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Myself, I would vote Stienitz. He, alongside Tarrach, established the Modern School, and debased the Romantic School, almost overnight.
And a close second to Nimzovitch, who along with Reti, invented the Hypermodern School. This never managed to debase the Modern School as it was intended to do. But it has certainly proven itself the Modern Schools equal.
Then there was the Soviet Revolution which took place in the late 40's, and throughout the 50's. As game-changing as either that I mentioned above, this School has never been attributed to a single person. Most likely included Bronstien, Keres, and Botvinik.
But I still vote Stienitz.
Silman is perhaps the best chess author out there today. His work is a joy to read. But his work is simply instructional. It is only designed to help us beginers catch up. "Influential" implies that you work to move the State-Of-The-Art forward. Silman nutures others to learn that art, so that hopefully one of them can someday be the person who makes those exciting new discoveries.
I nominate that daft king who agreed to give 1 grain for square 1, 2 grains for square 2, 4 grains for square 3 ... because this is the first time when many of us hear about a chessboard
Rofl I forgot about him.
If i remember correctly, he chose to decapitate that sage, rather than pay up.
I would advise beginners to read the following strategy books (in order):
Chess the Easy Way, by Reuben Fine This should be everyone's first and second chess book.
Simple Chess, by Michael Stean
Judgment and Planning in Chess, by Max Euwe
The Ideas Behind the Chess Openings, by Reuben Fine [get a version written in descriptive notation...I recently bought the algebraic version and it has a zillion typos]
The Middle Game in Chess, by Reuben Fine [I got a hardcover version in descriptive from 1952(!) recently on Amazon, having seen the horrible reviews of the algebraic edition] This is my new #1 Chess Strategy book recommendation. Yes, folks: a book from 1952 written in DN. The classics will not let you down!
What do the books above have in common? They get to the point without too many words and without trying to be entertaining. You will learn more chess, and faster, with less confusion.
This is the problem with authors like Watson, Silman, and to a lesser extent, Nunn. Get to the freaking point! Chess study is not storytime. Tell me what I need to do so that I can execute it in games.
But a lot of beginners will ignore me and still argue that Silman is one of the "best" authors out there...
The Ideas Behind the Chess Openings by Reuben Fine is available in descriptive notation as a free download here at Chess.com in the downloads section.
I'd much prefer an algebraic version but not if had a bunch of typos like you said.
Frankly, I found Silman's endgame book to get directly to the point and didn't tell any stories or anything like that...pure easy-to-understand and actionable instruction.
This, of course, is only my personal experience after reading dozens of chess books and finding many to just be a "puzzle dump" or otherwise out of touch with what the beginner can understand.
For a technical endgame book I would recommend Essential Chess Endings by GM James Howell. Another one that I love is Chess School 4 by GM Sarhan Guliev.
For strategic endgames, Endgame Strategy by IM Mikhail Shereshevsky is the gold standard.
Why has an interesting topic urned into a favourite book topic now?
I agree that Krylenko probably contributed more to chess than anyone else as far as popularizing the game in the Soviet Union, although it was a closed society and the chess popularity was not spread outside the USSR until after WWII. Krylenko was equvalent to the US Secretary of Defense and the Chief Justice of the Supreme Court until Stalin had him murdered for becoming too powerful. He was one of the most hated men in Europe (in charge of Stalin's purges), and perhaps the most hated man until Hitler came along. He was the chairman of the chess section of the USSR All-Union Council for Physcial Recreation (would any other country have chess as part of physical recreation? Not the USA). He was able to get State sponsorship of chess as early as 1925. He was not a strong player himself. He was below expert strength. In 1918, the USSR abolished the death penalty. As chief justice, he sent admirals and generals to the firing squads. He declared that they were going to be shot, not executed (twisted logic). He changed the name of Russian concentration camps to "corrective labor camps." He marked out 5% of all peasants to be exterminated. He had 2,550 people executed alone in 1924. It got worse in later years. If you liked Fischer and his rantings, you would love Krylenko. Source: Stalin and His Hangmen by Donald Rayfield.