"... string theory has uncovered beautiful relations between physics and different parts of mathematics, mostly differential geometry, enumerative algebraic geometry and complex analysis. In fact string theory started like this. At the very beginning when and others were starting string theory motivated by the for strong interactions they found solutions to the duality equations for the scattering amplitudes in terms of s and these were nice mathematical functions like generalized s which are very natural in terms of complex analysis. It was then realized, by and others, that these models could be understood geometrically from the propagation of strings. It is a very powerful idea to “test” a given complex space using the space of complex curves inside or of maps from s to that target space. And physicists could use all the arsenal of which is quite powerful. This generated a very interesting group of people that do a kind of “physics motivated” mathematics which rejuvenated some parts of complex geometry. They adopt a rather free attitude towards mathematics, which is original and productive and had a very positive influence. It started as mathematics and had a very positive impact on mathematics up to now."
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Alain Connes
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