Relevant context: it’s very hard to learn from research-level math talks, because the material is almost absurdly complicated even when presented well. This advice is for grad students who are often totally at sea as to how to get anything useful or real out of attending a math talk.
As a research mathematician, I find seminar talks to be like someone describing a backpacking trip in the wilderness. Someone might discuss how they planned, what they saw, what obstacles they encountered and how they resolved them.
If you were listening to such a talk, you might get excited about following in their footsteps, or about going on a different hiking trip entirely. You'd learn some useful advice, gain confidence, and understand better how to cope when something went awry.
But you wouldn't mistake listening for having been on the trail yourself.
I listen to talks about climbing Mt Everest knowing that I will never do so, and so that will be my only experience. I've been to other wilderness areas on my own, and so I know enough to partially relive it through their talks, pictures, videos; and I have to consider that good enough.
My Everest is not safe to climb. We make it somewhat safe for tourists on the backs of many dead or mistreated locals, a lot of litter that cannot be safely cleaned up, and a bunch of other harms that I can't remember.
The point of attending those talks is to get a flavor of the area. To get a sense of the language the practitioners use, and how they reason about things. Perhaps what sort of results they consider important. These are incredibly important things, if you want to work within the social institution of academia.
And of course, sometimes you are presented with a wonderful theorem, that just makes you open the book/paper and start seeing why it is true.
Much like cliffhangers in fiction, sciences should be taught this way as well. Cause the student to anxiously seek out what happens next. Some will, some won't. Those who do are the ones the program should want to keep.
By practitioner I mean, you are one in your own research areas. And not in other areas of math.
People in different areas of maths have radically different languages and ways of thinking about things. And subareas will develop their own ways of thinking and talking about things. If you are a young researcher, you almost certainly have to learn these, if you want to understand the area. A more mature researcher can be confident enough to understand the new area in their own language.
Doesn't this all go back to, sort of, "teach a man to fish"?
I never passed a math class after my second try at pre-calculus. Before that I never even had to look at a book. Looking back I think it was a failure for me to ask the right questions or a failure of the teachers to help me visualize how to work out the systems starting from basic principles. I couldn't solve anything without starting from scratch. Still can't. I get paid ludicrously well for making a marketable skill out of that form of reasoning, so I can't think it's either a mental flaw or laziness that prohibited me from grokking calculus in 12th grade. Somewhere in there was a failure to provide the reality handle that mapped to something I could reinvent if necessary.
[edit] fwiw I think I've reinvented trigonometry at least six times when I needed to for games. I never remember how it worked the last time.
Keep in mind lots of high school math teachers are just bad at their job when it comes to calculus.
I do recall when first taking calc they briefly mentioned delta-epsilion proofs and limits but really hand waved past it, which i guess would be hard if you want everything on solid foundations.
8th Grade or so in Germany, my son got a tricky system of linear equations to solve. I showed him how to solve it in Python and also explained him how to quickly go back to fractional notation instead of floats (0.133333... = 2/15).
As the teacher looked at the results, he said I should receive a Nobel for my work. As my son told me that, I had a very long sigh...
I don't think you deserve a Nobel, but I do think that teaching your son to solve lots of different problems with algorithmic recursion is going to help him much more in life than memorizing the way to solve one problem on a math test.
I don't think I ever understood math except where it was logical, within the bounds of what I could deduce. But when I learned to write recursive algorithms, that capacity for deduction expanded exponentially.
I frankly don't know. I went to a "gifted school" as a 1st grader that required you to pass an IQ test to get in and have >150 on their chart. This was in the early 1980s. At least half the kids were what we'd now call "on the spectrum". A couple of them were already performing at college level in math by the time they were 11. One of them went straight to UCLA when he was 13. I was programming in HyperCard at the time and could simply not fucking grok the math that the kid at the desk next to me was just absolutely smashing. I was inherently intelligent and I was raised with the best possible chance of getting to that level of competence and ability, but I ended up being an art school dropout who programmed a bitcoin casino and still can't deal with multivariable math unless I write a block of logic for it. I have no idea how or why that kid (Eric Kim was his name) was so much more brilliant than me. We were in the same exact math class with a really great teacher who also happened to teach the afterschool "programming club" in the Mac SE lab, in HyperTalk.
One kid just groks the math. One kid groks the fun(){} ...in a perfect world, those brains should just complement each other, I guess.
Different mental starting points and a healthy dose of randomness and luck. To me, learning maths always felt like playing puzzle games. The more you play different games, the more you get used to the "secrets" behind the puzzles and the easier your brain makes successful connections. But when you're learning calculus, you barely have time to make those connections. Give the same starting point and same experiences, brains will make different connections and learn things a little different.
I have a similar story as noduerme, but for me it was interest and laziness. I got by in all my pre-college math just by listening in class. But, if I couldn't connect it to something I found fun (like taking apart and putting back together my NES for the 100th time, or playing some sport), I just didn't do anything beyond the minimum. Then college came around, and I got an F in my first math course. I retook the course and found a teacher who connected most topics to gambling and/or business and I was hooked. I managed to take that teacher for almost all the math I needed for my CS degree :)
> This advice is for grad students who are often totally at sea as to how to get anything useful or real out of attending a math talk
This does sound like a psychological crutch 'living in the moment' technique of feeling good that you've achieved something (learning 3 things) rather than understanding the material or atleast the nature of the area/problem described in the talk.
Would the same benefits be had from skipping the talk and reading the conclusions slide?
Not necessarily, as is stated, not everyone will get the same 3 things. These things are more like the most solid anchor points you can find to orient yourself in the communicated material. Without some kind of stable hold on anything in my experience the whole talk just flys right out of my brain, even if I've taken longer notes.
I view this really as a trick for the more obtuse talks. I can fully take and benefit from notes on something i understand. But if i end up in a talk that is going to be beyond me, having the goal of not taking notes, but picking tidbits is often the only way to get anything out of it. If i take full notes i forget to listen as there's simply far too much to write down. If i take no notes, then after the next couple talks I've totally forgotten everything i "learned". If i take very few, short notes then i can still pay enough attention to try understanding but i also have a couple anchor points from which to remember the talk.
It's just a balancing act, especially when you're in a conference where you have to pick a new talk every 30 minutes for six hours a day for 4 days. It can get pretty ridiculous and having a better strategy than "just remember it" or "well write everything down" can be very useful when the most interesting talk to you is in the middle on day 3.
Thats why I love that so much knowledge is on Youtube. You can go back in time. Speedup/Slowdown. Copy stuff from transcripts into your notes etc.
The ideas in the article here still apply, but being 'late' is not a thing.
Decent video + helpful chat community = all you need for Maths/CS stuff (below research level). You don't need university lectures where you need to madly cycle across campus to make it on time.
Wanna know what I prefer? Clearly written, succinct instructions. So much knowledge is being frittered away in podcasts and “smash that like, follow, and subscribe” videos it almost keeps me awake at nights.
Videos are useful when they're 3blue1brown style taking advantage of the format. They're a waste of bandwidth when they read from a script with some footage/stock photography in the background.
Even then, a lot of the video may not be useful to a particular audience. Being able to scroll past a sequence of short animations could be even more valuable -- especially because then you have the opportunity to include more optional branches via links or tabs or user preferences, and make the content even more accessible without making it excessively long for all audiences.
I landed on a classic "32 pt typing into notepad tutorial" the other day. What a weird concept that was. I guess it was an artefact of having no other way to post text to a large community as a lay person.
Assuming you meant "neither is better," I disagree. Text is far more susceptible to navigation—especially via searching, but also by way of formatting and hyperlinking. It also permits more flexible clipping, saving, or sharing.
You're right to suggest that video can be a good replacement for in-person lectures. But it's a terrible replacement for a transcript or other way of publishing content in two dimensions rather than binding it to the progression of time.
Well i think that's what they're saying. Videos are better than text for a college lecture. The big up video has on text is... video. Moving pictures, animations, words at the same time as images. These are all things text cannot do or cannot do well. You are right that it's hard to look at a video and know what's in the whole thing but a portion of that is solved by table of contents/chapter navigation and its honestly good enough for me. I can't read a paper while doing the dishes or other necessary chores that have to be done, but i can watch or at least listen to a video or podcast. Each medium has its own benefits and i will state again, neither is better outright. You're entitled to your opinion.
I've been working through an applied linear algebra textbook on my own this summer and have at multiple points encountered subjects that the book simply could not communicate to me well. I go search a video on the topic and find that the man who wrote the book also made video lectures from the time he released the book, so it's not like the book sucks and the videos are $100,000 dollar productions. If anything the book is ridiculously better produced than the videos. It's just him talking into what sounds like a crackly phone mic and drawing on pieces of paper under a bright but inconsistent light.
But you know what, I'll be damned if those videos didn't make sense of every difficulty i had in the book. And it's explicitly the benefits of video, he shows the process while talking and there's no editing for brevity or page count, just the raw facts that come into his head as he progresses. It's so good that I've honestly switched to the videos for at least a chapter. I find they're more succinct and usable, and i learn much faster from them. And that's nowhere near a 3b1b level of video!
Again, you're entitled to your opinion but i don't think the fact that you like books better gives you the ability to state the 'fact' that books are downright and unquestionably better than videos, podcasts, images, hell even vr some day maybe. Videos are also drastically more accessible. I can find videos on things that would cost me hundreds of dollars to get a comparable book on. It drastically lowers the barrier to learning and i think that's really important for children whose classrooms are not adequately challenging them
I'm transitioning to Bitwarden. It seems great, but the "how to get going" content is all in a series of 5 minute Youtube videos. I just want some text to read!
Yes, after working in the cs department with entirely international students from India or Nepal i learned to pick up on the speech patterns, grammar, and accent of the students. I don't do it but i learned once when challenged that i can do a near perfect Indian accent in English without ever having practiced.
Also, i knew they were talking shit about basically everybody cause the managers and professors couldn't understand what they were saying. One time the group leader came up to me all concerned to ask if i knew hindi because i guess i was laughing at a few too many of their jokes. I just nonchalantly didn't answer to keep em on their toes lol.
Do you have good examples of where this knowledge is on yt?
When I want to learn something like a woodworking technique video does help immensely to see someone do the physical thing they describe with the materials to get a level of understanding. Like oh that's how you position the wood on a jig to use your table saw like a jointer (an expensive tool I don't have). Rarely do I need to see the person/tools in play for anything software related.
Text is king for me when learning things regarding computers. Granted I learned CS the old fashioned way, in a lecture hall before google existed. I imagine for beginners maybe getting down early concepts is easier with video?
For everyone saying "this doesn't work because I usually have more than three takeaways" – that is kinda covered in TFA. You write down more than three but are forced to only choose three, and this process of choosing three actually makes you remember the ones you "scratched out" better.
And possibly that you may not fully remember after the 3 but you got your feet wet on 4, 5, and 6 and voluntarily go back to notes and additional research to get it all.
Several comments are about taking more than 3 things with you. For me it's the other way round, for me it's a success if I can keep ONE thing. And that's usually a new insight, something surprising, something I can link with other information, something inspiring...
When I have taken part in a conference or a series of lectures, an aggregation or 'best of' selection takes place in my mind afterwards (this can also be only one point in the end) and the whole event was only a success for me if this 'one' thing can still be recalled days and weeks later.
Can't say whether more or less is better, but I got a D grade in my Advanced Bio class in high school, then I retook that semester but did regular Biology. Got an A (maybe B+) and I remember almost everything from the regular class.
Depth has its merits but it's not reasonable to expect the participant to retain all that knowledge. Let them come back for more once those few things they retained tickle their fancy!
This seems like the opposite of why or how I would go for talks. Seminars are the biggest part of academic life I miss on the other side. Hearing smart people talk about genuinely interesting topics in great detail is not something you can see much in tech circles.
After years of doing it I classified talks as of two types: first is where you know you want to listen to this person because that topic is already of great interest and you’re looking for the details. You already know how pluripotent stem cells came about but it was fun to hear Shinya Yamanaka describe the actual experiments and how they came about. Or perhaps it’s your competitors presenting their latest “ready to be public” findings where you’re trying to read between each line and dot in figures to guess what else they have up their sleeves they haven’t published yet.
The second category is of talks where you have some interest or hook but that’s it. Maybe it’s a Nobel laureate (I can assure you most Nobel talks are the most boring and useless ones you can go to). Maybe it’s an obscure topic but has some interesting keyword that intrigued you. So you just go there. Perhaps you get totally captivated in that talk, perhaps you learn some nuggets of information that you never knew about, but perhaps worst of all you zone out quickly because it’s too arcane or boring.
I still see the second category as the most rewarding. Maybe you’re bored in the talk, but that puts you in a place where you typically can’t leave, someone’s yapping and seeding your random thought generator with kernels of factoids that your imagination can run wild in. I often come out of these talks with other ideas only vaguely related. Some other times I’d have refined some of my own project ideas since I have nothing better to do.
None of these trials and tribulations have anything to gain from a contrived exercise to jot three things down though.
I think this is more targeted at new graduate students.
I remember when I first started my PhD, literally all of the talks were completely over my head, and I did not understand enough to engage as you describe here :)
Gathering three key takeaways would already require a good deal of effort :) and, I appreciate that the author of this post absolves you of having to have the speaker’s message as a key takeaway, since as a beginner grad student that is frequently beyond reach.
Do you think there’s a “shortcut” though? Sure most everyone (though not all) starts clueless at the start of grad school, but either you get the science or you don’t, my experience is that a good majority of scientists today never actually get science and just play the part (even to themselves) of someone who’s figured it out.
I wonder: if we were more peripatetic about talks -- meaning, if we walked, in a group, rather than all sat down -- would we still struggle to get so much out of talks?
We sit wayyyy too much in business and tech. There is not nearly enough movement. Yet our bodies are built for movement, not for sitting on our duffs for most of the day.
This would never work for me. Sometimes I attend talks to look for specific information, which is often a lot more than three things. Sometimes I attend just to learn about a new subject, or for some inspiration. Often, it's not a talk but a dialogue, and many interesting points come up during the Q&A. If I needed answers for a specific point, I'd ask the question.
Imposing such an artificial and rigid structure when attending a talk will stress me out, get me less, and turn me off. I still remember my student days when the best lectures or talks served to inspire, and I'd often dig deep into a subject because of that.
I'd also add, photographing slides is not the same as writing things down. (especially if you're photographing every slide, to the degree where you're paying little attention to the speaker)
> the same as writing things down
Ah, I could go down this rabbit hole but (after a lot of trial and error), I have come to a (reasonably working) method. It's not enough to write down what you hear/see . I find it so much better to link what you write down to something you already know. That way, things tend to stick longer. Otherwise the notes are just that -- a random collection of things you have written down. No idea if they will ever surface in your memory.
As a YouTuber, I'm now wondering if I shouldn't focus on making sure people get at least three, and maybe only three, key take aways from my educational/opinion videos?
As a research mathematician, who knows the author (Ravi Vakil) personally --
This advice is for the audience, not the speaker. (There's lots of good advice out there on how to give a talk, too!)
If Ravi gave a seminar talk, and everyone listening wrote down their "three things", then I'm sure he would be delighted if everyone's note cards were different.
I've helped with giving a few talks and I guess I probably saw this page back in 2011, because "three things" has always been my guideline as well.
I've noticed that the tendency for most folks giving technical presentations is to want to advance to a new slide every 30 - 60 seconds for their entire speaking slot - usually 25 to 50 minutes. Not practical.
If, after its conclusion, most of the audience remembers just three important things then your talk will have been an unequivocal success!
This was good. Short and sweet. I might start applying this 3-thing rule in meetings I attend. It'll be nice to have 3-point summaries of every meeting I attend.
I used to do this when I participated in Toastmasters, to give evaluations. While listening to the speaking members speech, just focus on getting and memorizing three things to give them feedback on.
