I think my project for myself for the next couple of years (probably decade) is to work through the undergraduate sequence in mathematics. My goal is to get to the point where I can read a book on general relativity and on quantum field theory, as well as a few other math-heavy topics. So what I would like to do is:

1. Calculus I, II, III
2. Proofs
3. Linear algebra
4. Ordinary differential equations
5. Abstract algebra
6. Real analysis
7. Partial differential equations
8. Complex analysis

I don’t know where I am going to run out of steam, but if I want to get to general relativity, I will need to do a little more than this, at least some differential geometry. But I don’t know. That’s next level.

The standard sequence starts with calculus. I have taken calculus I & II twice in my life, once in college and once about 15 years ago. I started calculus III in college before temporarily dropping out. So even starting calculus over again is backing up for me. But when I took calculus, I was acutely aware that I wasn’t doing as well as I should have been because my algebra and trigonometry were too weak. So this time I want to make sure those skills are solid before proceeding. At first I decided that I wasn’t even ready for pre-calculus: I needed to go back and work on an algebra book first. The book I got is a college algebra book. Its first group of chapters is a review of intermediate algebra. After working through most of those chapters, I felt like I was too weak in even my basic algebra to proceed with this college algebra material. I could probably proceed and continue to improve basic skills as I went along, but having been burned by inadequate preparation the first time through, I want to make sure I am solid in one skill before moving on to the next. So now I am working through an intermediate algebra book.

It is kind of frustrating that I am moving backwards so quickly. At this rate I am never going to make it back to calculus. At this rate it’s going to take forever to get through calculus. It’s going to be years to get back to where I was thirty years ago. I am desperate to get to something new to me. I remember taking calculus and it just being so mind-blowing. I imagine since I did so little calculus III, it may have a similar effect (I remember the first time I saw a curve rotated about the x axis in the z plane and being, again, mind-blown).

I have spent my entire life wanting to be good at math. When I was a teenager, I wanted to be a physicist. In my early 20s, I wanted to be an economist. But for some reason I convinced myself that I couldn’t hack the math for either of these. Which is weird, because while I was never in the top math class in school, I never struggled with math.

But in the last few years I have decided that math isn’t an innate capacity, or at least requiring some core of innate ability. Well, maybe for like the top one percent of achievers there is some brain difference, but for middling achievement, what I am aiming for, it is a skill, like plumbing or painting: something that you get better at by practice. It is my plan to focus on doing the exercises and grind my way to understanding.

The problem is that I have been living my life at quarter speed. I have always just thought that there will be time later. But I am 50 years old now and there is not time. At this point in my life, one of the limitations on this project is that I am on the downside of my cognitive ability. At some point relatively soon, I am not going to be able to do this. I am spending the last 15 or maybe 20 years where it is still possible doing something I should have done thirty years ago.