The conjecture that the number of alternating sign matrices "bordered" by +1s A_n is explicitly given by the formula A_n = product_(j = 0)^(n - 1) ((3j + 1)!)/((n + j)!). This conjecture was proved by Doron Zeilberger in 1995 (Zeilberger 1996a). This proof enlisted the aid of an army of 88 referees together with extensive computer calculations. A beautiful, shorter proof was given later that year by Kuperberg, and the refined alternating sign matrix conjecture was subsequently proved by Zeilberger (Zeilberger 1996b) using Kuperberg's method together with techniques from q-calculus and orthogonal polynomials.
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