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Numerical homotopy continuation of solutions to polynomial equations is thefoundation for numerical algebraic geometry, whose development has been drivenby applications of mathematics. We use numerical homotopy continuation toinvestigate the problem in pure mathematics of determining Galois groups in theSchubert calculus. For example, we show by direct computation that the Galoisgroup of the Schubert problem of 3-planes in C^8 meeting 15 fixed 5-planesnon-trivially is the full symmetric group S_6006.

Galois groups of Schubert problems via homotopy computation