An international group of mathematicians hopes to do for math what Dmitri Mendeleev's periodic table did for chemistry by identifying the shapes in three, four, and five dimensions that cannot be divided into other shapes-the elemental "atoms" of geometry. Borrowing techniques from theoretical physics, they plan to sift through some 470 million 4D shapes in search of a few thousand fundamental building blocks. "We're using physics as a lens to view the mathematics," says team leader Alessio Corti of Imperial College London (ICL). Mathematicians have already identified all the 2D and 3D basic shapes-called Fano varieties-but need new methods for higher dimensions.
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