Two Potentially Promising Books

Really? Sounds like BS to me.

I can name maybe 1 GM who "excelled in Math" John Nunn.

Ok, now you name... 5 world champs for me. Ok Maybe Lasker and Euwe... Botvinnik I think would be a stretch. That's 2.5

The book said: "It may seem surprising, but chess is not so much a game of deep thinkers as one of skilled perceivers." Substitute "distant lookahead" for "deep thinking" and "pattern recognizer" for "skilled perceiver" and you get the same intent I mentioned. The book is saying that lookahead ability seems not to be the key ability that makes a chessplayer good, but rather memory of similar patterns.

The practical application is evidenced in one of the most frequent FAQs you see posted in new threads here all the time: "How do I get better at tactics?" The current default advice amounts to "Here, kid. Read this chess puzzle book and you'll somehow get better." But some of those people don't get better, or if they do get better they often don't recognize when such a position arises in a game they're playing, or they might encounter a situation that doesn't match any pattern they've seen before, or they might encounter a need to look ahead farther than the usual 3-5 moves in puzzles, or they might fail because the tree was too thick, or whatever.

Computers haven't essentially changed since that book was published. Many people don't seem to understand that. All that has really happened since then is that computers have gotten faster, so they do the same stupid things they did in the '70s, only a lot faster. The terms I'm using are largely from computer science, which is my background.

http://www.chess.com/forum/view/general/how-computer-works-in-playing-chess

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(p. 6)

What about those com-
binations that missed their mark entirely or even boomeranged owing to a
hidden zwischenzug tactic or just an obvious defensive resource? Why
weren't they included in Fred Reinfeld's book? Even worse, I felt that a
reader of such books could hardly benefit in actual practice. After all, Fred
wouldn't be there to tap me on my shoulders during a championship game
and whisper to me, "Now Yasser. Now you can sacrifice a piece for a win-
ning combination!" It seemed to me that I'd more often miss a combina-
tion than not.

Seirawan, Yasser. 2006. Winning Chess Combinations. London: Gloucester Publishers plc.

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(p. 14)
   Shannon's type-A strategy has some serious weaknesses. First, one can-
not examine even a moderately deep tree in a practical amount of time. In a
typical chess position there are around 30 to 35 legal moves. If one were to
use the type-A strategy with a 4-ply lookahead, there would be about
1,000,000 terminal positions that must be scored and about 30,000 non-
terminal positions at which all legal moves must be generated. If one as-
sumes a position can be scored in 10 microsec and that a move generation
requires 1 msec (these figures are well less than one-tenth the amount
of time required by most current chess programs!), then a move would
require 40 sec. The type-A strategy with a 6-ply look-ahead would con-
sume about 1000 x 40 sec or about 1 hours per move! Thus it is clearly
impossible to look ahead more than four ply.

Newborn, Monroe. 1975. Computer Chess. New York: Academic Press.

Ok, I think I'm getting your point.  If I understand you right then I agree with what you're saying about training beginners.  I believe you're talking about the ability to see patterns vs the ability to (correctly) calculate the possiblities (and pick a move).  

There is both a visual and a logical piece to chess, and both need to be trained.  

Beginners need to know basic tactical motifs -- both what they look like (visual), and how they work (logical).  For the visual piece they need to know, for example, that a bunch of pieces in a line could be a tactic (pin, skewer, discovery, fork, etc), pieces on the same color square as the knight can be forked, or what loose pieces look like.  Then they learn the logical piece that generate candidate ideas like "attack pinned pieces", and "loose pieces drop off".  

Once a beginner has these basic concepts down, and has been taught to be aware of/look for (the visual piece) these things in their games, the next piece is the calculation step (or "deep thinking"/"lookahead" as you call it).

Say a beginner who has been taught to be aware of basic tactical patterns "sees" a bunch of pieces in a line, and thinks it might be a pin.  First of all that beginner needs to stop right there and do a happy dance!  Visually seeing patterns in games is a huge step for beginners.  It is frustrating as a more experienced player to watch beginners play, and you "see" lots of things happening (even though you might not have calculated any actual moves), but the beginner is completely clueless as to what opportunities are right in front of them.  As you improve, you learn to see more and more, and hopefully miss less and less.  There is a great quote about Kasaprov's ability to see things:

"I thought I was playing the World Champion - not some 27 - eyed monster who sees everything."  -  (on losing May 1986 match 5-1/2 - 1/2)  -  Tony Miles

Beginners have problems "seeing" things on the board in front of them.  More advanced players have problems "seeing" things several ply into the future -- for example, a series of captures could lead to a mate pattern that would be completely obvious if on the board in front of you, but is much harder to "see" deeper into al ine.  Exact same problem though.  

Ok, so back to the example...our beginner finished his happy dance, and goes back to looking at the pieces in a line.  What now?  This is now the "logical" piece, and where I agree with you training fails for beginners.  But this process is simply calculation and every beginner can learn some basic stuff.  The process is to generate a list of candidate moves, calculate each one to the end, evaluate the final position and pick the move that leads to the best evaluation.  It's not actually that hard to do, and there is a very specific logic used to calculate that anyone can learn.

Continuing with the same example, our beginner needs to compile a list of candidate moves.  In order to do that, he needs candidate "ideas".  Luckily he remembers something he heard once: "attack pinned pieces". So he starts to search for moves that attack the pinned piece.  Most beginners can get this far -- and it is at this point they begin to fail.  They find one move that attacks the pinned piece, does another happy dance, and makes the move...wondering how in the world his opponent is going to reply to his vicious tactic.  And then he gets mated.

The beginner needs to learn to do a few things.  First, identify as many candidate moves as possible based off of the candidate "ideas" you found when looking at the position.  Look wide first, not deep.  You should always try to force yourself to find more than one candidate move.  Second, calculate each candidate move to the end.  Look for your opponent's refutations first.  I have a whole blog series on how to do line calculation (I taught my daughter at 8 how to do this -- I call it the "logic of forced variations").  Third, evaluate the final position.  Beginners should just stick with a basic "material" only evaluation, and as you get more advanced you can add "activity" to your list.  But keeping track of what happens to your pieces and pawns during an exchange is really hard for beginners to do accurately.  Evaluation is a skill that will come with practice, and evaluating future positions can be pretty daunting.  So having evaluated the final positions, you either scrap both candidate moves because they suck and you have to start all over in looking for candidate ideas, or find you get something good out of one of the candidate moves and make that move.

The visual and logical are indeed very different skills, and I agree that beginners should learn/be taught how to calculate variations as part of learning tactics.  

Yes, you understand completely now. You don't need me anymore.

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(p. 47)
Visualizing positions

All this analysis is carried out in the player's head. How do players keep
track of the new positions generated in analysis? Keeping track involves
memory and some imagery and is susceptible to spatial errors. Occasionally
a blunder can be traced directly to the "imagining" operation. A player
will fail to "notice" that moving a piece to a certain square blocks another
piece from giving check at a later critical moment. (For an amusing
account of just such a hallucination see Chess Treasury of the Air [94,
p. 273].)

Frey, Peter W, ed. 1977. Chess Skill in Man and Machine. New York: Springer-Verlag.

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(p. 226)

Typical Psychological Errors

1. The "Impossible" Square

Very often a mistake results from improperly visualizing the
chessboard and pieces. When calculating variations, you have
only the current board position in front of you; consequently,
some features of that position may remain in your mind even
when you are visualizing a different position. Consider the
following example:

(p. 227)
   The explanation is quite simple. Look at the diagram again.
In the initial position the Black king cannot move to g8 for two
reasons--the bishop at b3 and the queen on the g-file. During
the calculating process, White subconsciously assumed that the
Black king could never go there. But after 2. Qh6+ Kxf7, the
bishop was gone from the board, and the queen no longer
covered the g8-square, so that Black was able to use the
"impossible" g8-square.

2. Disappearance of the Barrier

This is a different sort of error, but it bears some resemblance
to the previous case. In this example, White decides to crack
open the f-file:

(p. 228)
3. Forgetting about a Piece

This type of mistake is a variation on the previous theme.

(p. 229)
   Such absent-mindedness is a recurring theme at the board,
often leading to some sort of catastrophe.

Palatnik, Sam, and Lev Alburt. 2013. Chess Tactics for the Tournament Player. New York, NY: Chess Information & Research Center.

So the short answer is that you need to learn how to calculate :)

Kasparov is right-handed.

I have the Inner Game of Chess and it is really good.  Improve your Pattern Recognition has been on my radar since before it was released.

I have the former.  It's not bad at all.

You're confusing "excelled at math compared to math peers" and "excelled at math compared to the general population".  An engineer and computer scientist definitely has to excel at math compared to the general population.

Steinitz, Euwe and Botvinnik are three champs that excelled at math.  I expect you'll see less champs excelling at anything in later years as specializing in chess early on precludes having a real career.

I believe Alekhine had a PhD. I'm not sure in what field of study he obtained it.

Inner Game helped some people immensely. One person posted he believed that book along, teaching him that chess was all about calculation (his opinion), raised him 300 rating points.

Claims like this are dubious at best.  Which is not a knock on the book.

leiph18, Clearly you do not know all the masters and grandmasters that I do. Math is needed to get far in chess. Without you are going nowhere.

Perhaps. Nevertheless, multiple people have sworn this book helped them. Also, I am going from ancient memory. It may have been only 250 points lol.