Although Aristotle in general had a more empirical and experimental attitude than Plato, modern science did not come into its own until Plato's Pythagorean confidence in the mathematical nature of the world returned with Kepler, Galileo, and Newton. For instance, Aristotle, relying on a theory of opposites that is now only of historical interest, rejected Plato's attempt to match the Platonic Solids with the elements -- while Plato's expectations are realized in mineralogy and crystallography, where the Platonic Solids occur naturally.Plato and Aristotle, Up and Down-Kelley L. Ross, Ph.D.
Discover Magazine-06.16.2008-Photography by Erika Larsen-Article-"Is the Universe Actually Made of Math? Unconventional cosmologist Max Tegmark says mathematical formulas create reality."
It makes no difference at this point, which mathematics you choose to delve into the new model perceptions, because if one were to see how a projective geometry was built on previous platforms, then how is it we can see the universe in ways that the WMAP shows unless the mathematics could show that there was more to it then an artists picture displayed? You had to know the depth of the artists skill.
It does not mean that you are devoid of the possibilities of venturing where the philosophies of mathematics or science can venture. It is understanding that by taking yourself to a certain position in mind, an indecomposable one, one that is self evident, then it is understood that the deductive/inductive efforts bring you to a peak realization, contained in the "Aristotelean Arche."
This position is the question that one assumes in life, that having exhausted all efforts, and having seen all the information, one is to move their previous stalled position into a "third revolution" of a kind you might say?:)
See:Backreaction: Discover Interview with Tegmark
Also see:Theoretical Excellence