How Mathematicians Use Homology to Make Sense of Topology
Originally devised as a rigorous means of counting holes, homology provides a scaffolding for mathematical ideas, allowing for a new way to analyze the shapes within data. The post How Mathematicians Use Homology to Make Sense of Topology first appeared on Quanta Magazine
At first, topology can seem like an unusually imprecise branch of mathematics. It’s the study of squishy play-dough shapes capable of bending, stretching and compressing without limit. But topologists do have some restrictions: They cannot create or destroy holes within shapes. (It’s an old joke that topologists can’t tell the difference between a coffee mug and a doughnut, since they both have...
Originally published in Quanta Abstractions.
