Does a straw have one hole or two?

Topology, the branch of mathematics concerned with properties preserved under continuous deformation, treats a straw as equivalent to a torus, meaning a donut. It has genus one, which is the formal way of saying one hole. The two things you can see at either end are openings or ends of the same hole, not separate holes, in the same way that a tunnel through a mountain is one tunnel with two portals rather than two tunnels. Under this definition, stretching and squashing a straw could turn it into a donut without cutting or gluing, which is the test topologists actually apply.

The counterargument that gets the most traction is definitional rather than mathematical. If a hole means an opening in a surface, then a straw has two, since there are two places where the material ends. That definition also produces odd results elsewhere, though: a coffee cup would then have one hole in the handle plus one opening at the top, and a T-shirt would have four holes counted as openings while topologists count three. The disagreement is genuinely about which definition you are using, not about any fact concerning straws, which is why the argument is durable and why both sides feel obviously correct.

The reason it works as a debate is that it exposes something real. Everyday language treats hole as a single concept when it actually covers several distinct ideas: a depression in a surface, a perforation through material, and a topological feature of a shape. A pothole is a hole in the first sense and has no topological hole at all, since filling it in requires no cutting. Once people separate those senses, most conversations converge on one hole for the straw and lose interest, which is the fate of most settled debates and the reason the unsettled ones like the hot dog question survive longer.