History of Mathematics

Day 2 (Wednesday 20 April) @ 11:30–13:00

Theories of chess have a longer tradition, but mathematical theories of the game date back slightly more than a century. None other than the later world champion Max Euwe in 1929 contributed with an intuitionist theory of chess. Euwe was one of the respondents in Adriaan de Groot’s ground breaking study Het denken van de schaker. In a twist of history, the book written as a psychology of chess was re-read as a stepping stone towards an Artificial Intelligence of chess. The session proposes a tour from the history of AI, to the mathematics of chess, and back to an interplay of AI and the psychology of chess.

Nathan Ensmenger (Indiana University)

From Deep Blue to Alpha Go: Games as the Experimental Organisms of AI

For almost fifty years, the possibility of a computer being able to play chess as well as a human being seemed to be the ultimate achievement of artificial intelligence.  The pursuit of this goal shaped the agenda of the discipline for decades.  More recently, Go has replaced chess as the game of choice among AI researchers.  This paper explores the role of games in the history of AI through the concept of the “experimental organism.”

Max Laboyrie (University of Amsterdam)

Euwe’s best move: Intuitionism and intuition in chess

In 1913 Zermelo embarked on a mathematical theory of the game of chess. The result was mathematics, but at the expense of such practicable notions he had wanted to determine as “best move” or “value of a position.” In the 1920s König and Kalmár generalised Zermelo’s results.

Then came Euwe, with a  mathematical treatise on the game of chess, based on the notion of “spread”. Brouwer’s intuitionist alternative for “set”, allowed Euwe to represent a sequence of chess positions in what appeared as a most natural way. Euwe even returned to Zermelo’s “best move.”

Outside mathematics, Euwe went on to become world champion of chess in 1935.

Han van der Maas (University of Amsterdam)

Psychology of chess: from Adriaan de Groot to Alpha zero chess

I will first present an overview of the psychological study of chess thinking. Chess research on both expertise and cognition has been strongly influenced by the pioneering work of De Groot (1946/1978). Chess has also been very important in the development of AI. However, programs such as Deep Blue mainly told us how humans do not play chess, as it depended on a brute force computing approach, evaluating 200 million positions per second, that humans are particularly bad at. The renewed interest in AI among psychologists is based on novel techniques that have also revolutionized computer chess in the last five years. AlphaZero chess (Silver et al., 2018) combines a deep learning network that values positions and predicts next moves, with a reinforcement learning system. Not only does this system play superior chess, it also provides new insight in human chess thinking.