Mathematical Structures 1170 One could also question whether we are looking for a single overarching math-
ematical structure or a combination of different complementary points of view.Does a fundamental theory of Nature have a global definition, or do we have to
work with a series of local definitions, like the charts and maps of a manifold,
that describe physics in various “duality frames.” At present string theory is
very much formulated in the last kind of way.
0 As a whole, the study of quantum geometry takes on the form of a mathematical
program, very much like the Langlands Program. There are many non-trivial
examples, strange relations, dualities and automorphic forms, tying together
diverse fields, with vast generalizations, all in an open ended project that seems
to encompass more and more mathematics.
0 Finally, there should be word of caution. To which extend should mathematics
be a factor in deciding the future of theoretical physics? Is mathematical ele-gance a guiding light or a Siren, whose song draws the Ship of Physics onto the
cliffs? Only the future will tell us.Acknowledgement
Let me end by thanking the organizers of the XXIII Solvay Conference, in partic-
ular Marc Henneaw and Alexander Sevrin for their tremendous efforts to arrange
such a unique and stimulating scientific meeting following a distinguished tradi-
tion. Let me also congratulate the Solvay family on their long-time commitment to
fundamental science by which they are setting an example for the whole world.
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