For centuries, the concept of infinity has captivated mathematicians and philosophers alike, stretching far beyond the simple idea of endless counting. Recent groundbreaking discoveries, however, have ...

One question has preoccupied humankind for thousands of years: Do infinities exist? More than 2,300 years ago Aristotle distinguished between two types of infinity: potential and actual. The former ...

The original version of this story appeared in Quanta Magazine. All of modern mathematics is built on the foundation of set theory, the study of how to organize abstract collections of objects. But in ...

Infinity used to be the place where mathematics ran out of road, a hazy horizon rather than a mapped landscape. Now a pair of new, exotic infinities is forcing researchers to redraw that map and ...

A set of the six sides of a die matches up one-to-one with a set of red shoes, helping illustrate Georg Cantor's set theorem. Image courtesy of GBH/NOVA It can be easy to take math for granted. But ...

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 ...

This is what happens when you mess with infinity. You might think that if you simply started adding the natural numbers, 1 plus 2 plus 3 and so on all the way to infinity, you would get a pretty big ...

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