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

I'm still learning mathematics (I don't think the learning phase ends). I used to worry about "reading" notation. I think what's changed is that I have gotten used to not understanding unfamiliar notation. And I realize that if the notation appears unfamiliar, the mathematics may also be unfamiliar. Being able to "grok" notated mathematics is much more about understanding the mathematics than about being able to read notation.

Therefore I would be cautious about jumping to the conclusion that your problem is as simple as "simply cannot read" (unfamiliar notation). Maybe that's true in some cases, but it's also likely that the notation stands in as a kind of shorthand for elaborate, maybe even arcane, concepts that you don't understand very well (unfamiliar mathematics). Working out which concepts/theories you need to study may be a better place to start than worrying about the notation per-se. Eventually you'll drill down to some level where you do understand the notation, or it is explained in a way that you can understand. Also consider that learning to read and write go hand in hand -- reading a notation gets much easier once you start writing your own sentences in the same notation (e.g. do exercises, learn to write proofs.)

With few exceptions, don't expect the notation in one area to be useful, or to mean the same thing, in another area. However there are a couple of generally useful things to know: (1) Greek letter names (so you can recognize, write and pronounce them without being confused) -- just learn the ones that show up in your reading, and (2) set theory notation plus some basic set theory (read Halmos' Naive Set Theory book up to the point that it becomes confusing).

Others have mentioned it, but be aware that it is common for one field to have multiple notation conventions. Often the notations originate from seminal papers or widely used books. Different authors frequently use slightly different notation, even within the same field, and sometimes a single paper may contain multiple contradictory notations. I've even had lecturers who switch notation half way through a lecture. If you're studying multiple texts you may want to translate all of the key theory into one consistent notation -- but at a minimum you need to be able to keep track of the correspondence between the different notations as you're reading.

Just because you choose to believe you need to be fed your information doesn't mean others do. I've tutored people carrying the thoughts you're expressing ("I need someone to teach me this because I'm not smart enough to learn it on my own"). The quickest way to success with them was shattering that myth. I did it by talking to them about their feelings/beliefs and helping them figure out practices for changing their minds about themselves. Here's a great paper called The Debugging Mindset on cultivating a growth oriented perspective an why it's important: https://queue.acm.org/detail.cfm?id=3068754

I hope you can develop a more empowered perspective of yourself and others though reading it.

I've taken reasonably advanced math courses (I was, for a time, a math major), and I have a great deal of difficulty with machine learning papers. They often reference domain-specific formulas that are prerequisites, sometimes without naming them, and rarely does a paper actually define every symbol used in a formula (in fact, I don't think I've ever seen a paper do this - it's usually none, and they only define a few elements of the notation). The worst part is that they'll use a known formula, but change the notation slightly without explaining why.

These are bad academic habits. If you're using a formula with a dozen variables - at least state what they are, as well as any more unusual or overloaded notation, subscripts, etc. If you're using a formula from elsewhere, it's better to restate what these symbols mean in your paper, rather than send the reader off on a hunt. Be clear, be explicit, leave no doubt. You don't have to explain all of probability theory, but it takes only a line or two to vastly improve the readability of your paper.

The real answer.

Other people have listed great books and resources.

What I don't see, however, is to ask a friend. Find someone who is familiar with the notation, if not the material, and ask questions. You'll likely get a more clear answer.