<p><span style="color: rgb(0, 0, 0);">It is an open problem of several years' standing whether every idempotent Schur multiplier can be written as a sum of contractive idempotents. We survey some of the history and background surrounding this problem, discuss some motivation coming from the field of communication complexity, and describe some recent progress. (Joint work with Hamed Hatami.)</span></p>