formal · 1913 to 1927

Zermelo and Borel: The first theorems of the game

Before game theory had a founder, two mathematicians proved its first theorems: one showed chess has a determined answer, the other showed that in some games your only rational move is to be unpredictable.

Facts reviewed 2026-07-11.

Ernst Zermelo was a German mathematician best known for his foundational work in set theory. Emile Borel was a French mathematician who helped build modern probability theory. Neither set out to found game theory, and neither is usually remembered for it, but each proved a result that the field was later built on.

They worked before the subject had a name or a framework. Their theorems were isolated insights, recognized only in hindsight as the first rigorous statements about strategic games.

In 1913 Zermelo proved a theorem about chess: in a finite game of perfect information with no chance, one of the players has a guaranteed strategy, either a forced win or at least a forced draw. The outcome is determined by the structure of the game, even though no human can compute it for chess. That was the first formal theorem about strategic games, establishing that such games have a mathematically definite answer.