John von Neumann once said, "Young man, in mathematics you don't understand things. You just get used to them."
While probably not the originally intended meaning, you can take the quote as saying that, after reading a lot of papers in a given field, you will “get used to it” and recognize recurring patterns and what they mean. This is particularly important as more often than not, part of the math is left out (presumably because it’s too trivial for the authors or the want to fit the page limit). So, part of being able to “read the math” is to infer what’s going on in between.
Many papers, especially im engineering, use a lot of mathematical notation that doesn’t benefit the reader, it’s just there to show off. Often, there are mistakes in there too, because no reviewer typically goes to the trouble of checking every single equation. When reading a paper, don’t get bogged down by all the equations. Read it once or a few times before getting down to that level. Often it’s helpful to read other descriptions of a particular algorithm, for example in a student’s thesis, which contain more detail and contextualize some of the math.
While you may not find this comment particularly helpful, as I’m not pointing to a guide or something, you could take away from it that it takes practice and that one shouldn’t be discouraged when you don’t understand the math in a paper, as I guarantee you there are maths professors that couldn’t make sense of it either.
That is true, unfortunately, in much of the mathematical literature. Way too often authors use the formalized language where the plain language would suffice. This kind of abuse is extremely widespread. It is one thing when a formula is used to represent, say, a complicated integral; it is another when a formula is used to express something just as easily said in a couple of words.
When I first began writing papers I tried to describe using prose. I found that readers were confused and there was much more ambuigity than I anticipated. By using mathematical notation, it becomes a lot less likely that you are misinterpetted and often takes less space. It's kind of like the difference between providing code versus a written description of the algorithm.
My math professors would teach maths under the presumption we knew mathematical notation. I felt I got thrown in the deep in during first-year calculus units but I also now feel strangely adept at reading maths so it had a positive effect.
the other problem is assuming the reader knows nothing, going too deep into the foundations supporting the conclusion.
mathematical knowledge is like scaffolding. a reader has to gradually build up and buttress the lower layers before attempting to move up. skipping steps does no one any favours.
Natural language can be extremely ambiguous though, and while the ambiguity may be resolved easily from context, someone in OP's situation doesn't have that context. The precision mathematical notation can afford (more readily than, say, English) actually helps. But of course, only of one knows the meaning...
I'm in a somewhat similar position to OP, it's extremely rare that I'd find a whole paper accessible, the best way I know is just to get gradually more specific, from a broad undergraduate textbook on 'logic' or whatever other similarly broad area, and hone in on the more specific area of interest. Notation will be introduced, and by the time the last 5% is, 80% will be second nature, and the remaining 15% will be familiar and 'let's see.. I think it was used in this book..'
Thank you for bringing the Neumann's quote. At times I get so bogged down because of these complex mathematical notations. This was particularly frustrating as mathematics is an area where I shine. I started reading between the lines and rewriting those equations in a way I understand.
I'm glad to know that many people resonate with this and I'm not the only one that struggles. Thanks HN!
Many papers, especially im engineering, use a lot of mathematical notation that doesn’t benefit the reader, it’s just there to show off. Often, there are mistakes in there too, because no reviewer typically goes to the trouble of checking every single equation. When reading a paper, don’t get bogged down by all the equations. Read it once or a few times before getting down to that level. Often it’s helpful to read other descriptions of a particular algorithm, for example in a student’s thesis, which contain more detail and contextualize some of the math.
While you may not find this comment particularly helpful, as I’m not pointing to a guide or something, you could take away from it that it takes practice and that one shouldn’t be discouraged when you don’t understand the math in a paper, as I guarantee you there are maths professors that couldn’t make sense of it either.