Just to chip in on maths..

Doing "drills" for maths - working through proofs etc is an awful idea beyond a point. If you're teaching 18 year olds basic maths (e.g solving basic differential equations) there is some merit in rote learning but at higher levels you learn through challenge and enjoyment of that challenge.

As a parallel.. you will never become a good writer by learning all the definitions of all words in the dictionary or even being a fully conversant in all the nuances of grammar. You won't even become a good writer by reading lots of good books.

Go has the well known nickname shudan (手談), with the literal translation "hand talk". This describes go in two ways. First, every move you make is a declaration of something to your opponent, so as the game progresses the moves form a conversation of sorts. Second, every move you make shows something about your thinking and state of mind. Because of this a good mental attitude and self-confidence are necessary to play strongly. You need self-knowledge and confidence to hold up your end of the conversation/argument successfully.

I think that I can understand your point, but I think that I have fear of failure, at least, in other areas of life, including doing a math test, for example (although, I'm not that knowledgeable about philosophy).

I do feel, however, that this feeling is stronger for me in go than in other areas of study.

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be immersed

This is very much false. Working through a bunch of proofs is quite literally the only way to learn higher mathematics.

How high are we talking here?

I've supervised maths students to Phd level and managed at post doc....

I'm still an undergraduate, but have been doing proof based courses for two years, and am starting with graduate courses later this month. I'm talking about anything at a similar level.

What would you say is the way to get better than math, if not to work through proofs, and write one's own?

IMO, in mathematics, proofs are useful to get a real understanding of a particular idea.

Without being able to prove something is true (within a system like mathematics), how can you say that you understand it?

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be immersed

i think mathematics are as much an art as playing go. in go you can choose a good move based on intuition and get away with it, in mathematics you have to make an exact proof. but while proving, you often need your imagination and creativity to find the correct way to link your knowledge and given premises with the final result. in a way, i think go requires less creativity than proving mathematical thesis'

as for improving at go, i could shorten my method (analogue to principles already mentioned) to "don't try to approach kami no itte, try to get further from baka no itte"

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Spilling gasoline feels good.

I might be wrong, but probably not.

I've never met a good writer who hasn't read lots of good books.

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Patience, grasshopper.

I think we can square this circle by putting it this way: math students at the master's level are like insei or 1-dan professionals. Most of their drilling is behind them, but they still are plowing through the Igo Hatsuryon. But once they're ABD, even if some continue to drill the basics, that's a personal preference; the main ways to get better at this point are studying pro games (both the classics of the field and the latest uploads to arxiv) and playing your own games.

Try to prove something new?

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Occupy Babel!

Trying to prove something new is way beyond the ability of most students. I just spent the entire summer trying to do so, and did not get very far. In math, it's not unheard of for a student's first publication to be their thesis.

Try is the key word. You don't have to succeed to learn something, right? But also I've talked to students who had proved something, albeit not the kind of results you could base a whole paper on. You're still learning something about problem solving and doing proper research as you do that sort of work.

I didn't mean to suggest that first year grad students learned by going out and attempting to find substantial results that develop their field. Even in philosophy, which has a substantial "make it up as you go along" component, that doesn't happen. In philosophy, I think it works like this: good undergrads write a 20 page paper criticizing someone's argument. As a first year grad student you write a short paper on the same subject. When you're dissertating, you spend a page on it.

As a tenured professor, you write one sentence on the argument, and you get it wrong. But if you're good, the whole of your work has enough insights that it doesn't matter that you're saying false things all over the place.

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Occupy Babel!

Just like some of the comments in forum discussions here, eh?

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be immersed

That is true, but I'd say that it's more important while learning to actually work on problems with known solutions. It's like starting with tsumego with solutions before tackling that one from the igo hatsuryon.

For me it was always repetition and focusing on my strong points rather than my weak points, but then again I'm more of an instinctual player. I tend to let my intuition point out where the big spots are, and get a feel of where the big points are. I've done thousands of tsumego problems, but I have read little on strategy outside of "Attack and Defense" and "Lessons in the Fundamentals" which I think every Go player has read. For me, improving hinges ENTIRELY upon how well I can perform stone for stone reading. When I'm at the point where I just instantly know the vital points in a shape I start to go up in strength.

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Nein Mann, ich will noch nicht gehen, ich will noch 'n bisschen tanzen.

Why do you think that this is important? It's an interesting comment, I think...



Can you explain what you mean by this? These seem like contrasting ideas here: intuition vs. reading. Can you elaborate?

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be immersed

1. My strong point is finding tesuji and shape weaknesses and steering the game to exploit them. I fumble with full board thinking and finding the big points on the board. I used to try playing games where I didn't fight so that I could try and resolve this weakness, but it didn't work out really well. Instead I got better at steering the game so that I felt comfortable.

2. When I pick my next move I literally just see the next spot in my mind like the point on the board is lit up, or a general area. Then I start working out the details. Whenever I feel more confident that the sequence I see in my head are good or are correct I am getting stronger. I'm a meticulous reader. I once spent 20 minutes a tournament reading out 5 different branches of one sequence. The fight was for the life of a group so it was important that I not screw up. I won because there was nothing he could do that I hadn't already planned for and hadn't read out 10-20 moves ahead.

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Nein Mann, ich will noch nicht gehen, ich will noch 'n bisschen tanzen.

Having reached 1k is a good indicator of a principle potential of becoming stronger because reaching 1k requires abstraction and reading abilities that are similar to those at higher levels. There is a major difference though: After 1k, the exponential growth of necessary effort and knowledge volume becomes relevant. (For some, it becomes relevant already at 5k.) Without much effort, you have little chance to improve. OTOH, 3d is still relatively easy. 4d+ is the really tough part. The knowledge required up to 1k doubles each time up to 3d, to 4d, to 5d.



Good, necessary and insufficient. You also need:
- reading ability
- problem solving accuracy
- positional judgement ability and accuracy
- improve your endgame
- psychologically overcoming of making blunders / big mistakes at all (average 5d means fewer than 1 per game on average)



Everybody has a preferred or most suitable learning style. Until a teacher knows your learning very well, you need to find out your best learning style by yourself.



Strength is a mixture of knowledge, reading, strategy, judgement, time-control, psychological control and probably more.



Sure... BUT strength is also blocked by your greatest weaknesses. Your 9p fuseki is useless if your reading is 1k - you will be 1k. To improve, you have to improve in MOST (or better: all) fields. All is not strictly necessary because each player has his relative weaknesses and strengths. Your strengths must be able to hide your weaknesses though. So a too great lag for weaknesses blocks your progress.



ONLY IF the above mentioned other fields are also improved AND none of your weakneses lags behind too much.

Besides extraordinary knowledge is useless if you cannot apply it.



That is part of the knowledge but does not cover all the other mentioned fields above.



Nonsense.



Yes.



Consiously or not - a priority making and selection is always necessary. (See Joseki 2, Strategic Planning.)



Insufficient. Almost always more than one aspect is necessary.

ez4u, to summarize a point of yours, more knowledge and analysis is required to then better reduce the information amount for the sake of choosing good moves.

I disagree WRT to mathematics. Mathematics is the most profound means to research in go theory. During a player's decision making, only results of mathematical research (propositions, procedures, values) are needed while the proofs can be ignored. It suffices to trust the mathematicians that their created results are correct and therefore truths. A player needs to apply some applied mathematics (e.g., when making positional judgement or endgame calculations).