For most people, soap bubbles are little more than ethereal, ephemeral childhood amusements, or a bit of kitsch associated with the Lawrence Welk Show. But for Johns Hopkins University mathematician William Minicozzi, the translucent film that automatically arranges itself into the least possible surface area on the bubble wand is an elegant and captivating illustration of a mathematical concept called "minimal surfaces." A minimal surface is one with the smallest surface area that can span a boundary.