Two mathematicians just solved a century-old geometry problem

IN 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 quarantine have taken a huge leap towards a solution.

Imagine a serpentine belt in an engine. Like a closed curve,). Researchers proved this for ‘smooth, continuous’ closed curves in 1929, but throughout the COVID-19 quarantine, modern mathematicians Joshua Greene, of Boston University, and Andrew Lobb, of Durham University, sought to generalise the proof from squares to all kinds of rectangles, broadening Toeplitz’s ‘square peg problem’ into a ‘rectangular peg problem’.