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Beyond Infinity

Eugenia Cheng — category theorist, musician, essayist — is the author of Beyond Infinity: An Expedition to the Outer Limits of Mathematics, a lovely book that describes itself perfectly at the end of Chapter 1:

In a strange way, this book isn't about infinity at all. It's about the excitement of a journey into the abstract unknown. Jules Verne's Journey to the Center of the Earth wasn't really about the center of the earth, but about the excitement of an incredible journey. This is a book about how abstract thinking works and what it does for us. It's about how it helps us pin down what we really mean when we start having an interesting idea. It doesn't necessarily explain the whole idea; mathematics doesn't explain everything about infinity. But it does help us become clear about what we can and can't do with infinity.

...

You can get by perfectly well in life without understanding anything more about infinity than you did when you were five years old. But for me, the usefulness of mathematics isn't about whether you need it to "get by" in life or not. It's about how mathematical thinking and mathematical investigation sheds light on our thought processes. It's about taking a step back from something to get a better overview. Flying higher up in the sky enables us to travel farther and faster.

Let's go.

... and an awesome journey it is! Further quotes and commentary to follow ...

(cf. Transfinite Meaning (1999-07-31), Roots of Commensurability (2000-01-26), Roads to Infinity (2010-10-06), Meta Math by Gregory Chaitin (2011-08-30), Cakes, Custard, and Category Theory (2016-02-14), Roads to Infinity Revisited (2016-06-16), Ingressive vs Congressive (2017-07-08), ...) - ^z - 2017-07-24