Why Maths Matters: Why Geometric Analysis Matters

Make a loop of wire, twist it however you like, immerse it in soap solution, and lift it out. The resulting soap bubble will form a special surface, called a minimal surface, with boundary the wire loop.

Geometric Analysis, part of pure mathematics, predicts the shape of these surfaces. Minimal surfaces minimise area, and hence the energy embodied in a surface. They occur throughout nature: as the shapes of cell membranes, on an atomic scale as the shapes of certain catalysts, and as the apparent horizon around a black hole.

Their beauty also leads to their use in architecture, such as in the Water Cube (水立方) at the 2008 Olympics in Beijing. For example:

https://www.nature.com/articles/437633a

https://link.springer.com/content/pdf/10.1007%2Fs00004-013-0147-7.pdf          

https://en.wikipedia.org/wiki/Beijing_National_Aquatics_Center#/media/File:国家游泳中心夜景.jpg