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EMILY KWONG, HOST:
You're listening to SHORT WAVE from NPR.
Today is March 14, known to many as just another day in March, but it's known to math lovers as Pi Day. See; 3.14 is also the beginning of pi, that mathematical constant representing the ratio of a circle's circumference to its diameter, that weird-looking symbol that looks like a table. That inspires math frivolity in schools around the U.S. every March 14. Like, I don't know about you, but Pi Day was beloved in my high school. There were pie-baking contests, pi digit memorization contests, Pi Day T-shirts. I made one one year with the pi symbol inside the Superman symbol. It was pretty cool. Dr. Eugenia Chang is also a fan. Though originally from the U.K., where the date is written 14-slash-3, she's since warmed up to the notion of Pi Day.
EUGENIA CHENG: I think that we should take any opportunity we can to portray math in a way that is fun to people. Just associating math with fun instead of with trauma is a good start.
KWONG: Eugenia is a scientist in residence at the School of the Art Institute of Chicago. She teaches art students math and has authored numerous books about math in our world, including a book called "How To Bake Pi," spelled P-I, like the mathematical constant. But let it be known - Eugenia also loves to bake.
CHENG: I mean, I started baking with my mother, like we did math together, when I was about 3. I probably did more eating of the cookie dough than baking of it.
KWONG: Since childhood, baking and math have always been linked for her because baking, at least the way her mom taught her, isn't about the ingredients. It's more about the process. Her 2015 book, "How To Bake Pi," starts with a recipe for clotted cream, that fluffy staple of British teatime. And it has just one ingredient.
CHENG: (Reading) Here is a recipe for clotted cream. Ingredients - cream. Method - one, pour the cream into a rice cooker. Two, leave it on the keep-warm setting with the lid slightly open for about eight hours. Three, cool it in the fridge for about eight hours. Four, scoop the top part off. That's the clotted cream. What on Earth does this have to do with math?
KWONG: For Eugenia, pure mathematics is just like this recipe. It isn't really about the ingredients. It's about how you use and transform the ingredients. It's about the process itself.
CHENG: That's why I love pastry because pastry also has very simple ingredients, and it's all about the process. And that's why I love pure math because pure math is all about process. It's all about the magic that you can do with your brain, starting from very little stuff.
KWONG: Eugenia is very persuasive when it comes to math. She even got Stephen Colbert to fold a 4,000-layer puff pastry on "The Late Show" to make this very point.
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STEPHEN COLBERT: All right. How many layers do we have?
CHENG: Four thousand. I looked it up earlier on my phone.
COLBERT: So did I.
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COLBERT: All right, all right.
CHENG: Because math is not actually just about numbers.
COLBERT: No?
CHENG: The principle of this is we use some really tiny numbers - two, three - very small numbers.
COLBERT: Those are two - there's a smaller one...
CHENG: And it quickly - yeah. It quickly became a huge number. We made something delicious by the power of exponentials.
KWONG: This is how Eugenia approaches math - by piquing people's interest, usually with something delicious, and then pulling back the curtain on how math actually works. She goes beyond rote memorization of numbers and rules and associates math with something creative instead of something constraining. So today on the show, break out your aprons. We're going to pi you in the face with a delicious lesson in pure math. I'm Emily Kwong, and this is SHORT WAVE, the daily science podcast from NPR.
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KWONG: So, Dr. Eugenia Cheng, welcome back to the show. We are going to crack open your book, "How To Bake Pi." You cover quite a bit of math in this book, and yet it never feels like a textbook.
CHENG: Oh, thanks.
KWONG: I want to start with the chapter on abstract math, Chapter 2, which you start off with a really helpful example - another recipe, actually. Can you read it for me?
CHENG: OK. (Reading) This is a recipe for mayonnaise or hollandaise sauce. The ingredients are two egg yolks, 1 1/2 cups of olive oil and seasoning. The method is that you whisk the egg yolks and the seasoning using a hand whisk or an immersion blender, and then you drip the olive oil in very slowly, while continuing to whisk. And for hollandaise sauce, instead of the olive oil, you use half a cup of melted butter.
KWONG: I was laughing so much reading this recipe because for some people, this would be blasphemous that you would, like, write one recipe for both sauces.
CHENG: (Laughter).
KWONG: Some would say, no, no, no, no, no, no, no, no. These are completely different. How dare you? You're making this larger point that there's something similar to these recipes, mayonnaise and hollandaise. What do they have in common?
CHENG: Right. At an abstract level, they're the same, that the method is the same. It's just that you're having to start with different ingredients. And the point is to incorporate some kind of fat into egg yolks. And I believe, scientifically, this is an emulsion. And so you can do that with all sorts of different things. And it just so happens that if you do it with olive oil, it's mayonnaise. And if you do it with melted butter, it's hollandaise. They do both end in A's.
KWONG: That's true. So with this example in mind, what is abstraction in math? Can you define it?
CHENG: So I think of abstraction as being a process where you forget some details about a situation so that it becomes a little bit further away from the real-life situation, but it takes you to some kind of heart of what's going on. So if you're thinking about emulsion, for example, then you're thinking about fat being combined with egg yolk, and then exactly what kind of fat it is is not relevant to that particular process. What's relevant is that it is some kind of fat. And so we can forget the detail of exactly what kind of fat it is. And math is really like that as well, that the reason we do abstractions is to unify a lot of different specific situations and see what we can understand about all of them at the same time.
KWONG: So the idea of abstraction in math, just like when you're developing a recipe for something, is you're looking for similarities between things that you only need one recipe for, like one recipe for pie crust that allows you to make a variety of pies, in the same way you're developing something in math. And to do that, you need to, like, ignore some details so that the broader picture can come into focus, and you can worry about the details later as you're plugging in different numbers and stuff.
CHENG: Right. Yeah.
KWONG: Is there an example in math that comes to mind, that's classic abstraction?
CHENG: Well, the basic abstraction is numbers because numbers...
KWONG: Sure.
CHENG: ...Are about similarities between different situations. And so you could look at two bananas, and you could look at two cookies, and then you say, well, there's a similarity between these situations, which is the concept of two. And that's a huge deal. And I think we don't think enough about what a big deal it is when children make that leap. And it's quite hard for children to make that leap. You know, you keep counting things in front of their face, and you can't make the leap for them. They just - it just has to click one day. And it can be very frustrating for them if they don't understand why you're doing it. And then it clicks, hopefully. And so most people have made that leap of abstraction. But then at each level of math, there's usually another leap of abstraction. And if it's not sufficiently guided and motivated, then some people fall off every time.
KWONG: Have you ever talked to a parent whose kid was struggling to understand that two was an abstraction?
CHENG: Do you know - I haven't, actually, now that you mention it. But I do remember - and I think I wrote about this in "How To Bake Pi" - there was this fantastically feisty mother at a school where I was helping first grade, and she said that the other mothers were all saying, oh, my child can count up to 20 or whatever. And she said, well, my son can count up to three, but he knows what three is. And I just thought that was fantastic because, yeah, in a way, counting up to 20 is just like reciting a string of words, and it doesn't mean you understand anything. But understanding what three is, that's really profound.
And, you know, there's - there are probably quite a lot of mathematicians who say, well, we still don't really understand what three is. All we have is a lot of different models of how we could understand three, and they're all useful in different ways. But what is it, really? And then philosophers probably write entire books about what three is, and then they all disagree with each other, and they probably think the mathematicians have it all wrong as well. But we keep going, and we can still use it. And that's why I think that the idea of having to understand things completely is really not the point.
KWONG: Is there anything else you want to say about abstraction?
CHENG: Yes. Abstraction is often thought of as difficult, and abstract math is often thought of as difficult, the hardest kind of math, and that you have to get there after doing all the things like times tables and solving equations and that abstract algebra is an advanced undergraduate course. And I think it's a mistake to make it a hierarchy like that because some people are much more drawn to abstract mathematics than to things like numbers and equations. And this is what I found from teaching art students with the School of the Art Institute. Many of them do not care about numbers or equations. They did not get on well with school math, and it doesn't seem interesting to them at all. But abstract math and abstraction does seem interesting to them, and they feel much more motivated to think about it and that, as a result, they're much better at it than they ever were at times tables and things. And so I think declaring that one of them is harder than the other or that you have to do one before the other is a mistake.
KWONG: You know, you really care so much about how math is taught, and it's all over the place in your book. And I'm wondering, where does that passion come from?
CHENG: I have always loved math. I did not always love school math. But I was very lucky because my mother is mathematical, and so she showed me the true essence of math at home so that when I was bored by having to do times tables and answer questions at school, I knew that there was more to math than that. And I held out that hope and that belief all the way through school, until the very end of school when it got interesting again and then university, when it finally got really interesting, and then, finally, research - that's when I really thought it got interesting. And I just thought it's a real shame that, first of all, most people don't have a mother at home who will do that for them, and secondly, why do we keep people away from those interesting, expansive parts of math for all those years?
I decided that I wanted to sort of be that person who would provide that hope to everybody if it had been dashed out by the education system. And I'd just like to stress that I'm not saying - it's not the teacher's fault at all, but it's the system, the system that is all about standardized tests and test scores and ranking people and ranking schools and then ranking teachers according to the test results of the students and ranking the students to get them into universities and ranking the universities. It's all about those - that ranking and having to assign numbers to people to pass judgment on them. So we miss out on this expansive part of math, which I think is much more inclusive and also much more like what math actually is.
KWONG: Eugenia, thank you so much for talking to us about baking and math and, you know, setting aside the time tables for the pie pans.
CHENG: Thank you so much.
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KWONG: If Eugenia's voice sounds familiar to you, that's because she's been on SHORT WAVE before talking about a different book, "x + y: A Mathematician's Manifesto For Rethinking Gender." We put a link to that episode in our notes.
This episode was produced by Berly McCoy, edited by our managing producer Rebecca Ramirez and fact-checked by Anil Oza. The audio engineer was Robert Rodriguez. Brendan Crump is our podcast coordinator. Our senior director of programming is Beth Donovan. And the senior vice president of programming is Anya Grundmann. I'm Emily Kwong. Happy Pi Day, everyone.
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