When mathematician Georg Cantor first glimpsed the true nature of infinity, it changed mathematics forever. He demonstrated that infinity isn’t just endless—it exists in different sizes, each opening ...

The notion of infinity is fundamentally beyond the human ability to comprehend, but that hasn’t stopped mathematicians from trying. So just what is infinity, and why is there more than one of them?

Last week, my first grader came home with thoughts about math (I love it when she does that!) She said that, since one hundred plus ten was “one hundred and ten”, that, therefore, infinity plus ten ...

NOVA: How do mathematicians define infinity? Netz: Something which is equal to some of its parts. That's really the technical definition. NOVA: Is there a difference between the mathematical concept ...

A starry firmament, or sand cascading through one’s open fingers, or weeds springing up time after time: the first conception of infinity, of the uncountable and the unending, is not recorded, but it ...

Albert Einstein famously said: “Two things are infinite: the universe and human stupidity. And I'm not sure about the universe.” The notion of infinity has been pondered by the greatest minds over the ...

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Few ideas have had a racier history than the idea of infinity. It arose amid ancient paradoxes, proceeded to baffle philosophers for a couple of mil-lennia, and then, by a daring feat of intellect, ...

The four-color map problem can be understood by a bright fourth-grader (the question: whether four colors are enough to ensure that no two countries with a common border share a color). By junior high ...