A talk given by Edward Witten, of the IAS, at Atiyah80: Geometry and Physics (in honor of Sir Michael Atiyah's 80th birthday), held at the Royal Society of Edinburgh in April of 2009. The conference website, which includes the videos as well as numerous other interesting features, can be found here: www.maths.ed.ac.uk/~aar/atiyah80.htm The slides for this talk can be found at the following address: www.maths.ed.ac.uk/~aar/witten.pdf The reference for this talk is: www.maths.ed.ac.uk/~aar/wittenpaper.pdf