32 November/December 2020
ILLUSTRATIONBYALYSE^ MARKELDeep Math
9
// BY CAROLINE DELBERT //Two
Mathematicians
Just Solved
a Century-
Old Geometry
Problem
I
N 1911, GERMAN MATHEMATICIAN OTTO
Toeplitz first posed the inscribed square
problem, predicting that “any closed curve
contains four points that can be connected to
form a square.” A proof for Toeplitz’s theory
still eludes experts, but according to Quanta
magazine, two mathematicians in quaran-
tine have taken a huge leap toward a solution.
Imagine a serpentine belt in an engine. Like a
closed curve, it can settle into almost any shape,
as long as there are no “corners.” Toeplitz sug-
gested that in any of these shapes, there must
be four points along the curves that, when con-Researchers have
finally proved that all
continuous, closed
curves contain four
points that create a
rectangle (fig. 1).