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In the 1780s, Leonard Euler  demonstrated methods for constructing Graeco-Latin squares where n is odd or a multiple of 4. He further proved that no 2×2 square exists and conjectured that none existed for n=4k+2, where k is a natural number.

In 1901, Gaston Tarry demonstrated that there was no 6×6 square by enumerating all the possible arrangements of symbols. However, in 1959, Parker, Bose and Shrikhande constructed a 10×10 square.

In 1978, the French writer Georges Perec used the 10×10 square (believed then to be the only one possible) for the structure of constraints underlying his novel Life: A User's Manual.