Mills, Robbins, and Rumsey conjectured, and Zeilberger proved, that the number of alternating sign matrices of order $n$ equals A(n):=(1!4!7!...(3n-2)!)/(n!(n+1)!...(2n-1)!). Mills, Robbins, and Rumsey also made the stronger conjecture that the number of such matrices whose (unique) '1' of the first row is at the rth column equals A(n)[({n+r-2}\choose{n-1})({2n-1-r}\choose{n-1})]/({3n-2}\choose{n-1}). Standing on the shoulders of A. G. Izergin, V. E. Korepin, and G. Kuperberg, and using in addition orthogonal polynomials and q-calculus, this stronger conjecture is proved.