Foundations of Mathematics and Physics One Century After Hilbert: New Perspectives

Preface : Where we stand today, Joseph Kouneiher.- Mie's Electromagnetic Theory of Matter and the Background to Hilbert's Unified Foundations of Physics, Leo Corry.- Hilbert and Einstein, Joseph Kouneiher, John Stachel.- Grothendieck on foundations for the rebirth of geometry, Colin MacLarty.- Understanding the 6-Dimensional Sphere, Michael Aityah.- A dozen problems, questions and conjectures about positive scalar curvature, Misha Gromov.- Geometry and the Quantum, Alain Connes.- What Every Physicist Should Know About String Theory, Edward Witten.- Quanta of Space-Time and Axiomatization of Physics, Ali Chamsddine.- Twistor Theory as an Approach to Fundamental Physics, Roger Penrose.- What are we missing in our search for quantum gravity?, Lee Smolin.- A schema for duality, illustrated by bosonization, Jeremy Butterfield and Sebastian de Haro.- The dressing field method of gauge symmetry reduction, a review with examples, Thierry Masson et al.- Syntactic Phylogenetic Trees, Matilde Marcolli.