Proof of Ira Gessel’s lattice path conjecture

Abstract. We present a computer-aided, yet fully rigorous, proof of Ira Gessel’s tantalizingly simply-stated conjecture that the number of ways of walking 2n steps in the region x + y ≥ 0, y ≥ 0 of the square-lattice with unit steps in the east, west, north, and south directions, that start and end at the origin, equals 16