Ask HN: How can I learn to read mathematical notation?

I love how there are these two parallel threads going in HNville: (1) COLLEGE SUCKS BURN IT DOWN and (2) "I'd like to learn complex things like machine learning and math that take more than reading 5 blog posts to master, how do I do it"?

Sometimes this place just cracks me up.

I honestly think the answer is pretty simple: go to college. It doesn't have to be expensive. Take a community college course in calculus or undergraduate-level probability. Skip the gen eds and don't worry about the degree if you want to learn something narrow like this.

In any case, just find a mentor. On-the-job if you can, otherwise pay for a class.

What you shouldn't do is try to self-study by reading a book. You can perhaps do this but only if you're smarter than average and more motivated than most. Since you probably aren't, just take a class. Night school, maybe a MOOC. Preferably something heavy on analysis or proofs.

But you should do it with others. Math is a very social discipline, it's good to be able to discuss and have partners to work through things when you get stuck. And if you're like me, you WILL get stuck on things. This stuff is hard.

Another thought: this whole "college is great"/"college is terrible" dichotomy seems to occur people people don't think enough about quality. I think bad colleges are terrible and great ones are fantastic. I don't know any way I'd have learned all the complex topics in math, stats, probability, etc., I did without attending a big 10 engineering school (UIUC in my case)

OP says in the comment that he _went_ to university and didn't pick it up.

There's a long version and a short version. The long version is you have to learn to write mathematics by yourself. Start with an intro course and start deriving theorems by yourself. Do not look at the proofs. At this stage, details are very important and can't be overlooked. You need to be your own critic and keep asking why and how to every single detail and step until you can convince yourself that you would be able to naturally come up with the theorem and proof. Continue doing this to higher level courses. This is how I learned Math since middle school all the way throughout graduate school.

The short version is you have to ask the right questions. Naturally for every theorem or equation, there are 3 big questions:

1) What does the theorem/equation say? What's the intuition behind it?

2) Why is it true?

3) How does one come up with it?

One must ask these questions in the exact order. To understand what the equation really means, you should break it down further to smaller components. What is this variable? What does it represent? What is the intuition behind what it represents? What's the implication when the variable increases, decreases, etc? Do that for every single component in the equation/theorem. One should fully understand the intuition and clearly describe all quantities before trying to look at the equation/theorem as a whole.

To understand why an equation/theorem is true you need to build up a repertoire of theorems related to the quantities of interest. The bigger your repertoire, the easier you can prove or disprove something. The more advanced way is to build up intuition around the quantities of interest then come up with intuitive hypotheses. The hypotheses are often easier to prove/disprove. The process repeats.