Recently, a student visited me a couple times asking how to self-study mathematics. In particular, they want to self-study machine-learning by reading through a book on their own. My answer is:
Don’t do this. It will probably be really frustrating.
The reason behind this is that nobody1 really reads through textbooks alone to learn anything. It is a probably mis-use of a textbook to do that. Textbooks are designed to facilitate teaching courses with lectures, homeworks, term-tests, etc. Of course, there are a few exceptions; there are some rare books designed primarily for self-study.
A book won’t mind if we mis-use it. There’s no harm to the book if you try to read it cover to cover. The real harm will be to yourself. It will be confusing, boring, and time-consuming. Most people give up on reading hard things pretty quickly. So what should you instead?
Start a blog, make a website, reading group, YouTube channel, or seminar. Audit a course. Do something socially that gets you involved in the field. Do something which creates a positive benefit for the world, and yourself.
Why do I think this is will go better? If you create some kind of social network around this material, then you will get two benefits: First, you’ll engage socially. Humans are social animals. You’ll have a reason to be doing this. Second, you’ll have some kind of support network. If the going gets tough, you’ll have some people to work with.
For this particular student, I want to point out that machine-learning and data science can be heavily applied. If you want to learn this stuff, do it. That is to say, come up with some reasonable problem and actually attempt to solve it. For example, off the top of my head, it would be great to have an application that used machine-learning to make an optimal meal plan for my family. I’d input my grocery store receipts, and it would output a meal plan. You should really pick your own problem to work on. Your self-study will make a lot more sense if you’re working towards something.
If you really want to go the reading route, then Paul Halmos has a great piece of advice: read the first ten pages or so of a bunch of a books. Here are some great guides to reading for depth:
Here are a couple “expository” blogs that I’ve admired over the years:
While putting this post together, I found this Youtube video:
For example, I’ve never read a whole mathematics textbook cover to cover. I can’t think of any of my friends who have, either. ↩︎
Published: Apr 7, 2025 @ 09:49.
Last Modified: Apr 10, 2025 @ 08:48.
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