Yes, it’s really about spotting similarities between different situations, and then finding a unified way to think about them - essentially so that we can use our brains better. Is that, is that right?Ĭheng (04:35): Indeed. Which may be very fitting, actually, since the whole subject seems to be about unification of so many different things. Strogatz: I’m happy you could be reunited with or. It’s like you have this long-lost paradise or a place that you were seeking, not subconsciously, but -Ĭheng (04:21): It really did feel like that. Strogatz (04:11): I love this sense of you kind of coming home. And even now, when I go back to some of the things that intrigued me when I was little - and these are some of the examples I give, when I give talks about category theory - I realized that the thing that intrigued me was really something to do with category theory, deep down. I realized that that was what I had been really looking for without realizing it. And when I finally met category theory for the first time, it was like coming home or finding the home that I had sort of been dreaming of all along. And then within algebra, it was category theory. And then within pure math, it was algebra. (03:35) And then within math, it was pure math that gave me the most satisfying answers. And math was always the thing that gave me the most satisfying answers to why things are true.
The kind of child who asks why repeatedly not just to annoy the grown-ups but actually because I wanted to know. And although I didn’t realize category theory existed at all, I was always interested in deep explanations. Because ever since I was little, I was interested in patterns and arguments - not in the sense of people yelling at each other, but in the sense of building justifications for how we know things. Is it something that you’ve been interested in your whole career? When did you start getting interested in it?Ĭheng (02:56): I’m going to go out on a limb and say I’ve been interested in it my whole life without realizing that’s what I was interested in. So it’s about finding patterns in patterns and making arguments about arguments. It’s about how we build arguments and how we find patterns between things. Remember that mathematics is not just about numbers and equations. What would you say? And just spit it out very quickly.Ĭheng (02:32): Like you say, I would say that the category theory is the mathematics of mathematics. So how about if you get us started with - Imagine you were making a TikTok video to define category theory. And I honestly, until I started looking at your book, didn’t appreciate how it’s begun to reach out into so many other disciplines - and even everyday life, as I just said. Category theory is such an interesting subject in our world of math. I’ve been a big fan of yours for many years. Strogatz (02:01): I’m really excited to have a chance to talk to you. Eugenia Cheng,Įugenia Cheng: Thank you so much for having me. She’s a scientist-in-residence at the School of the Art Institute of Chicago, and the author of several books, including her most recent one, The Joy of Abstraction: An Exploration of Math, Category Theory, and Life. Eugenia Cheng, will help us understand category theory better. Though it began as an abstract branch of pure math, it’s turning out to be a whole new way of thinking about lots of things, including situations in everyday life. It’s now being used in computer science, physics, engineering, chemistry, linguistics, and more. (01:16) Lately, though, category theory is all the rage. What’s the point of it? Even some of its most ardent practitioners have affectionately described it as “abstract nonsense.” (00:59) But some mathematicians, especially some grouchy old-timers, question what category theory is really telling us about math that is new. But what does that mean? If mathematics relies on abstractions, then proponents of category theory say it provides a sound scaffolding for those abstractions, a way to make connections and recognize patterns and relationships across a broad range of topics and scales, such as the various shapes of space, or different types of symmetry. It’s often described as the mathematics of mathematics - a kind of bird’s eye view of the entire subject. (00:28) Which brings us to category theory. In this episode, we’re going to ask: Is there more to math than the equal sign? In other words, can we use the logical power of math to talk about what it means to be essentially the same, without having to be exactly and strictly equal? I’m Steve Strogatz, and this is The Joy of Why, a podcast from Quanta Magazine that takes you into some of the biggest unanswered questions in math and science today.
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