# Doughnut = Coffee Cup

Did you know that a doughnut and a coffee cup are one and the same?  You didn’t?  Well, to a topologist, they are.  Topology is an area of math that is concerned with properties of space.  These mathematicians like to take shapes and see what can be made of them by deforming them without tearing.  For example, supposed a doughnut is made of a soft, pliable rubber.  The topologist will start to turn that rubber into other shapes without changing the number of holes already present.  In this way, a doughnut with a hole in the middle can eventually form into a coffee cup with a hole in the handle.  Items with the same number of holes are of the same genus.

What the heck sort of use is this crazy math?  Well, in topology, you have people who analyze knots all the time.  They like to look at messy tangles of string and try to see how many knots are in the tangle and how to possible straighten out the string without cutting it.  This sounds like child’s play but has an important application in fighting infectious diseases and cancers.  How can we untangle the messy DNA involved with these illnesses without cutting the strings?