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Published online by Cambridge University Press: 25 June 2025
This introduction to TheEightfold Way and the Klein quartic waswritten for the sculpture's inauguration. On thatoccasion it was distributed, together with theillustration on Plate 2, to a public that includednot only mathematicians but many friends of MSRIand other people with an interest in mathematics.Thurston was the Director of MSRI from 1992 to1997.
Mathematics is full of amazing beauty, yet the beautyof mathematics is far removed from most people'severyday experience. The Mathematical SciencesResearch Institute is committed to the search forways to convey the beauty and spirit of mathematicsbeyond the circles of professionalmathematicians.
As a step in this effort, MSRI (pronounced “Emissary“)has installed a first mathematical sculpture,The Eightfold Way,by Helaman Ferguson. The sculpturerepresents a beautiful mathematical constructionthat has been studied by mathematicians for morethan a century, from many points of view: geometry,symmetry, group theory, algebraic geometry,topology, number theory, complex analysis. Thesurface depicted by the sculpture was discovered,along with many of its amazing properties, by theGerman mathematician Felix Klein in 1879, and isoften referred to as the Klein quartic or the Kleincurve in his honor.
The abstract surface is impossible to render exactly inthree-dimensional space, so the sculpture should bethought of as a kind of topological sketch. Ridgesand valleys carved into the white marble surfacedivide it into 24 regions. Each region has 7 sides,and represents the ideal of a regular heptagon(7-gon). The 24 heptagons fit together in triples at56 vertices.
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