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The idea of infinity is probably about as old as numbers themselves, going back to whenever people first realized that they could keep counting forever. But even though we have a sign for infinity and can refer to the concept in casual conversation, infinity remains profoundly mysterious, even to mathematicians. Steven Strogatz explores that mystery with Justin Moore…

No one really knows where the idea of infinity came from, but it must be very ancient — as old as people’s hopes and fears about things that could conceivably go on forever. Some of them are scary, like bottomless pits, and some of them are uplifting, like endless love. Within mathematics, the idea of infinity is probably about as old as numbers themselves. Once people realized that they could just keep on counting forever — 1, 2, 3 and so on. But even though infinity is a very old idea, it remains profoundly mysterious. People have been scratching their heads about infinity for thousands of years now, at least since Zeno and Aristotle in ancient Greece.

But how do mathematicians make sense of infinity today? Are there different sizes of infinity? Is infinity useful to mathematicians? And if so, how exactly? And what does all this have to do with the foundations of mathematics itself?…

All infinities go on forever, so “How Can Some Infinities Be Bigger Than Others?“, from @stevenstrogatz in @QuantaMagazine.

See also: Alan Lightman‘s “Why the paradoxes of infinity still puzzle us today” (source of the image above).

* Buzz Lightyear

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As we envision endlessness, we might send carefully-calculated birthday greetings to Gaspard Monge; he was born on this date in 1746. A mathematician, he is considered the inventor of descriptive geometry, (the mathematical basis of technical drawing), and the father of differential geometry (the study of smooth shapes and spaces, AKA smooth manifolds).

During the French Revolution he was involved in the reform of the French educational system, most notably as the lead founder of the École Polytechnique.

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