Memorizing is clearly a necessary, but not sufficient part of learning. If you are to become an expert in any subject whatsoever, from math to football fandom, you will need to develop an ability for remembering huge amounts of raw facts. One of the first hurdles in a math education is memorizing the multiplication tables. In biology or medicine you have to learn literally hundreds of systems that happen to exist in a certain way, and from all of the raw facts, could very well be a different way.
> Some people understand math trivially with no effort and no work memorizing (they wont remember the formulas, but they can explain how it works and can reproduce something similar to the formulas), others don't understand even with massive amounts of effort and memorizing every formula.
Sure, you can wing it at a primary or high school level if your teachers are impressed by your understanding. But you will never become a math expert if you don't remember the specific formulae, and many other more complex things. Even if you are fully able to deduce the theorems from scratch, you won't be able to function if you have to invent and then prove every single theorem you want to use.
> Memorizing board states is deep blue, it is much worse than AlphaGo etc, so that is for sure not the best way to get good, and for sure not the way humans get good, humans get good similar to how AlphaGo gets good, not how deep blue did it.
No, it is precisely the other way around. DeepBlue is deducing how good a board state is by trying to calculate all possible follow-up moves up to a depth of 13 or something. In contrast, AlphaGo has memorized patterns occuring in billions of games (in a lossy archive format, of course) and basically can recall games that are close enough to the current game and what you need to do to win from the current position. And this is exactly how chess masters mostly work as well, to the extent that it has been studied, and based on their own reporting. They just recognize positions or certain aspects of a position, and can recall how the game works from that position.
> Some people understand math trivially with no effort and no work memorizing (they wont remember the formulas, but they can explain how it works and can reproduce something similar to the formulas), others don't understand even with massive amounts of effort and memorizing every formula.
Sure, you can wing it at a primary or high school level if your teachers are impressed by your understanding. But you will never become a math expert if you don't remember the specific formulae, and many other more complex things. Even if you are fully able to deduce the theorems from scratch, you won't be able to function if you have to invent and then prove every single theorem you want to use.
> Memorizing board states is deep blue, it is much worse than AlphaGo etc, so that is for sure not the best way to get good, and for sure not the way humans get good, humans get good similar to how AlphaGo gets good, not how deep blue did it.
No, it is precisely the other way around. DeepBlue is deducing how good a board state is by trying to calculate all possible follow-up moves up to a depth of 13 or something. In contrast, AlphaGo has memorized patterns occuring in billions of games (in a lossy archive format, of course) and basically can recall games that are close enough to the current game and what you need to do to win from the current position. And this is exactly how chess masters mostly work as well, to the extent that it has been studied, and based on their own reporting. They just recognize positions or certain aspects of a position, and can recall how the game works from that position.