cult), but to me it felt great, like I was upgrading my CPU at the cost of a couple hours of math problems.]

I plan on continuing Math Academy (today I started Math Foundations III and it estimates completion in mid Jan 2025). Following that there’s a machine learning course I’ll take next. Now technically I passed multivariate calc, linear algebra, and differential equations in college…. however going back over this material, I realized I never gained mastery in these topics, and worse than that it was due to more fundamental concepts not being mastered.

Sometimes friends and former colleagues ask me, “so what are you doing with your life,” and what does it have to do with relearning high school and college mathematics? The truth is I don’t know the destination but if my life is as a captain of a ship, I can feel which way the wind is blowing.

“The River” and decision-making

I recently finished Nate Silver’s book “On the Edge,” where he describes a diverse community of gamblers he calls “The River.” I firmly belong in this community and spent my career there (as a market-maker / quant trader). But as that chapter in my life has now ended and I look to explore other pastures, one way or another I can’t leave “The River.” It’s how I think. I picture it more as a web or a city with rings of neighborhoods spreading from the center. With pure gambling type neighborhoods such as options trading, poker, advantage gambling, sports betting at the dense urban core, but stretching outwards are areas related to the core ideas of probability and rationality, but having a more diverse set of players / ideas. These “suburban” ideas include longer term investing, AI safety, effective altruism, and many more.

Reading through the theory behind Math Academy, there’s a link here too. Choosing your HS course load, college major, which college is another form of “decision-making with incomplete information,” as I would call it - gambling. Part exploration, part gauntlet/contest, with real costs to choosing incorrectly, and uncertainty both in the material, your own ability, and the rewards at every step.

What MathAcademy.com is - is a way to dramatically accelerate the pace of your math learning and strength of your fundamentals, with a relatively low cost. The value of the education is going to be different for every person (and the cost in that each individual’s ability varies), but fundamental math skills I would argue have a high payoff compared to other skills in unlocking future opportunities.

I wish I had tried to quantify (or even deeply think about) these tradeoffs when I was in HS / college. I had picked ECE (Electrical and Computer Engineering) because 1) I had gotten an engineering scholarship which mandated one of several majors or I lose a significant amount of $, and 2) had thought “hey, microchips look cool and I’d like to know how they work.”

So why would I spend hours doing math problems on this website? There is a real cost in terms of time and effort. It’s unclear if there will be any financial reward in it for me (depends on what I do next I suppose). Mostly because many of the things I enjoy involve math, and as I feel the foundations of my math ability getting stronger, I can see the limits of my ability pushing further out… and I really like that feeling.

If you try out math academy let me know about your experience. I’m also curious if there are similar courses/tools in other domains (gah I wish there was one for writing).