Topology is a branch of mathematics that is concerned with the study of how shapes or objects are arranged in space and whether they can be converted into each other. Objects that can be converted into each other are said to be topologically equivalent. In the video below I provide an example of how two circular strips of paper are equivalent to a square.
Far from being an abstract branch of mathematics, topology has many practical applications. For example, in the field of biology a branch of topology called “knot theory” is used to describe the many spatial configurations that the molecule of life, DNA, can adopt and how it interacts with other molecules. Other large biological molecules that can fold in many ways such as proteins are also studied with tools from the field of topology. Another example is physics where the application of topological principles to the area of quantum physics has ushered a revolution in the understanding of the properties of matter that may lead to many applications.