But of course, those bubbles hardly skittered there of their own free will. Creating this frothy confection took a lot of steel, a lot of manpower, and not least, a lot of fancy mathematics.

The motivating idea for the building was that it would express the spirit of water. Its designers first thought of liquid water, vapor, or ice, but finally settled on foam. The bubbles, they decided, really would be bubbles: pillows made of a transparent plastic called ethylene tetrafluoroethylene (or ETFE ) filled with air, attached to a steel framework outlining the edge of each bubble.

A basic challenge was that they wanted the foam to look random and organic. But for the engineering to be practical, it had to have some underlying order. So Tristram Carfrae, an engineer at Arup, the Australian engineering firm on the project, looked into the mathematics of foam.

The trail led all the way back to an idea from the 1880s. The physicist Lord Kelvin decided that the ether, the mysterious substance then believed to fill the universe and transmit light waves, must consist of foam.

George Darwin (Charles’ son) declared the idea “utterly frothy,” but Kelvin was undeterred. He set out to understand the shape that ether-foam must have. The fundamental thing keeping bubbles together, he realized, is surface tension, which tends to pull bubbles into a shape with the least surface area for the volume. That’s why a single bubble forms a sphere. The same principle determines the complicated shapes bubbles form when they are packed together.