"Here's a stumper: How many parts can you divide a line into?"

"It seems like a simple question. You can cut it in half. Then you can cut those lines in half, then cut those lines in half again. Just how many parts can you make? A hundred? A billion? Why not more?"

"You can keep on dividing forever, so every line has an infinite amount of parts. But how long are those parts? If they're anything greater than zero, then the line would seem to be infinitely long. And if they're zero, well, then no matter how many parts there are, the length of the line would still be zero."

"That's the paradox lurking behind calculus. The fight over how to resolve it had a surprisingly large role in the wars and disputes that produced modern Europe, according to a new book called Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World, by UCLA historian Amir Alexander."