You can read my other comments of how I use Anki to learn math, especially about how I put in proofs and stuff.
But specifically:
> [...] I'm curios, if you cram a piece of knowledge that is so interconnected as math is in flashcards and you rote learn all the definitions, theorems, proofs and examples - are you then capable of seeing the connections between them?
Well, I wouldn't think of using Anki as rote learning things. A basic principle is that you must understand (at least in something like math) before you put it in Anki. I wouldn't make a card without first understanding what it says. In fact, the very fact of making a card will often make me understand the proof much better, just by trying to write a more minimal and easy flowing version of the proof, or trying to put in a mnemonic or visualization that will make the proof clearer. (Btw, even after doing this process, I still find that I often can't recall the proof easily even 4 days later! Such is my memory, at least. I can sometimes reprove, but not always.)
Hopefully, if the exam asks to prove a new lemma, having lots of examples in your memory of how to prove things or how to solve exercises in e.g. linear algebra, will make it much easier to do it.
Look, I'm no scientist, but the science here is pretty solid - active recall helps a lot. It's essentially what lots of students are doing when studying for tests, only (scientifically shown to be) more efficient - solving example problems/proofs, etc. And it has the benefit of being inside a system that will hopefully keep the knowledge alive even in 10 years, not just for the exam and that's it.
> are you then capable of seeing the connections between them?
This is probably the best hidden feature of Anki. Because I often will get basic cards surfacing a few months after learning them, I will often find connections that I didn't think about (or couldn't know) the first time! I've even had some cases where I will recall a definition or theorem that I wrote from the beginning of the study, and realize that actually, I got part of it wrong! And now that I know a lot more, I easily see "wait, that can't be right" and dig deeper to discover what was my misunderstanding!
But specifically: > [...] I'm curios, if you cram a piece of knowledge that is so interconnected as math is in flashcards and you rote learn all the definitions, theorems, proofs and examples - are you then capable of seeing the connections between them?
Well, I wouldn't think of using Anki as rote learning things. A basic principle is that you must understand (at least in something like math) before you put it in Anki. I wouldn't make a card without first understanding what it says. In fact, the very fact of making a card will often make me understand the proof much better, just by trying to write a more minimal and easy flowing version of the proof, or trying to put in a mnemonic or visualization that will make the proof clearer. (Btw, even after doing this process, I still find that I often can't recall the proof easily even 4 days later! Such is my memory, at least. I can sometimes reprove, but not always.)
Hopefully, if the exam asks to prove a new lemma, having lots of examples in your memory of how to prove things or how to solve exercises in e.g. linear algebra, will make it much easier to do it.
Look, I'm no scientist, but the science here is pretty solid - active recall helps a lot. It's essentially what lots of students are doing when studying for tests, only (scientifically shown to be) more efficient - solving example problems/proofs, etc. And it has the benefit of being inside a system that will hopefully keep the knowledge alive even in 10 years, not just for the exam and that's it.
> are you then capable of seeing the connections between them?
This is probably the best hidden feature of Anki. Because I often will get basic cards surfacing a few months after learning them, I will often find connections that I didn't think about (or couldn't know) the first time! I've even had some cases where I will recall a definition or theorem that I wrote from the beginning of the study, and realize that actually, I got part of it wrong! And now that I know a lot more, I easily see "wait, that can't be right" and dig deeper to discover what was my misunderstanding!