A more mature appraisal of Tegmark's Mathematical Universe HypothesisThe thesis that all physical things are mathematical and that all mathematical structures are physical. - it includes an important survey of many important but lesser-known philosophical and mathematical ideas. Later, I argue that the assumptions built into MUH aren't very good but show an alternative approach that would lead one to Pythagoreanism anyway - that we need to blend these two into a better hierarchy of ontological concepts.