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Chess Math by Dr. Harvey Friedman

Below is an explanation of Chess Math by Harvey;

Greetings from Harvey M. Friedman, who is interested in mathematics, piano, and chess!

I have been talking to Courtenay about a December 1 meeting of the CCL community. Here are the plans.

We will meet at 1 PM on the second floor of Harrison on Fifth, 579 W. 5th Avenue, Columbus, Ohio 43201. This is near Grandview and opposite Batelle. Parking is available here and nearby. Snacks and drinks will be available. Additional food items will be determined. The meeting will last through 5 PM, with flexibility for late departures for chess-related activities. The lectures will be given with a TV screen(s) within everyone's sight.

1:00 PM - 1:30 PM. Meet and greet and get settled into the venue.

1:30 PM-2:30 PM. Mathematical Chess/1. Lecture presentation by Harvey Friedman, Distinguished University Professor of Mathematics, Philosophy, Computer Science Emeritus, and Professor of Music for ten years, all at the Ohio State University in Columbus.

Harvey will discuss several mathematical aspects of chess that make it a particularly rich resource for mathematics and computer education at the elementary, middle, high school, undergraduate, and postgraduate levels, as well as a rich source for challenges at the professional mathematical research level.

Harvey is planning a series of lectures on Mathematical Chess, to form the basis for a book on the topic.

2:30 PM - 4:30 PM. Informal discussions and chess playing.

4:30 PM - 5:00 PM. GoChess. Second Lecture by Harvey Friedman. Harvey will present his chess variant which combines the spirit of Go together with standard Chess. GoChess is played with the standard chessboard and pieces with no extra pieces available for pawn promotions. GoChess has two phases. In the first phase (the Go-like phase), the players alternately place all 32 pieces on the empty board with no checks allowed. In the second phase, the players play standard chess starting from the position just set up. Harvey will present a few GoChess games he has played with Alan. The current plan is to organize a CCL GoChess tournament with $1000 in prize money. A trial tournament will be arranged to qualify for the prize tournament, as this game is entirely new.

We attach some details concerning ideas planned for the Mathematical Chess/1 lecture.

1. Elementary mathematics at the elementary school level. Chess squares as points in geometry, (i,j), 1 <= i,j <= 8, 8x8 = 64 squares. Rows, columns (ranks, files), diagonals, planar addition, black/white squares mathematically. But light on algebra. Etc.

2. Basic mathematics at the middle school level. Thorough treatment of 1 with standard mathematical notation. Exact mathematical descriptions of the way the pieces move and capture. Chess distances between squares. Symmetries of the chessboard are treated mathematically. Etc.

3. Mathematics at the high school level. Mathematical definition of a (two person, perfect information, 0,1/2,1 payoff) game. Mathematical definition of a winning and a drawing strategy. Strategy theorem stated carefully (not proved). Showing that chess is a game through an exact mathematical description of the rules of chess. Retrograde analysis is used to create endgame databases. Retrograde analysis theorems stated carefully (not proved). Chess distance theorems (not proved).

4. Mathematics at the gifted high school level and undergraduate level. Proofs of theorems stated in 3. Game trees and basic ideas in chess engine search.

5. Mathematics at the graduate level and the professional mathematical research level. Work in progress will be discussed in future lectures.

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