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be captured in beautiful formulae. In this lecture I want to argue for the reverse effect: Nature is an important source of inspiration for mathematics, even of the purest kind. In recent years ideas from quantum field theory, elementary particles physics and string theory have completely transformed mathematics, leading to solutions of deep problems, suggesting new invariants in geometry and topology, and, perhaps most importantly, putting modern mathematical ideas in a `natural’ context. ---- visit Perimeter Institute's website to find this and other speakers http://www.perimeterinstitute.ca/video-library http://pirsa.org/