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

I was just like you. Here's what I did.

1. Picked up a High School Algebra Book. Read from beginning to end and did all exercises.

2. Repeat #1 for Algebra 2, Statistics, Geometry and Calculus. (Really helpful for learning those topics fast was Khan Academy).

3. Did MIT Opencourseware's Calculus and Linear Algebra Courses w/the books and exercises.

Now, this took me about 2 years maybe you can get it done quicker, you're at a level where you can pretty much pick up any book, I think I picked up Elements of Statistical Learning, and actually start parsing and understanding what the formulas mean.

One thing I always do is tear apart formulas and equations and play with little parts of them to see how the parts interact with one another and behave under specific conditions, this has really helped my understanding of all kinds of concepts from Pearson's R to Softmax.

I think “mathematical maturity” is an important aspect of this discussion. Mathematical maturity is basically the ability to read a paper or textbook without assistance. It takes years to develop, and you still have to be familiar with the topic! For example, I feel comfortable reading statistics papers, but I would be totally lost reading number theory. As others have commented, familiarity with the foundational ideas is just as important as the notation.

So how do you get mathematical maturity? A bachelor’s in math, or equivalent. Meaning, approximately 4 years of focused, ideally guided, practice. I don’t think there are any faster ways.

Edit: Also important to know: most papers are poorly written, so that definitely doesn’t help. It’s especially important early on to identify who the leaders are in a field, and focus on their writings. In statistical Machine Learning, I recommend anything by Trevor Hastie, Rob Tibshirani, Bradley Efron, and Martin Wainwright.

Frankly, I don't think you can without it being specific to the field you're learning. That's why having a symbolic reference is always amazingly helpful in textbooks.

For example, the lowercase sigma symbol is used for a half-dozen different things depending on the field you're working in.

In Machine learning, if you use a logistic function as your activation function you'll use the lowercase sigma symbol to represent the sigmoid variable. However if you're working in Physics, the lowercase sigma symbol is the Stefan-Boltzmann Constant. So any good text or otherwise will explicate what the function symbols represent.

Some algebraic/calculus functions such as sum over set, divisor, sets etc...should be the same, and I haven't been able to learn how to crack that specific question as to generalizing all of those operations that isn't "go back to get a mathematics degree."

[1] https://en.wikipedia.org/wiki/Activation_function

[2] https://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_const...

Not OP, but in my experience experts everywhere have a blind eye to the conventions they are so used to that they end up skipping giving a definition for them them.

>What you shouldn't do is try to self-study by reading a book.

My experience has been that this is exactly how college math works; you pay for self-study. The professor reads directly out of a book (in poor English), or off of pre-made slides provided with the book, for 2-4 hours per week, and then you are left to do the problems from the book on your own time.

Class populations are so large that if everyone had asked clarifying questions, we wouldn't have completed the readings.

If your college experience was different I'm envious of that.

Edit: as a fun side-note, our calc professor was well known for taking up the entire class to draw out a single proof on the chalkboard. As the chalkboard got full, he would incidentally erase his previous writing with his giant belly as he putzed across the room.