Eugenia Cheng: “The Art Of Logic: How To Make Sense In A World That Doesn’t”

Dr. Eugenia Cheng is Scientist In Residence at the School of the Art Institute of Chicago. She won tenure in Pure Mathematics at the University of Sheffield, UK, where she is now Honorary Fellow. Alongside her research in Category Theory and undergraduate teaching her aim is to rid the world of “math phobia”. Eugenia is also math columnist for the Wall Street Journal and a concert pianist.

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Eugenia Cheng
Image source: YouTube Video Screenshot

Emotions are powerful. In newspaper headlines and on social media, they have become the primary way of understanding the world. With her new book "The Art of Logic: How to Make Sense in a World that Doesn't", Eugenia has set out to show how mathematical logic can help us see things more clearly - and know when politicians and companies are trying to mislead us. This talk, like the book, is filled with useful real-life examples of logic and illogic at work and an essential guide to decoding modern life.

Eugenia Cheng: "The Art Of Logic: How To Make Sense In A World That Doesn't"


Thank you very much. Well first of all thank you to google for inviting me here to speak to you and thank you for coming in what I suppose is your lunchtime to listen to mass during a lunch break which is pretty amazing. So I am going to talk about logic and about how to make sense in a world that doesn't. Because a lot of the world does not make sense at the moment. In particular many people don't seem to make sense in the world at the moment. I have previously written books to show how maths is fun and delicious and amazing. And this is. Less about how it's fun more about how it's important because the previous books were about how it's important. But recent events in the last couple of years have driven me to feeling the need to say slightly more urgent and more dare I say political things about how maths can help us. And this might be surprising because usually pure maths is thought of as being pure and remote. I'm a pure mathematician. I am a category there is that is my research and category theory is sometimes thought of as the most abstract type of mathematics. Well I say that pure maths is a framework for agreeing on things. But in general pure maths is often thought of as really only being relevant to applied maths and applied maths is then helpful to science possibly in science is helpful to engineering and medicine and engineering and medicine are helpful to the world and maths is helpful to kind of the numerical parts of the world and we might think of differential equations or solving equations and calculating things in finance and science and business and and those are the ways in which maths is useful but that enables people to say well that's fine.

I'm glad somebody does that but it doesn't have to be me. It's not relevant to me someone else can do it and I'm sure many of you do do it. And there are many people in the world who just ignore it and hope for the best. Well I say that actually because pure maths is a framework for agreeing on things it's a framework for how to think well and because it's about how to think. It's actually about the entire human world or least the parts of the human world that thinks which might not be all of it. But wouldn't it be great if everyone were able to think better. That's what I say and I truly believe that pure mathematics is a discipline for thinking better and for how to have better arguments. Because I don't I'm not claiming to tell everyone what to think but I wish we could have better arguments because at the moment we seem to be mired in conflict divisive arguments fake news yelling bigotry prejudice hate exploitation victimhood. And it doesn't seem like it can sometimes seem like there is not a productive way to have a discussion. But I think there is a productive way to have a discussion. It just might not be on social media necessarily but we can try. And so this is what my book is about. It's about how can we have more productive conversations using lessons from abstract mathematics. So I'm going to talk about analogies and how your maths uses analogies. I'm going to talk about the interconnectedness of things and how we should always think about how things are interconnected grids talk about relationships of various kinds. I'm going to talk about pivoting between different contexts so that we can help ourselves understand other people from that point of view. And finally I'm going to talk about what I think intelligence really actually is. So first of all analogies I say that pure maths is a framework for agreeing on things. It's also a theory of analogies because fundamentally what it says is there are lots of different situations that have something in common. If we just forget some of the pesky details about them and then that takes us from the real world of things into the abstract world of ideas where more things become the same. By analogy but what pure maths does that we don't.