Memorization is crucial for a subject like math. In a highly technical branch of math like, say, topology, definitions fly at one like bvllets from a m@chine gun. Just to solve a problem you might need immediate access in your head to some 12 definitions, 5 lemmas, 3 theorems, 4 corollaries and 6 prototype/canonical examples meaning you want to keep them all(along with their proofs as proofs carry important techniques and ideas) at the tip of your tongue and top of your head. Just because you "understood" them once in the past doesn't mean much if you cannot recall them immediately right where you need them. Obviously, you can look them up one by one (granted you know what you're looking for). Along the way, you'd have to re-understand them cause understanding is often fleeting in math, but this will make you lose time, momentum and get/keep you stuck in a thick quagmire making the original problem massively more difficult than it is.

Many very important results in math (that have become staples) are made up of extremely specific techniques that are very hard to reproduce even after 5 minutes one has read (and presumably understood) them. Even understanding in math comes in waves. To get a deeper understanding of an idea you'd need to have some preliminary grasp on it.

I often see the sentiment "in math if you understand something, you don't need to memorize it" on English speaking side of Internet. Contrast that with the old Soviet school (& modern Indian one?) philosophy which was "understand -> drill -> memorize". IMO, the former philosophy produces weaker, barely able mathematicians.

This vid below about Hitler learning topology echoes some of what's typed above.

https://www.youtube.com/watch?v=SyD4p8_y8Kw

How universal is this experience?

I remember a math grad student friend who said "math is a young man's game". He compared it to cycling; nothing you do in your old age would compare to what you could do earlier.

In fact according to him math is worse than cycling, if I'm correct that cyclists peak in their early 40s. Contrast that to economics, which specifically offers the Clark Medal for the best work performed by someone under forty, because old-timers would otherwise snaffle up every prize.

People repeat that quote a lot, but I don't think there's much evidence for it. The main thing is people have kids, and kids take time. Boom 10 years gone from high-performance productive individual-contributor work. It was uncommon for people to go back to school at a later age, but maybe not anymore?

I am not sure I understand the connection you're making between the cumulative and highly technical nature of math and the age of a mathlete.

That's fair. I didn't relate that my friend went on to say that the reason math is a young man's game is that it's only the young who can read and memorize results fast enough, and keep enough of that information in their head at one time, to do important work at the frontiers of math. The brain has physical limits, just as the rest of the body does.

I am revolted by that idea. And I'm certainly a better coder than I was in my thirties, and I was better then than I was in my twenties. (Not that I'm under the illusion that my work compares to PhD-level math.)

Why’d you censor bullets from a machine gun? Is there some HN autoban for them?

Some things just need more memorization than others. I used a ton of flashcards for Latin vocab and learning the farsi alphabet but almost none for my CS classes (used notes for those).

I'd enjoy seeing a complete list of the disciplines that require such rote learning. I think the broad categories might be "areas where people invent lots of arbitrary rules" (law, accounting, medical coding) and "complex systems we don't understand well" (chemistry, biology, neurology). Others?

since I'm largely in the same boat: I think it has more relevance in some fields than in others. E.g. programming is relatively good at naming things descriptively, but less-so many fields that name tons of things based on the discoverer, e.g. biology-related things have a fair bit of this. And obviously there are numerous exceptions in both directions.

For programming: I'm quite happy saying "learn concepts, not terms/frameworks". There's obviously some value in things you use a ton daily, but you'll naturally remember those through use - for the rest, thankfully, programmers are great at making things searchable, and there are loads of tools to search even when not (e.g. grep). Terms can be useful for communication purposes, learn them as needed and meh beyond that. Frameworks though are basically the programming-world equivalent of fashion, they change with the weather / at the whims of popular tweets. Yolo - learn how it works instead of the API, that's waaaay more useful, and is probably transferrable to dozens of other frameworks.

But as an example: I routinely forget the argument order and finer details of the various "split a string" funcs in the 3 or 4 languages I use ~weekly. Because I only use them every few months. And in my next language, quickly-recall-able memory of those other-lang patterns won't help me in the least (if anything, they might slow me down). Splitting a string though, and choosing which end to start from, and how many times to split, and the various i18n complications, is a general concept that's applicable in all languages.

It's a blessing I hadn't noticed, that my work does not require the perpetual memorization required by, say, pharmacology.

It's funny that society doesn't normally classify programmers as creatives. (Then again, it doesn't classify scientists that way either.)

I use Anki for infrequent power-user commands and e.g. Python modules I don't use often. There's a class of tasks that I do regularly, but infrequently enough that I have to hit Stack Overflow every time unless I've put it in Anki.

I have never needed to do that sort of memorisation in the past but have done recently. When I was a student my memory was good enough that I could skate through based on what I remembered from lessons/lectures/basic revision. In my professional life I've never needed it.

Recently though I've been learning to fly (in the UK). You have to take some theory exams. The "How the aircraft flies" exam works in the way it has in the past - read through the material a couple of times and because it's a coherent set of knowledge that fits in a framework I already understand (Engineering) I can remember everything. Air Law does not work like that though. There's lots of minutiae to learn (how much visibility do I need for VFR at 5000 feet as supposed to 1000 feet, what does the white ball above the T mean on a signal square). Anki let me learn all of that stuff over a few weeks for 15 mins a day (plus deck creation time - a couple of hours) and pass the exam with no mistakes.

I certainly take notes, specifically so that I don't need to remember things in detail. I know I can checkout my repository and have everything to hand in one-place.

But that said for learning a language these kind of tools are very useful.