October 30, 2024
The University of Chicago receives a mathematical wonder
On October 28, a Hungarian diplomat delivered a curious mathematical object to its new permanent home at the University of Chicago: a convex three-dimensional metal sculpture called a Gömböc.
Roughly pronounced “GUHM-buht,” the structure is “the first known homogenous object with one stable and one unstable equilibrium point,” according to the Gömböc website. This means that if you set it down on a horizontal surface in just about any position, it will return to its stable orientation, similar to a Weeble toy. Weebles wobble but they don’t fall down because they are weighted at the bottom, but a Gömböc’s ability to self-right is derived from its shape.
Yet, there is an unstable equilibrium point on the opposite side of its favored surface. It is possible to carefully balance the object on that point, but the slightest disturbance will make it topple, like a pencil balanced on its tip. The unique shape has inspired engineers, artists, and even vaccine developers.
The sculpture is a gift from Hungarian scholar Gábor Domokos, a professor at the Budapest University of Technology and Economics and one of the inventors of the Gömböc. This particular sculpture, created for the University of Chicago and named G1890 for the year of the University’s founding, is part of a program that places Gömböcs in renowned universities and museums.
The donation program, founded and sponsored by Hungarian investment banker Ottó Albrecht, aims to “establish visible cultural links to prominent academic institutions worldwide,” said Domokos.
Matthew Stephens, Statistics Department chair and Ralph W. Gerard Professor in the Departments of Statistics and Human Genetics, and the Committee on Computational and Applied Mathematics, received the special sculpture from Consul General Balázs Mártonffy and Economic Attaché Tamás Molnár from the Consulate General of Hungary in Chicago.
G1890 now resides in a custom-built cabinet on the second floor of George Herbert Jones Laboratory, home to UChicago’s Department of Statistics and the Committee on Computational and Applied Mathematics. Jones is a fitting home for the Gömböc as stability is a concept reflected in statistics as well as applied and computational mathematics.
Statistics professor Lek-Heng Lim explains that "a stable probability distribution is an essential concept in statistics, the stability of differential equations is a mainstay of applied mathematics, and the numerical stability of algorithms ensures accurate results in computational mathematics." Lim, who won the 2017 Stephen Smale Prize, whose insignia is an individual Gömböc model, adds: “An unstable equilibrium underlies the phenomenon of spontaneous symmetry breaking, which is paramount to several of my colleagues’ research.”
Domokos hopes that the exhibit will pique the curiosity of visitors. “The Gömböc is the visible, tangible proof of a conjecture of a mathematical giant, Vladimir Igorevich Arnold,” said Domokos. “It is rare that deep mathematical ideas can be expressed in physical objects, and this is one prime example.”