# Turning numbers into shapes offers potential medical benefits

Until recently, topology was seen as being among the most abstract fields of mathematics, one that bore out Henry John Stephen Smith’s 19th century toast: “Pure mathematics — may it never be of use to anyone!” But now the field, which deals with the shape of many-dimensional objects, has unexpectedly proved its usefulness in, of all places, medicine. Researchers have used topology to discover a new subgroup of breast cancer patients with a 100 percent survival rate. More generally, the method may prove powerful for making sense of the massive, high-dimensional, noisy datasets modern science is producing.

Genetics experiments can produce vast quantities of data — determining the activity of each of the approximately 20,000 genes in a sample of breast cancer tissue, for example. Each sample can be seen as a point in 20,000-dimensional space. But these readings aren’t absolutely accurate, so each point may not be in exac