Not an answer to your question, just an extended quote from the late Fields medalist Bill Thurston from his classic essay On proof and progress which seemed relevant:
Mathematicians have developed habits of communication that are often dysfunctional. Organizers of colloquium talks everywhere exhort speakers to explain things in elementary terms. Nonetheless, most of the audience at an average colloquium talk gets little of value from it. Perhaps they are lost within the first 5 minutes, yet sit silently through the remaining 55 minutes. Or perhaps they quickly lose interest because the speaker plunges into technical details without presenting any reason to investigate them. At the end of the talk, the few mathematicians who are close to the field of the speaker ask a question or two to avoid embarrassment.
… Outsiders are amazed at this phenomenon, but within the mathematical community, we dismiss it with shrugs. …
Mathematical knowledge can be transmitted amazingly fast within a subfield. When a significant theorem is proved, it often (but not always) happens that the solution can be communicated in a matter of minutes from one person to another within the subfield. The same proof would be communicated and generally understood in an hour talk to members of the subfield. It would be the subject of a 15- or 20-page paper, which could be read and understood in a few hours or perhaps days by members of the subfield.
Why is there such a big expansion from the informal discussion to the talk to the paper? One-on-one, people use wide channels of communication that go far beyond formal mathematical language. They use gestures, they draw pictures and diagrams, they make sound effects and use body language. Communication is more likely to be two-way, so that people can concentrate on what needs the most attention. With these channels of communication, they are in a much better position to convey what’s going on, not just in their logical and linguistic facilities, but in their other mental facilities as well.
In talks, people are more inhibited and more formal. Mathematical audiences are often not very good at asking the questions that are on most people’s minds, and speakers often have an unrealistic preset outline that inhibits them from addressing questions even when they are asked. In papers, people are still more formal. Writers translate their ideas into symbols and logic, and readers try to translate back.
Why is there such a discrepancy between communication within a subfield and communication outside of subfields, not to mention communication outside mathematics?
Mathematics in some sense has a common language: a language of symbols, technical definitions, computations, and logic. This language efficiently conveys some, but not all, modes of mathematical thinking. Mathematicians learn to translate certain things almost unconsciously from one mental mode to the other, so that some statements quickly become clear. Different mathematicians study papers in different ways, but when I read a mathematical paper in a field in which I’m conversant, I concentrate on the thoughts that are between the lines. I might look over several paragraphs or strings of equations and think to myself “Oh yeah, they’re putting in enough rigamarole to carry such-and-such idea.” When the idea is clear, the formal setup is usually unnecessary and redundant—I often feel that I could write it out myself more easily than figuring out what the authors actually wrote. It’s like a new toaster that comes with a 16-page manual. If you already understand toasters and if the toaster looks like previous toasters you’ve encountered, you might just plug it in and see if it works, rather than first reading all the details in the manual.
People familiar with ways of doing things in a subfield recognize various patterns of statements or formulas as idioms or circumlocution for certain concepts or mental images. But to people not already familiar with what’s going on the same patterns are not very illuminating; they are often even misleading. The language is not alive except to those who use it.
Okay, I liked that passage but maybe it wasn’t very useful. Ravi Vakil’s advice to potential PhD students attending talks seems more useful, especially the last bullet:
At the end of the talk, you should try to answer the questions: What question(s) is the speaker trying to answer? Why should we care about them? What flavor of results has the speaker proved? Do I have a small example of the phenonenon under discussion? You can even scribble down these questions at the start of the talk, and jot down answers to them during the talk.
Try to extract three words from the talk (no matter how tangentially related to the subject at hand) that you want to know the definition of. Then after the talk, ask me what they mean. …
New version of the previous jot: try the “three things” exercise.
See if you can get one lesson from the talk (broadly interpreted).
Try to ask one question at as many seminars as possible, either during the talk, or privately afterwards. The act of trying to formulating an interesting question (for you, not the speaker!) is a worthwhile exercise, and can focus the mind.
Not an answer to your question, just an extended quote from the late Fields medalist Bill Thurston from his classic essay On proof and progress which seemed relevant:
Okay, I liked that passage but maybe it wasn’t very useful. Ravi Vakil’s advice to potential PhD students attending talks seems more useful, especially the last bullet: