I don't think that's actually the best way to be great at chess, or math.
On chess, from a GM: "The key to their success is that they kept playing a lot, and learning from stronger opponents. Don't get me wrong: I am not suggesting stone age technologies in studying. Of course, you should take advantage of the best modern learning methods. However, the most important component of success (at least at weak GM and below level) is practice."
Well, wrt chess, we can have dueling GM quote battles over this point:
From "Andrei Istratescu's top 10 reasons for stagnation:"
1) Too much play
Playing chess - practice - is very important for improvement. When you play chess (over the board, at tournaments), you put into practice what you have learned, you use your brain to think chess, you are in the testing environment, you test your accumulated knowledge and skill against another person.
However, too much play and too little study holds you back. You can repeat the same mistakes over and over. You will tend to follow your own old patterns and not have time to develop a different, correct thinking process, and to learn proper strategy and new ideas.
In this case, you should take a long break from playing and concentrate only on study for several months. You will make a significant improvement.
In my experience, the first chess book I read (Logical Chess, Move by Move) probably bumped my rating by 400 points. Then, more specialized openings and tactics books another couple hundred. After that, simply playing got me mostly nowhere.
In chess below the master level tactics will dominate. How do you get really good at tactics? Not just by playing lots of chess, but by consistently devoting effort to studying tactics via printed collections of positions and/or tactics training software.
As to becoming great, after years of running chess camps for young players IM Greg Shahade formed his somewhat famous hypothesis:
There is one very reliable sign to how much potential and how strong a young chess
player is or is going to be, and it’s probably not what most people would think.
It’s not how quickly a student solves tactics or sees combinations (although
these two things always seem to be correlated with the main point of this article).
It’s not the student’s positional understanding. It’s not even how much they
claim to study chess.
Instead it is “How likely is this student to recognize a famous game/position
and know the players involved?” [1]
As one data point illustrating Shadade's point, the current world champion seems to be a whiz at what ordinary people would consider chess trivia. [2] Carlsen's comment:
"I like chess, I like chess books. You'd be surprised – I do read
as much chess as I can."
Completely agree. I never truly understood discrete math until I had to teach it. I didn't understand sales until I ran a vendor booth for my wife's sci-fi novel. I didn't understand ballistics until I built model rockets and potato cannons from scratch. I didn't understand cooking until my coworkers at Waffle House marooned me at the grill during a Sunday morning rush. I didn't understand linear algebra until I had to write a software rasterizer and a best-fit modeling function. I didn't understand money management until I was poor. I didn't understand relational algebra and database systems until I wrote an ORM. I didn't understand digital electronics until I had to build a kiosk system from scratch (for a client!). I didn't understand analog electronics until I had to build a music synthesizer. I didn't (really) understand AC until I had to rewire my house!
Maybe some people can read a book and just know how to do things based on that. I used to be very caught up into thinking I needed a book to learn things. But that's not really me. I have to do. Most books aren't written in that regard. The authors want to pontificate on minutia. Now, I know I just need to jump in the deep end of making something and--somehow, be it through Wikipedia or Wolfram Alpha or StackOverflow or MSDN or MDN or what have you--I will learn what I need to get it done. Give me a cheat-sheet, some pliers, and a bail of wire any day. Until then, it's all just noise.
I think it ties in naturally to the Lean Startup ideology, i.e. the whole "release early, release often" thing. Using the example of chess, if you're just reading books on chess and are not playing games, then you're no better off than a startup who is working out of someone's basement, no marketing plan, no market feedback, just coding away based on some blue-sky ideology. "Release early, release often" isn't so much about success as it is about getting out of the basement, seeing the flow of things, and opening your eyes to reality.
When I was in "prépa" (see https://en.wikipedia.org/wiki/Classe_pr%C3%A9paratoire_aux_g... ) my English teacher, an American told us that the way he saw the system was to train us at math, just as a way to discriminate us between those who'll get to pick the best school and those who will take what's left. And he said, they might as well train you to do chess for 2 years and let the strongest one pick his school.
He also told me that back in the US where he came from, with his local chess club he went to a prison play with the inmates. They got destroyed, because the inmates played chess all day long so they were all very good.
a lot of people out there don't have access to mentors, so I (unfortunately) feel that the self-learning by books approach is still the most practical, generally speaking.
This is a pattern of behavior I see in people, that they think they need a "mentor" to get good at anything. I've even had people explicitly ask me to be their mentor. Like, people here, on HN, reading my comments, contacting me through my email address in my profile, asking me to be their mentor.
Frankly, now that I'm experienced, if someone were to agree to be my mentor when I was a beginner, I should have been suspect of their expertise, because I don't know anyone who is actually any good at what they do who has time to do anything called mentoring.
Where does this idea of mentorship come from? I have never seen it. I've had examples in my life of people to look up to, but when people talk about mentorship they seem to be talking about some sort of creepazilla relationship where the student sits at the feet of the master and receives wisdom. Yeah, no, that doesn't exist in the real world, at least not for the vast majority of people.
If that's what it takes to be successful, to be reallly good at anything, then buddy, we're all in a world of hurt. It's an appealing idea, but who the hell does it ever actually happen to? I'm convinced it's a fantasy.
Strictly speaking, you don't need a mentor to get good at anything. However, it can really help in the areas that are defined more by people than by things working or not.
As a mentor, I have found that is mostly about reviewing others work and thinking and giving feedback. For instance, you don't really need a mentor to get better at solving problems. You may need a mentor to help you communicate details about the solution.
On chess, from a GM: "The key to their success is that they kept playing a lot, and learning from stronger opponents. Don't get me wrong: I am not suggesting stone age technologies in studying. Of course, you should take advantage of the best modern learning methods. However, the most important component of success (at least at weak GM and below level) is practice."
http://www.chess.com/article/view/getting-better-in-chess-cr...
Math is similar. You really have to do math. Reading books and watching other people do math is not the critical part.