Ask HN: How do I improve my command of mathematical language?

First of all, sorry if my English sounds off, maybe weird; it's not my first language but I'm striving to improve.

Short story short: I went back to high school in my late 20s and next year I'll graduate. Over the years I went from hating math to really enjoying it, especially calculus, but there's still one thing that keeps bugging me, and that's my command of its language. I have no problem solving most of algebra or calculus problems, but if you asked me to explain what I'm doing I wouldn't be able to tell you, at least not using mathematical constructs/words. It doesn't help that I can't find any resources like you could for any natural language.

When I asked my teacher she said to practice over and over, but that's all I've been doing these years and it didn't do much to improve my oral presentation. So, I'm asking here in the hope that someone who went through the same struggle or understands the mental process very well and knows what it takes to "fix the computation-presentation bridge", could help me or guide me in the right direction, to overcome this obstacle.

Thank y'all for your time.

The issue is here: "I have no problem solving most of algebra or calculus problems, but if you asked me to explain what I'm doing I wouldn't be able to tell you, at least not using mathematical constructs/words." This is slightly unclear; there are two possible problems here from what I can see, and they're totally different problems to have.

Either you cannot do maths, and you're only good at solving repetitive problems of the same genre from school textbooks. Or you can do maths, and you struggle to follow the generally accepted set of notation.

If your problem is the first, you need to explore a wider range of mathematical problems, which will fundamentally require you to think, apply your skills to the problem in various new ways. Maths is a subject where learning to think and learning to solve a specific set of problems are two very different things. Good resources for this are the Art of Problem Solving, and various Olympiad questions. You can also just try to apply your mathematical knowledge to real life examples.

If your problem is the second, I don't know a solution, but this is a far better problem to have than the first. I'd rather have the problem solving ability and use my own set of notation that nobody else understands, than have less problem solving ability and understand the notation. But, in short, that'll just come down to practice, seeing the general notation, and somehow forcing yourself to use it. Alternatively, just try to define your own set of notation at the start of your solutions. It may depend on what kind of professor you have as to how many credits you'll get, though. A good professor will not penalise you that much for making up your own notation, if your solutions are correct, but may try to encourage you to use standard notation (as this is required for any kind of collaborative mathematics).

The problems in Spivak are pretty good I think - they'll show if you can do maths or not.

Some also have answers (and an answer book for the rest), so there's examples of explaining what was done, for harder ones. The explanations are sometimes too concise, but at least it gives some guide for how you can explain your answers.

At a much easier level, Khan Academy videos mostly are explaining how a specific problem was solved - another resource.

I feel like I have some kind of mathematics dyslexia. I can understand all the concepts, but I find formal mathematical notation almost completely incomprehensible. Expressions with all kinds of strange symbols, often variables introduced that are either completely undefined or defined ad hoc locations remote from the usage, integrals and sums with no subscripts / unclear scoping, etc etc. Clearly other people just read these and I even know people who will ignore all the text in a paper and just look for the equations. I wish I could master it because in some areas it is a genuine barrier to me achieving my goals.

yeah I have a similar thing - I’m trying to read a computational geometry textbook (for a code project) and I end up skipping the equations and trying to glean the meaning from the prose... it’s a slow process. There must be a resource out there for decoding unfamiliar equations but I don’t know what it is