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

I firmly believe people have hitherto been a great deal too much taken up about doctrine and far too little about practice. The word doctrine, as used in the Bible, means teaching of duty, not theory. I preached a sermon about this. We are far too anxious to be definite and to have finished, well-polished, sharp-edged systems — forgetting that the more perfect a theory about the infinite, the surer it is to be wrong, the more impossible it is to be right.

How can we possibly test, or improve upon the truth of a theory if it is built in such a manner then any conceivable event can be described, and explained, in terms of its principles? The only way of investigating such all-embracing principles would be to compare them with a different set of equally all embracing principles- but this procedure has been excluded from the very beginning.

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