====== Neil Spalter (Binghamton) ====== ====== ====== ===== Abstract for the Combinatorics Seminar 2012 November 6 ===== After 150 years, Euler's conjecture that there is no pair of orthogonal Latin squares of order 6 was proved by Tarry around 1900. The proof was long. Almost a century later, two short proofs were found. I will present one of them, due to Stinson in 1984. ----