(I wish to remain anonymous, so I've omitted many details here. If those details make this question unanswerable, please don't hesitate to vote it down or close it.)

I've been a PhD student in mathematics for about two years. Whenever I am at a conference, summer school, or a small seminar talk in our university, I usually don't understand anything about the talk after the first two minutes. Sometimes the speaker goes quickly through some basic concepts about group theory, finite fields, or similar, that I'm able to follow because I know the stuff already. But when the new stuff starts, most of the time I get so lost that I can't even answer the simple question "What was the talk about?" when my friends ask. So I just sit there with an open notebook, and after the first few minutes of each talk, I start scribbling some unrelated things to kill time before the next talk. If I see an interesting formula or similar on the slides, even if I don't know what the speaker is talking about, I sometimes try to see if I can figure out what that formula means, just because simple mathematics is still fun - what I do still does not help me understand the topic of the talk.

The problem might be partly about being able to focus, but I guess it's mostly about the actual scientific content. When taking courses as an undergrad, I never had problems of this magnitude while attending lectures because I had time and material for studying the topic before and after the lectures, and the lecturers had a decent estimate of what the students know before the lecture.

Do you have similar experience? Is there something I can do to actually benefit from listening to conference presentations? I hope this is not the impostor syndrome - if everyone in the audience feels like this, conferences are horrible waste of money, time, and natural resources.

I came up with a few ideas but they don't seem practical.

  • "You're not really supposed to understand anything as a PhD student. Just sit there and wait for a familiar term, theorem, concept, whatever to appear. Conference by conference, talk by talk, you'll probably encounter more and familiar stuff, and before you know it, you don't have this problem any more." If I had to decide, I'd never fund a learning process this slow. Or probably it is much quicker than I can imagine.

  • "Go to conferences with topics closer to your research." Well, they don't exist, unless I organize a conference about my research. And the point of going to conferences is to learn about things in your field that are not exactly your research (of course in addition to telling others about your research).

  • "When the conference schedule is published, pick one interesting presentation title for each day and try to learn something about that topic before conference." It might take a few days of focused study for each talk, so some weeks before the conference. I guess that time would be better used doing research.

  • Are you saying conferences don't exist in your research area? Just at your university or anywhere in the world? If it's the former, you need to change your research area. – Kimball Dec 13 '14 at 2:06
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    Anyway, yes, everyone has this experience, and it's a slow process with little noticable progression. 2nd year in your PhD studies is still early. Be patient. Try to hang on to little victories, and go to student seminars. Focus on main ideas and think about specific examples when you can't follow the details (most talks). Sometimes you may not follow most of a talk, but thinking about a particular comment the speaker makes (or even your misunderstanding of this comment) can be very fruitful and make your time there not wasted. – Kimball Dec 13 '14 at 2:15
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    @Kimball I'm saying that conferences that are closer to my research area than those I've been to don't exist. – user26497 Dec 13 '14 at 10:57
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    Don't underestimate how bad the presenting abilities of some people are. They can turn anything into an incomprehensible mess. Unfortunately, many programs don't put any good effort in improving this. – Davidmh Dec 13 '14 at 21:09

It's not your fault if you don't understand a talk

Unfortunately, many speakers at scientific conferences do a poor job. Most speakers I've seen talk more for themselves than for an actual audience. Unwittingly, they focus more on exhibiting knowledge than on being actually helpful towards the people sitting in front of them.

This mostly happens because people don't know. They see bad examples, which they assume must be good because everybody does it and just do what other people do.

So if you did not understand, don't blame yourself. It's the speaker's job to make you understand something. It's quite a paradox that many speakers thank the audience for their attention (!) after a talk—as if the audience did them a favor by paying attention. Instead, good speakers should be thanked by the audience, because they made things understandable.

Become a better presenter yourself

What I recommend to understand other's presentations better is to start giving better presentations yourself. Effective scientific communication cannot be explained in a simple post, but here are some basic principles:

  • Before starting to introduce yourself or reading the title of your talk (which is unnecessary anyway), draw the audience's attention. Explain to them in a way they can relate to why your problem domain is relevant.
  • Then, explain the problem you are addressing (and why it is a problem).
  • Next, immediately state your conclusion. Don't make your presentation a cliffhanger. Tell people the main point upfront; this helps them (decide to) focus on the remainder of the presentation.
  • Continue with a preview of your main points that support the conclusion. This is a mental map for the rest of your talk.
  • Elaborate on your points as necessary.
  • Close the story by putting your points and the conclusion into perspective.

Many speakers fail to do one of the points above; especially postponing the conclusion towards the end is a common mistake that makes it hard for the audience to follow.

Why should you do this with your own talks?

  1. You become part of the solution. Other PhD students will now finally see a presentation they understand.

  2. You will inspire people to give better talks, which you will understand more easily.

  3. Doing the exercise for your own material, will eventually help you do it for others. If you see a poorly structured presentation, you will mentally start rearranging it into a better talk—helping you finally understand what others do more clearly.

Why is the above presentation structure relevant?

By stating the conclusion first, you give people a mental map. If they get lost during elaboration (like you often do), it's not a disaster: they know the most important thing already. Furthermore, the preview will help them get back on track if they get lost during one of the subpoints.

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    This. Many presenters are more interested in sounding "learned" than in "teaching" - reaching out to the audience and bringing them along on the journey of discovery of new and exciting knowledge. "Doctor" means "teacher" but many people with that title have forgotten. Truly great scientists (Richard Feynman always comes to mind) understand their subject so well, they can make it seem easy. Anyone who can't, probably doesn't understand it terribly well themselves. OK - that is an unfair generalization. Still, the advice in this answer is very good. "Become the solution". – Floris Dec 14 '14 at 0:39
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    "It's the speaker's job to make you understand something" I thought the speaker's job is to make their target audience understand, not everybody. – user26497 Dec 14 '14 at 9:31
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    @user26497 Well, if you're in the audience… you seem like a pretty obvious target :-) The target audience consists of the people who are present. It's very ineffective (and impolite) to target your message only to a part of those in the room. Your message should be broad enough to be understood by everybody in there—after all, people or their institutions have paid a lot to attend. – Ruben Verborgh Dec 14 '14 at 10:20
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    Conference talks are not tutorials. You cannot explain a specific research area in 20 minutes. – Alexandros Dec 15 '14 at 12:41
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    @Alexandros Of course you can—that's the whole point of a talk at a scientific conference. You explain the progress you made in a specific research area. – Ruben Verborgh Dec 15 '14 at 16:35

In brief: conscientious study and engagement with mathematics, perhaps more broadly than one imagines one's specialty requires, eventually makes most conference talks intelligible. The process takes some years, to say the least. At the same time, many conference talks, even the better-quality ones, are very specialized, maybe not of terribly great interest even to the immediate specialists, but are "novel" in a sense that makes them publishable and thus evidence (to deans and department heads and funding agencies) that one is doing one's job. But their extreme particularness is easy to misunderstand, if one is hoping for persuasive, enlightening reports, rather than CV padding.

And, almost surely, the much-less-senior people in the room, and many of the more-senior, have no real idea what's going on, almost all the time. The chief trick of relatively-senior people is to know that what they're missing is not terribly valuable, to say the least, except as CV padding for the speaker.

At the same time, trying to stay engaged, to become accustomed to a great variety of terminology and apparent goals, is a very good enterprise. For one thing, many "programmes" of course inflate their own importance enormously, whatever their actual, perhaps great, importance may be. In particular, they are presented in a fashion so as to be impressive, rather than "easy", all the more insidiously when the presentation pretends to give a shortcut, but doesn't really quite do so. But/and, especially in the face of hype, mere acclimatization to the buzz-words is psychologically reassuring, and eventually one will notice the repetition, and realize what the game is.

That is, for example, an array of ideas and definitions and notation that is impressive and baffling the first 5 or 10 times is much less so around 20th or 30th, especially when one notices that the scary/impressive/baffling part is 95% of all the talks in a given genre, and that the new stuff is small and innocent by comparison.

And, somewhat more subtly, by paying attention, one can eventually discover the discrepancy between the impressive hype and "how it's done in practice".

But there're few "textbook-style" approaches to reaching any good level of sophistication, for various understandable-but-also-complicated human-nature-based reasons.

In summary: (1) don't presume (impostor syndrome...) that everyone else is understanding, although a few might be, and the more senior people have learned to not worry about it. (2) Don't presume that what you're not understanding is incredibly valuable, magical stuff. Probably is not. (3) Do try to make yourself stay engaged, so that your brain can process things a bit, and not be so baffled next time you hear essentially the same things again... or maybe 5-10 times later.

  • I've read paragraphs 3-6 five to ten times now, and still fail to get the point. Are you saying that I should use my processing power to actively seek for signs that certain speakers present their research in a "wannabe-impressive" way? – user26497 Dec 14 '14 at 9:52
  • No, I'd not recommend bothering to "see" that people are (perhaps subliminally) trying to be impressive, rather than explanatory, because it is the style, and should be taken for granted. So make this a general assumption on your part... but that doesn't preclude the chance that there is some useful content, only that that chance is not great. In fact, one of the genuine "practice"'s for a listener is to become acclimated to all the standard set-up stuff, which is completely routine, but which might be incomprehensible to a novice who's not heard it a zillion times before. – paul garrett Dec 14 '14 at 13:26
  • What does "bother to see" mean? What is "because it is the style" - the fact that I shouldn't bother to see or the fact that people are trying to be impressive? What is "this" in "So make this a general assumption on your part"? How are the parts of your comment that are separated by "In fact" related to each other? – user26497 Dec 14 '14 at 20:04
  • That is, I'd recommend not trying to see subtle signs that people are trying to present "new" work in a maximally impressive fashion. Just assume that this is what people do. Instead, use the terse presentation of standard set-up formalism as a rehearsal for comfort with it (regardless of the purported "new result"). Familiarity may breed comfort. – paul garrett Dec 14 '14 at 20:19

The standard conference talk format is simply too short to give a presentation that can be thoroughly understood at a deep technical level. As such, I generally see people falling into one of two modes for conference talks:

  1. Attempt to present everything and make a horrible unintelligible mess that nobody can follow. This is especially true for mathematical talks, where few people can actually digest a complex set of symbolic manipulations in the minute or two that a slide is shown, let alone do it while their linguistic centers are being jammed by the speaker talking.
  2. Treat the talk as an advertisement for the associated paper(s), presenting a lot of intuition and motivation, but omitting most of the technical details.

When I am listening to a dense mathematical talk, I simply do not try to follow the math at all. I look at the motivation, I look at the results, and I look at any intuitions the person has presented. If it seems interesting, then afterwards I will go and read the paper to actually understand the material.

If the person doesn't give a motivation or concrete results... I'm not going to bother to try to understand.

  • I'm thoroughly in camp 2. I really dislike approach 1. At the same time after 2 years in you really should start getting at least the gist of what the paper is about. As an exercise, try reading (and comprehending) the papers independently of the talks. – Paul de Vrieze Dec 14 '14 at 22:24
  • Why is this upvoted? This answer contains some rant about bad speakers and a short list of what one person who is able to understand parts of the talk wants to hear. What is relevant to the question? – user26497 Dec 16 '14 at 21:51

You are definitely not alone in not understanding most of the presentations at a conference. Especially if you're new to a field, you tend to be very much focused on your particular research, and you don't have a wider view just yet. This is especially true if your work is highly specialized (and therefore is just a small subset of the material covered in a conference).

Additionally, most speakers are there to present their work and latest results, not to give an introduction to the field. Especially in smaller fields, you see the same faces at each conference, so the speakers will tend to focus on the latest and greatest rather than making a lengthy introduction for newcomers. The fact that unless you're a keynote speaker you probably only have around 20 minutes to speak further reinforces the issue. Every minute spent on the introduction is a minute less for the work you've actually done (as introductions typically tend to consist mostly of literature research and old results).

The understanding of conference talks will improve with time as you learn more about the wider field and the work of the conference-regulars. In the mean time, if you want to speed up the process you can go and talk to one or more presenters after their presentation and ask them to fill in the blanks. Almost every researcher will be happy to explain their work to a colleague from an adjacent field, because colleagues tend to have a sufficient level of thinking and plenty of general background knowledge (compared to a layman) to allow the researcher to quickly get to a decent level of conversation.

  • "you can go and talk to one or more presenters after their presentation and ask them to fill in the blanks" The blanks being everything in their research, I think they just explained them to colleagues who in their opinion have "sufficient level of thinking and plenty of general background knowledge" in their presentation. – user26497 Dec 14 '14 at 9:36

My personal attitude to conference talks is that I attend them for those 10 % to 40 % that I either understand since I am very familiar with the topic or that are not utterly horrible. I have found many people, including experienced scientists agree with me. As those numbers heavily depend on the field and scope of the conference (the conferences I attended range from medicine to applied mathematics) and given my experience with talks going in that direction, I find it easy to belief that conferences on pure mathematics have an even lower turnout rate. And yes, this is sad and mainly due to bad presenting skills.

Also, at least in my field, it’s quite common for senior researchers (and everybody else) to plan to use half of the time alloted to talks at conferences for other activities such as planning and discussing collaborations, sleeping, touristic activities, preparing their own talks or doing regular work. I would wager that the main thing that experience gives you is the capability to better predict which talks are a waste of time rather than understanding more talks.

So, as long as you understand some of the talks, this may be perfectly normal. And even if you don’t, this is not necessarily something to worry about: People approach and learn about new stuff in different ways. For example, if you prefer assessing new mathematics in small steps but with understanding these steps rather thoroughly, conferences may just not be made for you. (I once heard about a theory that there are two general ways to understand mathematics and similar, but I cannot find it right now.) So, if you do well with understanding papers and similar (still keeping in mind the impostor syndrome), I would not see any reasons to worry.

At the end of this answer I will try to give some advise on what you can do to understand a larger part of the talks at conferences and seminars (and this advice will be fairly specific to mathematics). But first, I would like to mention some things that influence how much of the talk you can reasonably be expected to understand. This is both because it is useful to have a good idea of this to see if you are doing enough to understand talks, but also because some of the advise is related to these points.

Factors that determine how much you should understand:

1. The topic of the talk.
This one should seem obvious, but the closer the topic is to your own specialty, the more you should understand.

2. The purpose of the talk.
There are various types of talks, with various purposes. The most common talk is the "by experts for experts" talk, where the purpose is to explain the speakers latest research for others who do work in the same or related areas (most seminars and conference talks are of this type). This type of talk generally sets a fairly high bar for the prerequisites needed to understand the talk, since usually the speaker will have at most an hour (often only 45 minutes), and they want to actually present their own research rather than just give an introduction to a topic a large part of the audience will already be fully familiar with.

In the other end of the spectrum are the talks specifically aimed at students, which generally do not present any new research but gives an introduction to some topic. Foe these, one should be able to understand most of the talk as long as it is not a topic too far from ones own specialty (note that these should not be confused with seminars or conference talks given by PhD students or early postdocs, which can often be even harder to follow since the new results obtained by people early in their career are often of a much more technical nature than for those with more experience).

3. How far you are in your studies.
Again a fairly obvious one, but the earlier you are in your studies (or your academic career), the less you should expect to understand of any give talk.

4. The speaker.
This has already been mentioned by others, but it bears being reiterated: There are some really awful speakers out there. If the talk is given by one of them, even those who are intimately familiar with the topic (or even the results presented) will not understand the talk.
On the other hand, there are also some amazing speakers out there who can make you understand a talk on a topic you really should not have been able to.

Figuring out where on this spectrum the speaker lies can be tough, but often one can tell by trying to get a feel for how much attention those in the room, who ought to understand the talk, are paying. If they seem to lose interest (even though the talk does not seem to be about something elementary), then probably the speaker is not doing a good job.

What can you do?

So, what can you do to understand as much as possible of a talk, relative to what you ought to understand, given the above? These will be some generic pieces of advise on how to get the most of a conference (I will mention single-talk seminars at the end).

Before the conference, make sure you get abstracts for all the talks (if possible). From these, single out a reasonable number of talks that seem the most interesting, or where you know the speaker tends to be really good. Look more closely at these abstracts, and do some reading prior to the talks, but not by necessarily looking at the relevant papers (unless the talk is on a topic very close to your own). Instead, you should look up all those terms in the abstract you are not familiar with (or which you are not familiar with in the context). This will give you a better idea of what the talk is about.
Next, see if you can find some of the main results about the objects mentioned in the abstract (often one gets a better understanding of an object if one known the "rules" it obeys rather than just knowing the definition). It can also be good to find some of the main conjectures about these objects, since this gives an idea of what sort of questions are considered the most interesting (not because it is likely that the talk will present a proof of such a conjecture, though it can happen, as I have experienced myself).

Further, one of the things that often causes a lack of understanding of a talk at a conference is simply being tired from seeing too many talks. To alleviate this as much as possible, I suggest you bring something to the talks that you can entertain yourself with in a non-obvious way once you get to a point in the talk where you have no chance of understanding more.
This might sound a bit rude to the speaker, but this is why I mentioned that it should be non-obvious. It should preferably be such that if the speaker looks at you, you will just seem to be taking notes (unless you are way at the front, you can often have your phone lying in front of you without the speaker being able to see this for example).

Along with the above it should be mentioned that it can also be quite alright to not see every single talk at a conference (though you should probably check with your adviser what the culture is at the specific conference to be sure). Which talks to skip can then be based on which abstracts seem to suggest that you will understand the least (or if you happen to know that some specific speaker always gives terrible talks, you can also skip that).

As a final note on this, I would advise that you try to see as many talks as you can. As long as the speaker is not completely awful, you will actually learn more than you notice as long as you pay attention.

In case of single-talk seminars, most of the above of course does not apply. I would say that for single-talk seminars, you can better afford to spend some more time on getting acquainted with the subject of the talk beforehand, so you should treat it like you would a conference talk that you have deemed to be of high interest to you (and don't bring anything to entertain yourself, but really try to pay attention all the way through).

First of all, it is not overly surprising that you are having trouble understanding research talks as a 2nd year PhD student. When I was at that level, I found talks to be completely incomprehensible. That being said, I do think attending them is worthwhile.

I wouldn't recommend randomly writing down formulas in an attempt to decode them. Instead, a useful exercise might be to to keep track of terminology that appears in various talks. If the same terminology appears in different presentations, this is a good indication that it is important. After the conference, you can follow up on what the term is all about, where it comes from, and why it is important. Ask your adviser.

The key is to look for recurring themes in talks. Say, in one talk, the speaker defines "hefelumps" and goes on to state three (incomprehensible) properties that hefelumps have. In another talk, the speaker defines "woozles" and goes on to list a very similar list of properties. It may well be that this list of properties are part of a standard argument in your field that gets a certain theory going, and knowing this will cue you into what the speakers are planning to do next. When you see these patterns, it's worth asking your advisor what the relevance is.

This has been said before, but I don't think it can be emphasized enough--many talks are "for experts, by experts". In particular, it is entirely possible that there are two or three people in the audience that the talk is directed to. These are potentially not going to be very useful. To recognized these, you need to know who is who in the field and what they are working on. It may be helpful to go over the conference schedule with your adviser before you attend. Maybe s/he can clue you in to some of the politics.

On the other hand, the expert-to-expert talks can also be some of the more amusing, especially if the experts involved are rivals. I was recently at a conference where three different groups were jockeying for the credit for a certain result. The interactions were priceless. With that in mind, I'll finish by saying that not everything you learn from a math talk involves mathematics.

Are sessions from previous conferences ever filmed and made available online? If not, are particular presenters (those who sessions you thought you might want to see) putting any talks of theirs online ever?

If so, try watching one of these, from some previous year, very slowly. Pause, copy things down from the slide, look things up. Rewind when the presenter connects what they're saying to something they said before. Try doing some of it yourself by hand or with the appropriate tool to "follow along." Work out how much effort it takes to figure out how the title of the talk connects to what is actually presented. This may be easier if you have access to the actual paper of the same title.

Once you've "deconstructed" one talk like this, you will know a lot more about the issues in the talks you attend. For example, perhaps the structure and organization of the talk is terrible, and you could now give the presentation in a way that would make sense to people who don't already understand the material. Perhaps there's a simple visual aid (diagram, graph, table) that would illuminate the topic tremendously. Or perhaps it's just insanely difficult and requires hours of work to even begin to understand. In some fields, that would make it ineligible as a topic for a one-hour talk, but apparently not in mathematics.

In my industry it's normal to leave talks that turn out not to be right for me. If I'm not sure a talk is going to work well for me, I sit towards the back so I can slip out. For the sake of the speaker's ego, I will usually pack up quietly, everything except my phone, then wait for a moment when the speaker is not talking (eg the pause right before/after a slide change) and stand up, holding and looking at my phone, frown, and run out of the room apologizing to those I go past. This allows everyone to tell themselves that I had to deal with an urgent call or email or something. I find that staying in a talk half listening while trying to do something else just wears me out and leaves me with nothing accomplished. Who knows, you might even have a great hallway conversation with someone else who couldn't follow the talk and left!

If you manage to "crack the nut" of presenting complex topics in a way that can be understood by those without the background, you'll surely have a long and successful career. Even if all you manage to solve is the shorthand and assumed background that these presenters are drawing on, you'll understand more talks in the future. And if you career depends on understanding talks, then it's a skill you should learn. Just keep in mind you're almost certainly not expected to understand every single talk at conferences you attend.

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