A Graeco-Latin square of order "n" is an "n[superscript x]n" array whose entries are the "n"[superscript 2] ordered pairs of numbers from 1 to "n", and in each row and each column the first elements of the ordered pairs are all different, as are the second elements. This article traces the history of the results that came out of work on a false conjecture of Euler, namely, that there are no Graeco-Latin squares of an order congruent to 2 modulo 4. The story covers more than two centuries, involves more than twenty researchers from five countries, and the proofs used.