Although it is interesting to consider that the universe may be the physical instantiation of all mathematics, there is a classic principle for restricting the possibilities: The mathematics of the universe should be beautiful. A successful description of nature should be a concise, elegant, unified mathematical structure consistent with experience.Even if you don't understand elementary particles, you should marvel at Lisi's use of the exquisite E8 lattice (a 120-year old puzzle solved early this year by MIT) to unify gravity with electromagnetism and the strong and weak forces. [Better yet, take about 20 min to first explore The Particle Adventure, an excellent web introduction to elementary particles.] The rotating E8 lattice makes a remarkable 2-min YouTube video.
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