Singulargeometrygovernsthephysicaluniverse：soapbubbleclustersmeetingalongsingularcurves，blackholes，defectsinmaterials，chaoticturbulence，crys-talgrowth.Thegoverningprincipleisoftensomekindofenergyminimization.Geometricmeasuretheoryprovidesageneralframeworkforunderstandingsuchminimalshapes，aprioriallowinganyimaginablesingularityandthenprovingthatonlycertainkindsofstructuresoccur.