In view of two-dimensional topological gravity coupled to matter, we study the Seiberg-Witten theory for the low-energy behavior of N=2 supersymmetric Yang-Mills theory with ADE gauge groups. We construct a new solution of the Picard-Fuchs equations obeyed by the Seiberg-Witten periods. Our solution is expressed as the linear sum over the infinite set of one-point functions of gravitational descendants in d<1 topological strings. It turns out that our solution provides the power series

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... around the origin of the quantum moduli space of the Coulomb branch. For SU(N) gauge group we show how the Seiberg-Witten periods are reconstructed from the present solution.