Abstract:

Geometry is the most ancient of mathematical disciplines and Euclid is its most famous expositor. It was Gauss who first dared to raise the question whether the geometry of the physical space we live in is Euclidean, and made empirical observations to test this.

However it was Riemann who understood that this question really does not make complete sense, and that only a composite structure consisting of geometry and physics can be tested against experience. Riemann was followed by Einstein who showed that physical phenomena already required that space be replaced by spacetime and that its geometry was highly noneuclidean.

In recent years, as what we know about the physical world has forced us to probe into ever smaller regions of spacetime, it is becoming clear that radically new models of spacetime are needed to organize and predict fundamental phenomena. In the 1970's a series of bold hypotheses were advanced by physicists which suggest that spacetime is a geometricl object of a type not investigated by mathematicians hitherto, called superspace.

In this talk I shall try to present a historical account of these ideas and point out some surprising consequences and predictions of the concept of superspacetime. Many people believe that in the Large Hadron Collider (LHC) being built now at CERN we may be able to see some of the predictions realized materially.