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It may be one of the most uncomfortable questions one can ask themselves, but after being a math student for six years (currently in my first year as a PhD student), this question seems to become more and more important for me.

Namely, since I started studying mathematics at a university, I have had trouble following the lecture. It was just too much new and complex information thrown at me at once. I couldn't follow the lecturer, as I forgot what they said when they started a new sentence. That's why I am talking about working memory and possibly IQ: I can't hold multiple sentences at once in my head simultaneously, my line of thinking and understanding is very linear, it's step-by-step, but when I make the next step, I've forgotten about the previous one. I often sit in the lecture trying to process what's been said fifteen minutes ago.

I tried taking notes like a stenographer, writing down the literal words spoken by the lecturer. I tried visualizing what the lecturer said as subtitles appeared at the bottom of my visual field. Nothing helped, and I was confusing myself even more. Another method I've tried was to "note down what you don't immediately understand". Still, I did not know what I didn't understand because, as I said, there was too much new information at once.

So, to this day, lectures and seminars are utterly useless to me. The only way to learn and understand new information is if I have it in the text; it seems like I can't grasp new information by just listening. My peers can understand and learn new information by listening, so they enjoy extra lectures, seminars, and conferences.

Now, to the funny part: I can understand spoken lectures and seminars about the humanities, like philosophy. It's not a problem for me to listen to them like a podcast and understand everything perfectly. I don't know why it is like that. I don't know what makes humanities lectures easier to understand and follow compared to science lectures.

Anyway, what is your opinion on that topic? Why can't some people get anything out of a lecture? Is it because of their working memory? Aphantasia? IQ? And what should one do to improve it?

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    "I can't grasp new information by just listening" I'm a bit confused by this sentence. During a math lecture the lecturer will typically write a lot of things down rather than just speaking, so I'm wondering why you feel that you need to grasp information by just listening? Commented Jun 15 at 17:40
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    I don't want to write a repeat answer but I'll reinforce here that everybody learns differently, and that learning in one's own way is the most effective. Trying to learn by following someone else's stream or logic is hit-or-miss. You might stumble upon an occasional lecturer who thinks similarly to the way you do once in a while, but mostly not. Don't worry about there being anything "wrong" with you or any arbitrary metrics. Build your own unique world of understanding in your own way, and perhaps maximize the lecturer's utility by asking specific questions in and outside of lecture.
    – uhoh
    Commented Jun 16 at 1:27
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    Don't worry about your IQ. As you can see, many (include me) have difficulty following lectures at times. My advice would be, if possible, to not take notes, or make them less detailed. Math takes extreme focus and concentration - personally, if I am writing everything down, I am not able to think. But some courses require good notes - for example, if no book is used and if exercises are only written on the board. If you have a classmate that takes highly detailed notes, ask if they might share. If the lecturer closely follows a text, or if notes are available online, no need to take notes. Commented Jun 16 at 17:07
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    Do you by any chance have ADHD? That sounds like what it could be (layman’s word total guess). I have some of the symptoms of ADHD though without a diagnosis and have trouble paying attention to a long speech if it’s really dry or I’m sleepy or I’m stressed. If it’s interesting I’m fine. Otherwise my mind can wander—I zone out thinking about other things and suddenly realize this person is talking and I have no idea what about. Anyway something to consider. If you’re good at math it’s almost certainly not IQ.
    – bob
    Commented Jun 16 at 17:11
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    Although I'm in engineering, not in mathematics, I found I was able to follow lectures MUCH better whenever I read up on the material beforehand. I know it's hard to prioritize this if there's a lot of coursework. But if you can, find an hour to read what the lecture will be about before going to that lecture, it might help.
    – Chris_abc
    Commented Jun 18 at 7:05

6 Answers 6

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Some aspects to consider:

  • Your working memory works better with terms and concepts that you are familiar with. A slightly different perspective on this is that you can hold a limited number of things in your working memory (roughly eight), but unfamiliar concepts take up more memory, since you do not have mental shorthands available. For a blatant example, your brain stores a (familiar) word as one item and not as the sequence of its letters or sounds.

    Mathematics lectures are generally on the border of what anybody can digest. Even for a decent lecture, being slightly less familiar with the concepts than expected, being slightly more prone to distractions (that fill slots in your working memory), or just having a slightly worse working memory can make the difference that you cannot follow the lecture at all anymore.

    By contrast, you have a basic familiarity with most concepts in the humanities (on account of them handling human life), even when they are discussed in a more abstract or thorough way. This may be why they are easier to process for you.

    I am a physicist by training now working on biophysics. Some more biological talks tend to be about a selection of molecules, genes, organisms, or similar, usually all with names that are not self-explanatory (some are literally random letters). I have listened to talks that introduce all of these things in a way that I can perfectly understand (and is sufficient for the talk), yet when they start working with them, I find it more difficult to follow than people familiar with biology, because every time one of these names gets used, I need to put in some extra work to process and store it. Therefore I find some of these talks very difficult to follow even though I could read the corresponding paper without major difficulties.

  • Mathematics is a strongly incremental field, with layers of layers of abstraction. A crucial aspect of this is that for building upon some concept, it does not merely suffice to understand some definitions, theorems, and proofs, but you have to have a certain amount of familiarity, fluency, automatisation, or similar, so it does not use too much brain capacity. An important strategy when learning mathematics is to realise this and spend time working with concepts, so you can build upon them. For example, there is a crucial difference between understanding the definition of an open set and being so familiar with it that it does not hinder you to understand advanced topological stuff.

    Most other fields are less incremental (but also much broader). A humanities lecture will usually have less strong prerequisites and thus it may be easier to digest. The challenges of such fields lie elsewhere.

  • People learn differently and also evaluate their learning differently. Some people are better at pretending (to themselves and others) that they understood something they didn’t. Some people are good at understanding something in broad strokes first and then go into the details. Others work better with understanding all the details first. I know quite a few excellent students who hardly benefitted from lectures and therefore rather studied with a book.

Obviously, I cannot diagnose you, but here are some suggestions:

  • Be aware of the above and see your difficulties in a more objective and less frustrating manner.

  • Try to prepare for lectures etc. by familiarising yourself with the core concepts, solving exercises, etc.

  • Try to understand lecture content in broad strokes at first and in detail later.

  • Accept that you prefer to learn with books. As long as you can stay up to speed that way with reasonable effort, it is probably not an issue.

  • Accept that some lectures are just bad.

  • Consider that your peers are not as good at this as you (and they) think they are. They may also need to work through their lecture notes, textbooks, etc. before they actually understand.

Mind that these are just suggestions and I can only guess what will work for you. So do not worry if you already tried some of them or they are not your thing.

You may also want to have a look at this answer of mine on Math Educators.

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    +1, especially for the first point that the difficulty of a lecture is hugely affected by your familiarity with the background. I remember in my first couple of years of grad school finding myself absolutely out of my depth in a lot of seminars — then looking back at the notes a couple of years later, much of the material was second nature. Even if on first exposure I can’t follow a lecture, I find it often does help build the familiarity which means that next time I read or hear about the material, I can understand it a bit better.
    – PLL
    Commented Jun 16 at 10:22
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    I would add that for PhD-level maths lectures (as well as many other lectures) there is often an expectation that students should spend an additional x hours studying the material per 1 hour of lecture time. Nobody expects students to actually understand the material at the speed the lecture throws it at them. They are supposed to work on the lecture notes afterwards and then understand it.
    – quarague
    Commented Jun 17 at 7:28
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    Mathematics lectures also have the specific issue that if you miss one point, you likely can't follow the entire rest of the lecture as easily. Commented Jun 17 at 16:38
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My opinion is that mathematics is inherently a written discipline, and that trying to talk about it is very close to a complete waste of time. So the issue of mathematics lectures is pretty orthogonal to IQ and working memory. And yet, so many people are such weak readers, lectures are the best we can do for many of them.

I'll also say that right near the end of my master's in mathematics, I realized that the best thing I could do is not take any notes in a lecture. So you might try a strategy of just intently listening/watching the lecture, and not doing anything else whatsoever. That is: don't distract focus by trying to take notes in parallel; give full attention to the speaker. Use the written book/article later as the primary source.

Fortunately, I'll observe that entering a PhD program, you're right at the threshold of when your primary work will be reading copious research articles on your own, and there won't be anyone around to talk you through them. So your skill set is marvelously well situated for the real mathematical work lying just ahead of you.

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    For me, ideally, any lecture is given twice. The first time I don't take notes and just try to understand what is going on; the second time I take notes. I do find lectures helpful; for me reading mathematics is just too hard to do too much of it. (One of my collaborators jokes that he is illiterate, and that's why he has grad students.) Commented Jun 16 at 18:42
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You're not the only one. I've often had this issue, though for me it's very dependent on the speaker and the presentation style.

I realise this advice won't necessarily apply, but the zoom era has been an absolute boon for me. If you can, always watch recorded lectures rather than live ones. Then you can pause to let your thoughts catch up whenever you need to, and you can even go back and repeat sentences until they sink in. As a bonus you can also increase the playback speed during the parts you already understand - just don't forget to slow it down again when it gets to the important part. The only real disadvantage is that you don't get to ask questions at the end, although of course you can always email the speaker if you want.

Another thing to keep in mind is that a lot of the time, if it's a seminar rather than part of a course you're taking, you're there to learn about the topic, rather than to learn the topic. By watching the seminar you get an idea of what the speaker is working on and what kinds of results they have, and based on that information you can decide whether to follow it up in more detail later. Even if you don't follow it up, you'll be aware of it if it ever becomes relevant to your work, and you'll know who to ask about it. For most seminars, unless the speaker is very accomplished or you're already quite familiar with the topic, this is all you can really hope to get. If you go into it with this as your goal then you'll take some pressure off yourself to follow all the details, and it will be easier to see the bigger picture.

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  • "learn about the topic, rather than to learn the topic" +1 for this alone. A lot of lectures are doing a combination of things. They prime new connections and reinforce existing connections.
    – David S
    Commented Jun 17 at 19:49
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It's been mentioned in a comment, but not an answer, so I wanted to put it here. What your describe sounds a lot like the experiences of someone with ADHD. Obviously we can't diagnose you here online, but what you describe would seem to me to be enough to try an talk to someone who can, to see if they have have any insights.

I have dyspraxia, which has some features in common which ADHD. Namely poor working memory and problems with executive function (that is the ability to choose what one focuses on and when).

Another answer mentioned that the average working memory can hold 8 things. Well, my forward recall digit span (the way working memory is measured in psychological profiling) is 5, my reverse digit recall is only 3! Your description of not being able to hold/ connect the beginning and end of the same sentence was very familiar to me. I don't really put much stock in the usefulness of IQ, but for what it's worth these difficulties mean that my verbal IQ is unaffected (or at least its still plenty enough for academia).

None the less, with the right help and strategies I have been able to have a career in academia, with postdocs in prestigious places, and now a permanent faculty position at a well regarded University.

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Some good answers already, but I'd like to raise two issues that I haven't seen mentioned:

First: Somehow, you got into a PhD program in math. So, somehow, you are working this out. People who really can't handle math flunk calculus 1 (or diff equations, or whatever).

Second: The contrast between mathematics and the humanities. There are, of course, many differences between these areas of learning, but two big ones are structure/formality and abstraction. I sometimes say that mathematics is the search for highly structured, highly abstract beauty. And, a long time ago, a professor of mine said that "in mathematics, they keep making things more abstract until almost no one can deal with it." I am not one of those people who says that math is inherently harder than the humanities. but they are hard in very different ways and for very different people.

In many ways, I think math is closer to the arts than it is to the humanities.

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It is common to meet people who do not know the answer to any question until they hear themselves say the answer: their internal mental communication just doesn't work as well as the channel out of their mouth, in through their ears.

Rarely, this is a noticeable effect of a mental insult such as a stroke: mostly it's just the way some people are. Even more common, some people don't know an answer until they have formed the words of the answer, and perhaps sub-vocalized (without having to actually listen to the answer).

IQ is a very blunt measure: nobody knows what it means, and it obviously means different things in different cases. The inability to answer IQ questions without using the very slow talk-listen channel would give someone a lower IQ value, just because that channel is so slow. Sub-vocalization is also slow (not as slow): this was a subject of debate when monks learned reading: is reading fast, without subvocalization, really proper reading?

It is entirely normal for different people to prefer different communication channels, and to be more or less effective with each channel, and for "measured IQ" to be dependent on channel preference: no blind person would score any meaningful result on any of the IQ tests I have taken.

Regarding working memory, I'll just say that there are mental strategies to deal with restricted working memory, and sometimes the observed effect is not of memory depth but of strategy choice. People sometimes have trouble with working memory just because their memory depth is so good, they've never learned to break down the problem and deal with it piecewise.

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    (I guess maybe this is downvoted because it goes so much on tangents that it barely connects back to the question in any way that is too direct or telling. Maybe it is worth recofusing, rewriting, or removing it to keep it simple).
    – matanox
    Commented Jun 17 at 6:59

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