Geometric Group Theory, Geometric Topology, Hyperbolic Geometry, Discrete Subgroups of Lie Groups, Arithmetic Groups, Reflection Groups, Coxeter Polytopes

Great theories are expansive; failures mire us in dogmatism and tunnel vision.

Philosophical theories or ideas, as points of view, instruments of criticism, may help us to gather up what might otherwise pass unregarded by us. “Philosophy is the microscope of thought.” The theory or idea or system which requires of us the sacrifice of any part of this experience, in consideration of some interest into which we cannot enter, or some abstract theory we have not identified with ourselves, or what is only conventional, has no real claim upon us.

The final test of a theory is its capacity to solve the problems which originated it.