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The number of Feynman diagrams which contribute (even at the classical level) to an n-particle scattering amplitude in Yang-Mills theory grows faster than factorially with n. The construction of more efficient computational methods which also expose otherwise hidden mathematical richness has benefited substantially from string theory input. In my talk I will show how to calculate scattering amplitudes from the topological B-model on the Calabi-Yau supermanifold P^{3|4} as an integral over the moduli space of degree d curves, as suggested recently by Witten. I show that in this formalism, the calculation of Feynman diagrams is recast into the problem of solving a certain set of algebraic equations.