See here and here; using the E8 mathematical structure, a man by the name of Garrett Lisi has proposed a new model of physics that basically explains the Standard Model and predicts a few new particles that the LHC may be able to detect next year. This sounds cool. Here‘s his paper. Oh also, since it uses only the geometry he did this without calculus!
Note: This is technically not peer-reviewed research yet, it has only been submitted online to a free online paper-publishing site, so holes may yet be found, or not.
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