Summary: String theory, on its modern incarnation M-theory, gives a huge generalization of classical geometry. Here the author indicates how it can be considered as a two-parameter deformation, where one parameter controls the generalization from points to loops, and the other parameter controls the sum over topologies of Riemann surfaces. The final mathematical formulation of M-theory will have to make contact with the theory of vector bundles, \(K\)-theory and noncommutative geometry.
For the entire collection see [Zbl 0972.00031].