I am a PhD student in math beginning to do research. My advisor has given me a paper they want to generalize. It's pretty long with many dense, technical parts, and so, so many typos. The entire paper is about defining/exploring a space, but the definition of the space has obvious typos which make it unclear what the author means. Many definitions are similarly broken. Often the author states something is 'immediate from blah' where blah is a broken definition or a statement that is totally unrelated. I feel like most of my time reading is spent resolving these errors or unhelpful writing.
When I do resolve them and explain to my advisor, they they seem to agree that the paper is gibberish and that what I say sounds right. There is a lot of confusion neither of us can resolve. It's so bad that when I can't understand part of a proof, I start to wonder if it's just wrong.
This paper is not isolated -- the last couple papers I've read have been like this. It's not isolated to my field either -- my peers tell me similar stories about papers with typos that look like key smashing and more. It could be a lack of ability to understand on my part, but from all outside metrics I appear to be understanding what's in front of me. A professor even told a story once in class 'So and so proved this theorem. His PhD thesis was about how blah spaces can't exist, and his first paper was an example of a blah space.'
It's mind blowing to me that published papers/theses can be so broken and impenetrable, or even just false. I would be embarrassed to turn this kind of work in as a thesis. So my question is: how are these papers getting accepted? These are a few explanations I can think of.
- Doing math is just really hard and explaining it is even harder, and most people who can do math don't put a high value on explaining it well.
- No one is checking. Because there is a culture of bad writing and everyone is too busy, the peer review process just doesn't catch this stuff.
- I am just a lowly grad student, still learning how to read papers, and eventually the process will be much smoother and faster so it won't really matter.
Edit: I think a more helpful question would have been this. What can I do as a student to make better progress through papers like this?