[jlev1]

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.

[impendia]

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.

[bluGill]

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.

[abdullahkhalids]

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.

[andirk]

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.

[nohuck13]

"To get a sense of the language the practitioners use, and how they reason about things."

Isn't the article assuming you already are a practitioner?

[abdullahkhalids]

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.

[noduerme]

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.

[bawolff]

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.

[Loic]

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...

[noduerme]

Hah. That's quite funny.

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.

[bawolff]

I'm not really sure what the difference is, at least at the high school level between writing algorithms and doing math.

(Eventually math switchs much more to be about proving things [inb4 someone yells howard-curry], but that is more mid-undergrad degree.)

[coldtea]

So, what made those who did managed to grok it, grok it? Given that they had the same teachers and material?

[noduerme]

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.

[lopis]

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.

[matwood]

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 :)

[helsinkiandrew]

> 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?

[wholinator2]

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.