According to mathematical legend, Peter Sarnak and Noga Alon made a bet about optimal graphs in the late 1980s. They’ve now both been proved wrong. Introduction It started with a bet. In the late 1980s, at a conference in Lausanne, the mathematicians Noga Alon and Peter Sarnak got into a friendly debate. Both were studying collections of nodes and edges called graphs. In particular, they wanted to better understand a paradoxical type of graph, called an expander, that has relatively few edges bu...