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Inside the symmetries of a crystal shape, a postdoctoral researcher has unearthed a counterexample to a basic conjecture about multiplicative inverses.
Representation theory was initially dismissed. Today, it’s central to much of mathematics.
New findings are fueling an old suspicion that fundamental particles and forces spring from strange eight-part numbers called “octonions.”
A type of symmetry so unusual that it was called a “pariah” turns out to have deep connections to number theory.