very true, in the sense that rote memorization is not the point.
but false in the sense that doing math requires fluency - in applying a small amount of technique up to lower division math, and in applying a large number of definitions/results after that. in areas like abstract algebra, failing to memorize will kill you. it is as disfluent as writing text in a foreign language without having memorized the working vocabulary and grammar; even if you can eventually recall, derive or look up what you need, it's just not practical to work like that. (and i say this as someone who prefers to mentally index information rather than memorizing...)
I have to disagree, especially about abstract algebra. Most concepts and theorems feel like abstract nonsense (not specifically talking about category theory here) when you don’t understand them, but should become pretty natural once you do. For true mastery you need to work with the concepts and results on a day to day basis for a while, by applying them; continually reading the text of definitions and theorems hardly helps if at all.
i agree that memorization by internalization (concepts) is different from (and superior to) memorization by rote (text); i was agreeing with the other fellow that rote memorization is not the end goal. however, to me they're both "memorization" because they both represent work to achieve fluency in application.
however, i made my comment because i think i disagree that spaced repetition has no place in learning. i think that if you dig around in the Polar guy's earlier comments, you'll find threads where folks like michael nielsen are talking about using spaced repetition tools for much more than purely textual memorization of theorems - basically, cycles of repetition and (re)synthesis. so i don't feel it's right to completely shut him down about card decks. you may disagree, of course.
When your definition of memorization encompasses all forms of learning, saying memorization is crucial to learning is pretty much a tautology. No one claimed that amnesia sufferers are perfectly good for mathematics. Same goes for repetition. No one expects you to understand and never forget the theory of cohomology by writing down a long exact sequence once.
The thing is, the root comment of this thread specifically talks about "continually review what you've learned and NEVER forget anything" through looking at highlighted notes in the software mentioned (a somewhat out-of-place plug, I'd say). That's not how math works. You refresh your memory by tackling preferably new problems. Reciting proofs is largely pointless (except for certain very elegant proofs, in which case you probably won't need to recite them anyway); reciting definitions and theorems is even less useful.
> it's meant to 'freeze' all of your knowledge so that you never forget it - ever.
Yeah, no, you don't "freeze" your mathematical knowledge.
I think there is absolutely nothing in math one should memorize. "In abstract algebra failing memorize might kill you" is nonsense. Memorize what? Axioms of group? Tactics that can be applied to problems?
please consider the statement from the position of a student just learning the material (like the OP). if you are working through a book with 1000+ problems, like pinter (as some people are suggesting), and you have to keep looking up stuff like how to verify a subgroup, how long is that book going to take you?
to me, memorization means to recall the important parts of something accurately and precisely so that they can be used fluently. that is not to say textually (rote memorization). i do not think it is enough to say "well, that's what learning is" because i doubt most people learn most things to that level.
"I now believe memory of the basics is often the single largest barrier to understanding. If you have a system such as Anki for overcoming that barrier, then you will find it much, much easier to read into new fields."
Also I just made an account to say thank you - polar looks awesome. I just wanted to start using anki and stumbled upon it.
https://getpolarized.io/
Polar is basically a personal knowledge repository.
The idea is that you use Polar for all of your education. Either official education or continued learning.
Every textbook or technical paper should go into Polar.
You can then annotate the textbooks directly including text highlights, comments, etc.
It supports spaced repetition systems like Anki so you can continually review what you've learned and NEVER forget anything.
It doesn't make sense to pursue a PhD or spend 6-12 months researching a topic to just forget 80% of it due to bit rot.
The reason I named it Polar is that it's meant to 'freeze' all of your knowledge so that you never forget it - ever.