I’ve talked about this set with many people, and it nearly always brings up a wonderful mix of functionality and mathematics. The top left isn’t a battery; the bottom right isn’t a cylinder.

When people wonder whether there is math in everyday life, or whether mathematicians just say that to make themselves feel important, I like to point to this kind of conversation. “Is a cylinder” is a property of three of things in precisely the same way as “Is a battery”. Once we have noticed that mathematical property, we can linger on it, or not, in precisely the same way that we linger, or not, on other properties.

Lingering on the mathematical properties might include wondering whether there are any other shapes that batteries come in, or which there are more of in the world—round ones or rectangular ones. It might include wondering whether a button battery is properly called a cylinder. Or it might include looking for other things shaped like cylinders.

Very young children can have these kinds of conversations. So yes, there really is math in the world. We just need to practice talking about it.