I'm Steve Strogatz and this is the joy of why.

A podcast from Quantum Magazine that takes you into some of the biggest unanswered questions in math and science today.

In this episode, we're going to be discussing infinity.

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 realize that they could just keep on counting forever, one, two, three, 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?

Joining me today to discuss Infinity is Justin Moore, Professor of Mathematics at Cornell.

His research interests include set theory, mathematical logic, and infinite combinatorics,

and their applications to other fields of math,

such as topology, functional analysis, and algebra. Welcome, Justin.

Hey, Steve. Thanks for having me.

Yeah, I'm very excited to talk to you. I should say maybe for full disclosure,

...