Abstraction Is the Tool

Mathematicians work by abstracting: stripping away details until only the underlying structure remains. A triangle, a friendship network, and a delivery route look nothing alike on the surface. Yet all three can be drawn as graphs, where dots stand for things and lines connect the ones that relate.

Because the structure is shared, one result can crack open many fields at once. Prove a fact about how dots stay connected in a graph, and you have just helped a biologist mapping protein links and an engineer routing internet traffic, in the very same stroke.