Mathematics is the pinnacle of logic and science. Most people assume that mathematics is based on solid foundations of logic, and that everything is well understood. Some sciences contain controversies and differing opinions, but surely mathematics is pure and definitive. At the very least the basics that are taught in school must be based indisputable.

And yet deep in the heart of mathematics lies a problem, known as the axiom of choice.

Suppose that you have a collection of boxes, each conta...

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