WE’VE all seen them, yet since the early 19th century no one could explain
why they are the way they are. Now, at last, four mathematicians have proved
that double soap bubbles could not be any other shape.
The mathematics of bubbles got going in the 1830s, when the physicist Joseph
Plateau began dipping wire frames into soap solution. He was astounded by the
results, and despite years of research, many of his observations still lack
rigorous explanations.
An especially notorious case, known as the “double bubble conjecture”,
concerns the angles at which the surfaces of two bubbles meet when…
