In 2004, two mathematicians hypothesized a powerful kind of sandwich.

They were studying graphs, which are collections of points (called vertices) and lines (called edges). Graphs might represent anything from social groups to the internet to neurons in the brain. The mathematicians hoped to understand properties of one type of graph — a type that’s ubiquitous in mathematics and computer science but difficult to analyze — by sandwiching it, in a mathematically rigorous way, between two simpler graphs.

If researchers could prove the existence of such a sandwich, they wouldn’t just be showing that the middle graph has one property of interest; they’d be showing that it has all sorts of important properties.…