Say someone sets out to prove, by contradiction, that something is a joke. You would have to assume the opposite of what she’s proving is true. You would follow her thoughts logically until a ...

When you hear the words "rational" and "irrational," they might bring to mind the relentlessly analytical Spock in "Star Trek." If you're a mathematician, however, you probably think of ratios between ...

The ancient Greeks wanted to believe that the universe could be described in its entirety using only whole numbers and the ratios between them — fractions, or what we now call rational numbers. But ...