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Obsessions of great mathematicians intrigue me because I believe that these stem from deeper intuition and perhaps even ‘revelations’ about truth.  I held on to my convictions regarding an S4 universe for four years before the redshift result which is solid quantitative evidence for it for various reasons of which the obsession of Hamilton regarding quaternions was one.  The four-sphere, as is well-known, is the quaternionic projective line and surely hides a rich mathematical structure which allows gravity and electromagnetism to coexist.  And Poincare’s obsession from his famous papers on dynamical systems where he worked on periodic solutions to the N-body problem was that these periodic orbits were the foundations for a Fourier-series like theory.  With the work of many people of whom I cite Vieri Benci who showed that periodic solutions exist for reasonable Hamiltonian systems in compact manifolds and James Ralston who has constructed quasimodes concentrating on periodic solutions of the classical system, we have a fulfillment of showing how the quantum mechanical system in the case of compact manifolds is approximating classical periodic solutions with an element of stochasticity.  Thus here we have a sort of fulfillment of Poincare’s obsession. When working on a four-sphere of appropriate radius, we don’t deal with a ‘semiclassical analysis’ at least from the approach I have taken.  We can say that Schroedinger equation is an approximation of the classical Hamiltonian and $h$ appears naturally in the shape of the universe.  Thus one could say that Poincare’s intuition and obsession with periodic orbits perfectly hit the correct physics.  Of course in between many great and talented people had paved the path, but Poincare’s instincts were extraordinarily sharp regarding the actual universe.