It seems Duchamp asked himself the same question. In 1920, after threatening to abandon the art world and study chess full time, he wrote, “Naturally this is the part of my life that I enjoy most.” His love of chess is evident in his work: The figures in The Large Glass recall rooks arranged carefully on a board. Duchamp wished to fuse art and chess. The popular opinion, espoused by historians, proposes that Duchamp saw the art world as a game, his opponent the entire history of Western aesthetics. (According to this theory, his infamous readymades were the equivalent of a checkmate.)

But anyone who’s played chess knows there is a difference between a game, where one player attempts to outdo the other, and a problem, which requires one to develop a scenario for another to solve. T...