Who Invented the Gromov-Hausdorff Distance?

TL;DR

This paper investigates the origins of the Gromov-Hausdorff distance, revealing that David Edwards introduced a similar metric six years before Gromov, and emphasizes the importance of acknowledging Edwards's contribution.

Contribution

The paper uncovers and highlights David Edwards's prior work on the Gromov-Hausdorff distance, which has been largely overlooked in the literature.

Findings

Edwards defined the metric in 1975, predating Gromov's work by six years.

Edwards proved the basic properties of this metric.

The paper advocates for recognizing Edwards's contribution to metric geometry.

Abstract

One of the most beautiful notions of metric geometry is the Gromov-Hausdorff distance which measures the difference between two metric spaces. To define the distance, let us isometrically embed these spaces into various metric spaces and measure the Hausdorff distance between their images. The best matching corresponds to the least Hausdorff distance. The idea to compare metric spaces in such a way was described in M.Gromov publications dating back to 1981. It was shown that this distance being restricted to isometry classes of compact metric spaces forms a metric which is now called Gromov-Hausdorff metric. However, whether M.Gromov was the first who introduced this metric? It turns out that 6 years before these Gromov's works, in 1975, another mathematician, namely, David Edwards published a paper in which he defined this metric in another way. Also, Edwards found and proved the basic properties of the distance. It seems unfair that almost no one mentions this Edwards's paper including well-known specialists in metric geometry. The main goal of the present publication is to fill this gap.