You might think you're not a "math person," but maybe that's because math doesn't mean what you think it means. Mathematical and logical thinking can open up new ways of thinking about everything from social and political issues to art to even gender. And on this episode, Dr. Eugenia Cheng, author and Scientist in Residence at the School of the Art Institute of Chicago, explains how to tap into it. Additional resources discussed: Dr. Eugenia Cheng (Official Website) "How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics" "Beyond Infinity: An Expedition into the Outer Limits of Mathematics" "The Art of Logic in an Illogical World" In Defense of Polymaths | Harvard Business Review Toni Morrison's tweet about writing books Why Don't Figure Skaters Get Dizzy When They Spin? | Scientific American The Brutal Neuroscience of Figure Skating: How Spinning Athletes Overcome Dizziness | LiveScience Follow Curiosity Daily on your favorite podcast app to get smarter withCody Gough andAshley Hamer — for free! Still curious? Get exclusive science shows, nature documentaries, and more real-life entertainment on discovery+! Go to https://discoveryplus.com/curiosity to start your 7-day free trial. discovery+ is currently only available for US subscribers.
You might think you're not a "math person," but maybe that's because math doesn't mean what you think it means. Mathematical and logical thinking can open up new ways of thinking about everything from social and political issues to art to even gender. And on this episode, Dr. Eugenia Cheng, author and Scientist in Residence at the School of the Art Institute of Chicago, explains how to tap into it.
Additional resources discussed:
Follow Curiosity Daily on your favorite podcast app to get smarter with Cody Gough and Ashley Hamer — for free! Still curious? Get exclusive science shows, nature documentaries, and more real-life entertainment on discovery+! Go to https://discoveryplus.com/curiosity to start your 7-day free trial. discovery+ is currently only available for US subscribers.
Full episode transcript here: https://curiosity-daily-4e53644e.simplecast.com/episodes/mathematical-thinking-can-open-new-worlds
CODY GOUGH: I'm curious, what is so exciting about math?
EUGENIA CHENG: For me, what's exciting about math is that it satisfies my curiosity and feeds my curiosity. So it's great to be talking about curiosity. Because for me, math is not about getting the right answers. It's not about right and wrong, and it's not solving problems. It's about asking why repeatedly and never being satisfied with the answers and always asking why again and asking why again, and I'm basically that two-year-old who never stops asking why.
[THEME MUSIC]
CODY GOUGH: Hi, I'm Cody Gough with the possibility of exploring curiosity.com.
ASHLEY HAMER: I'm Ashley Hamer. And today, we're going to change the way you think about math. Every week, we explore what we don't know because curiosity makes you smarter.
CODY GOUGH: This is the curiosity podcast.
[THEME MUSIC]
You might not think you're a math person but maybe that's because math doesn't mean what you think it means.
ASHLEY HAMER: What does math have to do with social and political issues or art or even gender? It turns out more than you might think.
CODY GOUGH: Dr. Eugenia Cheng is trying to change the way we think about math. She's the scientist-in-residence at the School of the Art Institute of Chicago and an honorary fellow of Pure Mathematics at the University of Sheffield.
ASHLEY HAMER: She's written the books, How to Bake Pi, that's P-I, get it? An Edible Exploration of the Mathematics of Mathematics, and Beyond Infinity: An Expedition Into the Outer Limits of Mathematics. And she has another book coming out soon called The Art of Logic in an Illogical World.
CODY GOUGH: And I've never thought of myself as a math person, but our conversation still taught me more than I knew that I didn't know.
I don't think most people see mathematics that way.
EUGENIA CHENG: I think you're right and that's why I decided to start writing books for a very wide audience and to reach out beyond the math majors I had been teaching in university before that. Because as you say, unfortunately, most people meet math in-- high school and middle school and elementary school math lessons are all about getting the right answer and doing what you're told. And math just isn't really like that at higher levels.
CODY GOUGH: Yeah, you're really good at talking about math as a concept and an area of study that relates to lots of other things. So what's the thing you say to someone who does not care about mathematics that really gets them to stop for a second and say, OK, I can get into this, I'm listening?
EUGENIA CHENG: First, I need to know why they don't really care about mathematics. And it usually is because they think it's all about numbers and equations, and they usually acknowledge that it's important that somebody is doing it but that it doesn't have to be them. And for the stuff about numbers and equations, it's true. We're probably all glad that somebody calculated that the bridge would not collapse when we went over it, or that someone calculated that the train would go and the plane would stay in the sky.
But we can, too, easily say that's for somebody else to do. And so if mathematics is emphasized as something that's really useful for things like that, then it can turn people off because they go, well, that's fine, someone else can do it. But instead, what I like to say is that you may well get on perfectly fine without math yourself, but I get on better.
CODY GOUGH: Wow. [LAUGHS] That's quite the challenge.
EUGENIA CHENG: It is.
CODY GOUGH: And you said that there's a lot of things people can do with it. But I feel like it kind of saying mathematics can serve a purpose and then mathematics can also kind of be fun without serving a purpose.
EUGENIA CHENG: I think it always serves a purpose, but it's not the same kind of direct purpose that people usually think of with math. There's an implicit purpose, and I like to think it's-- it's a bit like doing core exercises at the gym to strengthen your core. There is no single thing in life that just uses your core. There is no Olympic medal in core, But having a strong core enables you to use the rest of your muscles and access more of your strength better. And I think that mathematics is like that for our brain.
It's the core of our brain. So that if you can think logically, then you can access all the rest of your thoughts better. And mathematics, at its essence and in its best form, is about how to think better and how to think logically. And when I say to people, well, don't you think it would be better if everyone were able to think more clearly? And then everyone kind of chuckles and goes, yeah, yeah, it would.
CODY GOUGH: To take the next step, we've talked a little bit about the physical applications of math, but looking at the description of your new book, it is described, at least on Amazon, as how logical and emotional reasoning can help us live better in our post-truth world. So I find that fascinating. What does math have to do with fake news?
EUGENIA CHENG: Well, first of all, let's just point out that that description is on the internet. So it must be true, right?
CODY GOUGH: Of course.
EUGENIA CHENG: Of course. So what I have observed is that in this day and age that what counts as important mental capacities has changed a lot over the last 10, 20 years, and certainly over the last hundreds of years. Because it used to be that knowledge is power, and that having access to knowledge was what was important. So having access to books was important, being able to read and, of course, that's still true.
But knowledge is everywhere now, and we all have the entire internet basically in our pockets the whole time. We can look anything up. And when I was young, I was never the kind of person to just remember tons of facts in my brain. And I never really valued knowing tons of facts. And I feel like I've been vindicated now because there are facts everywhere.
And what's much more important, as we all know-- well, we should know-- what's much more important than having access to those facts is being able to evaluate them and being able to tell where they came from, and to assess how they were established and whether they've been established and so that we can evaluate the quality of those facts. Not just drink them in and then sort of regurgitate them out again in an argument with somebody else.
ASHLEY HAMER: Pop quiz. Without using the internet, how well do you think you could answer this question. Why does Swiss cheese have holes? If you're anything like the people in the 2015 study published in the Journal of Experimental Psychology, you're fairly confident.
Yale researchers gave people questions like the one I just asked you. Simple but tricky things like, why did tornadoes form? And why are there jokers in a deck of cards? Half of the participants were allowed to Google the answers and the other half had to answer them on their own.
Next, researchers gave the volunteers another set of similar but unrelated questions, and asked them to rate how well they thought they could answer each one. As you might expect, those who had just searched the web were more confident in their abilities than those who hadn't. The team switched around the order, the questions, the search engines, they even had one group go straight to a website, and the other search for the same site. It didn't matter. People who used search engines demonstrated an inflated sense of their own knowledge across the board. You don't know what you don't know, so the ability to find any answer in seconds flat can easily make you assume you know a lot.
Look, I'm just as guilty as the next person on this. Just ask anyone who plays HQ Trivia with me in the office. Yikes. But it's important to be aware of your shortcomings, especially when the stakes are high. The next time you have a conversation about the facts of the world, s try leaving your phone in your pocket. See just how much you really know.
EUGENIA CHENG: So for me, what I think is that my training and my aptitude as a mathematician enables me to think very clearly and logically through all of those facts and pieces of evidence and things that people try to tell me, so that I can evaluate them for myself and not simply be at the mercy of other people telling me things.
CODY GOUGH: It sounds to me like you're talking about critical thinking skills.
EUGENIA CHENG: Which I like to call thinking.
CODY GOUGH: [LAUGHS] So you think people should think. I think that's pretty reasonable.
EUGENIA CHENG: Yeah, because if you're thinking but not critically, does that really count as thinking? I don't think it does.
CODY GOUGH: Well, see, I find this very interesting because I consider myself reasonably good at critical thinking, at least some levels. But at the same time, my mathematical history with curriculum is kind of all across the board. I'm pretty sure I failed geometry at one point, and yet this was a year after I excelled in college algebra well ahead of where I should have been.
I got like two questions wrong on the ACT on the math portion, somehow. But again, C's and D's kind of at best growing up. I've never been good at the classes but there's a type of mathematical thinking I've been good at. So look at science, you've got biology, chemistry, physics, those are all very different things. Mathematics, I kind of see as clumped together. Do you think that there needs to be more of a separation of types of thinking required for mathematics?
EUGENIA CHENG: In a way, I think the exact opposite. Maybe I'll change my mind in a moment but my instinctive reaction is that biology, chemistry, and physics aren't that different, and that math isn't either. And that the boundaries that we have created between subjects are very man-made and they're very artificial, and they've been created more or less for bureaucratic purposes just so that we can organize things like who teaches what and what funding streams is. It all comes down to money in the end, where the money will come from for things.
But there is a scientific method, and the scientific method says we have a very clear framework for deciding what we are going to count as true and in what sense it counts as true. And that involves experimental data, and certainty, and having a hypothesis and testing it, and then adjusting your hypothesis according to what you then find about it. And mathematics also has a method, and the method for mathematics is logical proof.
But parts of science also use logical proof as part of their method as well, because that can't be separated. It's not like you only do logical proof in math and you do scientific evidence in science. And so the boundary, for example, between math and physics, well, it's not really clear where that boundary should be. You can say what's definitely math. So if you're doing algebra, that's simply manipulating symbols, that's definitely math and not physics.
And if you are looking at an object that's moving physically, then it's physics. But then there's some gray area in between where you're theorizing about things. So if you're theorizing about planetary motion, for example, you can't just prod a planet to get experimental data to see what would happen if you prod a planet. So you have to make theories about it using logic and then it has become a lot like mathematics.
So where's the boundary between that? I don't know. Really, there's a huge continuum between a lot of things and a lot of other things. And one of the things I talk about a lot in my next book is that we draw these artificial boundaries in between things, and we do that in arguments as well. We draw artificial boundaries between each other's arguments because I think we're a little bit addicted to antagonism, especially at the moment. Whereas, in fact, we're all kind of on a continuum around the same things a lot of the time.
ASHLEY HAMER: It didn't used to be this way. Aristotle was a philosopher and a scientist. Leonardo da Vinci was an artist and a scientist and an inventor. Benjamin Franklin was an inventor and a politician. I could go on. Why does everyone feel so much pressure to specialize today?
Well, it's partially because that's where the money is. These days, the more specialized you are, the more money you make. I mean, da Vinci knew a lot about the human form but I wouldn't pay him to be my doctor. There are a lot of benefits to thinking like a polymath. The more specialized you are, the less you can't see the forest for the trees.
As entrepreneur, Kyle Wiens wrote in the Harvard Business Review, quote, "the problem with deep specialization is that specialists tend to get stuck in their own points of view. They've been taught to focus so narrowly that they can't look at a problem from different angles. And in the modern work-scape, we desperately need people with the ability to see big picture solutions," end quote. So branch out, embrace your hobbies. If you know a little bit about a lot, you'll be able to approach problems from a different point of view.
CODY GOUGH: I would agree that there's lots of false separations that people put between people. I actually heard you coin a phrase that you have proposed to kind of replace masculine and feminine. Do you want to talk about that--
EUGENIA CHENG: Yes.
CODY GOUGH: --kind of separation?
EUGENIA CHENG: I'd love to talk about that. Because indeed, it is still very male-dominated in mathematics, although it has improved a lot at the level of undergraduates. And so math majors are becoming much more evenly distributed between men and women. But at the level of professors, it's still pretty bad.
And I have thought about this a lot being a female person in the field and remembering that when I was young and just starting out, I was nervous about this issue and I didn't want to draw attention to the fact that I was female in case it gave people a chance to say, oh well, she couldn't do it because she was female. And over the years I've gradually thought about this and realized that we should ditch the words masculine and feminine because it draws an artificial boundary between things men do and things women do, and it becomes prescriptive. Because if you are a female person and you do something that is described as being masculine, then it's automatically a disconnect between those two words, and it makes it sound like there's something wrong.
But also the other way around. If you're a male person and you're described as doing something feminine, then it also sounds like you're doing something wrong. Whereas, in fact, we can all do all sorts of things and maybe men are different from women in some ways. They certainly are in some physical ways but that doesn't mean that we should say that men can only be like this and that there's something wrong with you if you are like that. And I think that this has a bad effect on both men and women.
It has the effect of being oppressive towards women, because there's a commonly known fact that when women are confident and are self-assured, they get called aggressive and that it's something bad. But also that it can lead to a form of toxic masculinity when men are discouraged from expressing their feelings or showing emotions, and so they bottle it all up and they have nowhere to put those emotions.
So I have coined two new words-- "ingressive" and "congressive". Ingressive to replace masculine, and the idea is to think about going into other things. And congressive which is to replace the old notion of femininity, which is about bringing things together. But we can all be ingressive and congressive in different amounts in different situations. So we don't have to be just one thing or another.
CODY GOUGH: And you just spent two to three minutes talking about not a political issue but a social issue, but using the approach of a mathematician who's using logic. And I found that really interesting in your book, How to Bake Pi. You talk about everything from feminism to health care to the government, and not in a super political way but just in a mathematical approach, and come up with conclusions that way. So is your next book going to be more about social issues?
EUGENIA CHENG: Yes, my next book takes that idea and pushes it a lot further. And it's very interesting to me that you notice that in the first book because I've sort of forgotten it was there because it's become so much bigger in the next book I've written. And I have to thank the School of the Art Institute and my students there for pushing me in that direction because teaching art students, you have to think very differently about how to get them excited about mathematics.
And one of the things that gets them really excited is social issues. They are very, very socially conscious students. They're very self-aware, they're very socially-conscious, and they all want to change the world somehow. And so anything that's to do with social issues will get them absolutely excited about having a discussion. And the discussion will get pushed in directions I wasn't necessarily expecting.
And so out of those discussions where I was really teaching a piece of abstract algebra from my research called category theory, I found all these ways to link it to how we can think more clearly about those social issues. And like you say, I'm not exactly being political in the sense that I'm not pushing a political position, but I'm saying here are terms in which we could discuss these things more clearly. Because often, what I see is people having futile arguments. And regardless of whether I agree with one side or the other-- and honestly, quite often, I agree with nobody.
CODY GOUGH: [LAUGHS]
EUGENIA CHENG: But what I see is that the argument is futile because the terms in which we're having the argument haven't been agreed, or because we're arguing at cross-purposes, or because someone is completely misunderstanding, both sides are misunderstanding what the other person is saying, or we're declaring that something is a qualitative difference when it's really actually a quantitative difference if you think about it hard enough.
All of these things take more thought, more ability to think clearly through long chains of arguments. Of course, that's always too slow for an argument on Twitter. You can't fit that into 140 characters or 280, whatever it is now, which doesn't seem to have made that much difference. And so I hope that I can persuade people to take a bit more time to have slightly slower arguments.
CODY GOUGH: Yeah, you just talked about mathematics and artists, mathematicians and artists impacting social issues, which is very interesting to me. So I want to turn to what you do at the School of the Art Institute of Chicago. I mean, you're an artist, or you're the scientist-in-residence when mathematics isn't seen traditionally as either a science or an art, right?
EUGENIA CHENG: That's an interesting point.
CODY GOUGH: So [LAUGHS] what-- do you see it as one or the other?
EUGENIA CHENG: It's funny because in normal universities, mathematicians often do get lumped into the science division or whatever it is just because they don't really know where else to put us. And we're often slightly alienated from the scientists because we work differently from experimental scientists. We use much less money, we don't need equipment, we publish less. So in terms of publishing and the kinds of money we need to do our work, we're much more like arts people because we write fewer papers than experimental scientists, and we don't need a huge amount of money.
But then it means that scientists think we're not like them because they get million dollar grants. If I ever got a $1,000 grant, it was a big deal. That was great.
CODY GOUGH: [LAUGHS]
EUGENIA CHENG: Whoo, $1,000, you know. So it's interesting being regarded as a scientist. But what I really think is true and what the School the Art Institute is trying hard to portray is that, again, that's a boundary that is artificial. And there's a big drive to erase the boundary between art and science.
And it's funny because we get caught in linguistic knots because you can't talk about the boundary between art and science and erasing it except by saying art and science. So you've already made a boundary in the effort to try and erase the boundary. But through talking to my students about this, I've come to so many wonderful new conclusions-- not exactly new conclusions but different ways of thinking about it.
And what I've decided is that science is, in a way, all about trying to understand the world around us. And art is about interpreting the world around us. But in order to interpret the world, you have to understand it. And in order to understand it, you have to interpret it.
And so we're both-- we're all, artists and scientists, are doing aspects of the same thing, just emphasizing a different part of it. But it's not exactly different. And so that's what my role as a mathematician there, is to, first of all, just to show artists that math is important to them as well and to help erase those boundaries and show that really everything is for everybody.
ASHLEY HAMER: OK, I have to mention one of Eugenia Cheng's other very cool projects. That is her role as scientist-in-residence at Hotel EMC2, a Chicago hotel themed around the woman widely considered to be history's greatest female mathematician-- Emmy Noether. To decorate the space, Cheng created eight chalkboard installations illustrating Noether's life and work, like diagrams representing the mathematics of symmetry. Noether has a theorem named after her for that.
When you walk into the hotel, you see a quote from Leonardo da Vinci that should sound pretty familiar given what Cheng has said on this podcast so far. Quote, "study the science of art, study the art of science, develop your senses, especially learn how to see. Realize that everything connects to everything else," end quote. You can see the gorgeous pictures of Hotel EMC2 on curiosity.com.
CODY GOUGH: Yeah, I mean, you're a classically trained musician. You perform all over the place, it seems. And have quite the repertoire there. So clearly, you don't subscribe to the whole left-brain right-brain thing, right?
EUGENIA CHENG: No, and I suspect that's been debunked scientifically as well. I think it has been.
CODY GOUGH: I would hope so, yeah. I would hope so by this point but it's still kind of a myth that pervades a little bit.
EUGENIA CHENG: Right.
CODY GOUGH: So what are you teaching in terms of-- I mean, you're not just going into class and teaching equations and teaching certain things
EUGENIA CHENG: No.
CODY GOUGH: How involved are you with the art? And what is it that these art students are now using mathematics and applying in their art? How is it changing what they're doing?
EUGENIA CHENG: I'm showing them that math is a way of thinking, and that it definitely is creative, and that what we do more than trying to answer questions is create worlds in which different answers are possible to explore the natures of those questions. And because we're always creating worlds, it is creative. And where we build and imagine different worlds, and that makes us a bit different from physics because physics is trying to understand this world, the one that we've got around us. Whereas math is exploring how we think and the things that we can create with our amazing brains, because our brains are amazing.
And that is quite similar to what artists are doing. They're creating things with their brains. And one of my favorite things is when my art students show me work that they have done has been influenced by the things that we've been talking about. And one of my favorites was from, I think, the first semester I was teaching and someone had made a stained glass window and it depicted one plus one equals one.
And I always say to my students, anything can be true. You can make any rule up you want as long as you follow it using logic, and you accept all the consequences of it. And so I said to the student, what does your-- what does one plus one equals one mean here? And he said, well, I'm talking about mixing colors. When you mix one color with one color, you get one color. You don't get two colors.
And the stained glass window depicted all the different combinations of combining colors to produce other colors on this stained glass window of one plus one equals one. And I loved it because the instant reaction, even though I know that one plus one can be anything you want, my instant reaction when I looked at it was, what? And then it all became clear.
CODY GOUGH: Wow, are you a big fan of science fiction and fantasy?
EUGENIA CHENG: I actually am not.
CODY GOUGH: Because I feel like that's what those worlds are. And author or director or Harry-- you know, JK Rowling, or whoever it is, create a world that follows its own logical reality. And it has its own rules. And I see a lot of mathematics there and just from the way you're describing it, I see it a lot in board games as well.
EUGENIA CHENG: A lot of mathematicians do like all of those things. But I would like to reassure everyone out there who doesn't that you don't have to like those things to be a mathematician because there are so many stereotypes about that. Sometimes people think, oh but I don't like board games. That must mean I'm no good at math.
And in fact, I don't like games because I just don't like games. [LAUGHS] Well, part of it is because I'm very congressive, and so I don't like trying to win and beat people. And another is that if I'm going to go into fantasy world, I want it to be mathematics. That's just my favorite fantasy world. And if I'm not going to go into a fantasy world, I want it to be something real. So I like reading books that directly tell me things about us.
And I know that fantasy books do, and I do like the kinds of stories where one thing is changed a little bit but everything else is the same. For example, I love the Time Traveler's Wife where there's just one thing that's different, which is that the time traveler time travels spontaneously, but everything else is the same. So it's not a whole different world, it's just that one thing. And then you get to see the consequences of that.
And that's quite similar to what we do in mathematics where we just change one thing, leave everything else the same. It's a bit like doing a controlled experiment where you just change one thing and see what will happen. There, I also love-- one of my favorite operas is The Makropulos Case by Janacek. Well, there's one person who has drunk the elixir of life which makes her live 300 years more. Everyone else is a normal person but there's just this one thing, and we examine what would happen if we had the possibility of living forever.
And it's very interesting-- not to give a spoiler, but we always have spoilers in opera-- but what she discovers is that life becomes completely meaningless. And she doesn't want it anymore. And that is something that when I was writing about Infinity, I was thinking about this because we don't have infinity exactly in the world. We do a little bit because we can talk about infinitely many, infinitely small things.
But if we think about immortality, we're really thinking about infinity and how it would change our view of the world. And I love just thinking about that and thinking about, well on the one hand, I could procrastinate forever. On the other hand, things would become a bit meaningless. Maybe it is the finiteness of things that gives them meaning.
CODY GOUGH: Yeah, you've written an entire book about infinity-- well, beyond infinity, an expedition to the outer limits of mathematics. Why does infinity interest you so much? And how is it relevant in a concrete way to people?
EUGENIA CHENG: Infinity fascinates me because it's so easy to start thinking about it. But it's really difficult to pin down what it is logically. So it shows us several things. It shows us that you have to be careful because if you don't think about it really carefully enough, you just end up causing paradoxes, and weird things happen. Like you very quickly get to one equals zero if you're a bit precipitous about how you deal with infinity.
I love it because small children get so excited about the idea of infinity right away. And then adults can't figure out what the answers are. And so in between that initial excitement and the fact that it took mathematicians thousands of years to figure it out, there's a huge scope for exploring how we think and for what kind of weird things crop up in the mathematical jungle that is out there.
But loads of weird things happen when we start thinking about infinity. And it's an exploration, like I said, and it shows that mathematics isn't about looking for an answer. It's about exploring possibilities. And the fact that infinity is weird reminds me-- and is a place where I can help show people-- that those weird things are really interesting. It's like an optical illusion. I love the feeling of floating around in an optical illusion not knowing why it's going on or what's happening.
And it's the same with intellectual optical illusions as it were. I love that weird feeling where your brain is making strange shapes in your skull. And you don't know what's going on. And for some people, that makes them scared and makes them want to run away. But I hope to persuade people that that's really exciting and it's a place where you have the opportunity to become cleverer if you follow your curiosity about it rather than running away in terror.
CODY GOUGH: Well, I'm still interested in saying that I'm infinity plus one, whatever it is. You've worked with children before, younger children, I believe, on a curriculum. Why do kids stop being interested in math?
EUGENIA CHENG: That's a very complicated question. And I have-- I've mostly-- I've worked with all ages of children but the age group that I've spent the most time working with over my whole career is five and six-year-olds. And the reason is that every time I worked with anyone, it always seemed like something had happened the year before that was unfortunate.
CODY GOUGH: Oh no.
EUGENIA CHENG: And so I always thought, well, we should go back to the beginning then. And the wonderful thing when you help five and six-year-olds with math is that they haven't learned to be afraid of it yet. Just like small children haven't learnt to be bigoted and prejudiced and racist, they also haven't learned to be afraid of mathematics. And that they learn it later, and they learn it from all sorts of places. They learn it from adults who their parents might unfortunately pass that onto them.
And they also, unfortunately, learn it from when they're told they're wrong and they feel stupid. And I think this is one of the places where congressive people mind that much more than ingressive people. They mind other people thinking they're stupid, whereas ingressive people, they're spurred on by the idea of being right and having an accolade and they don't really care if they're wrong. And so the people who don't care if they're wrong keep going. And the people who really mind being wrong go off into something more that seems to be more creative without right and wrong answers like drawing pictures or writing stories or something like that.
And the other problem is when elementary school teachers are required to teach all subjects, and that's OK for five-year-olds. If you're just teaching them to count, that's OK. We can all teach children how to count. But once it gets a little bit more complicated than that, it can very quickly get to a point where adults who don't like math that much themselves start feeling uncomfortable, especially because children can ask deep questions that are difficult to answer. And if you're a bit insecure about your own mathematical knowledge, then that can be uncomfortable.
ASHLEY HAMER: I've got good news and bad news. The good news is that this discomfort doesn't affect all math students the same way. The bad news is that when female teachers are anxious about math, it disproportionately affects their female students. That's according to a small 2009 study published in the Proceedings of the National Academy of Sciences.
Researchers from the University of Chicago tested the math anxiety of 17 female first and second grade teachers by having them rate how anxious they'd be in certain math-related situations from reading a receipt to studying for a math test. They kept an eye on the math scores of each teacher's students along with asking them questions about their beliefs in certain gender stereotypes.
What did they find? At the beginning of the year, how anxious a teacher was about math had no bearing on the student's scores. But by the end of the year, girls whose teachers were anxious about math had significantly lower scores while the boys' scores were roughly the same. These girls were also more likely to believe that boys are better at math and girls are better at reading.
When people talk about needing more diverse role models, this is what they're talking about. Research shows that kids emulate the people who are most like them. And if the people most like you are anxious about math, you will be, too. Girls need to see that there are amazing female mathematicians and scientists out there. Eugenia Cheng, for one, but also people like CRISPR pioneer Jennifer Doudna, physicist Shirley Jackson, Antarctic Explorer and chemist Susan Solomon, and 24-year-old new Einstein, Sabrina Pasterski.
EUGENIA CHENG: So I think one of the problems is that we do have specialist math teachers and many of them are wonderful, but they arrive on the scene unfortunately a little bit late, after math has already become more complicated than general teachers can deal with. So one of the things I think we should do is have specialist math teachers a little earlier on, people who really love math and can convey the love of math, the open-endedness of it, the way you use your imagination and creativity in it, so that it's not what we have now, which is that children get put off, I think, towards the end of elementary school. And then it's left to the poor middle school math teachers to try and reverse what has already happened to those children.
CODY GOUGH: I have to follow-up on the open-endedness. I mean, infinity is about imagining possibilities. But if I'm filling out my tax paperwork, there aren't that many possibilities.
EUGENIA CHENG: Right, but that's not math.
CODY GOUGH: So yeah--
EUGENIA CHENG: It's arithmetic on taxes.
CODY GOUGH: Well, now, arithmetic, I would imagine many people think is math. So where do you draw that line?
EUGENIA CHENG: I really think is part of math but it's a very, very tiny part of math. And I've drawn the following analogy which is that when-- we had dance classes in school as part of sports. It was like one of the sport things we had to do. But the dance classes consisted the teacher telling us what steps to do and we had to memorize them and do them to really dreadful music that was awful.
So that, obviously, had no creativity in it whatsoever. But it would be pretty ridiculous for me to grow up thinking, oh well, dance isn't creative in that case just because my classes were like that. So yeah, arithmetic has some rules about it but it's such a tiny part of math. And it's a real shame to me that people end up getting the impression that that's all there is to math. That's not all there is to math, that's just arithmetic, that's like comparing spelling to writing poetry.
CODY GOUGH: Well, I have one final question. I know that you have made, again, in the baking pi book, many analogies to baking before. I've always heard that cooking is an art and baking is a science. You disagree with that? What are your thoughts on that?
EUGENIA CHENG: Well, first of all, as we've discovered, art and science aren't so different. But for me, math-- and I say this a lot in my next book-- math is often about not finding the right answer but finding the sense in which something is right. And there is a sense in which that is true because there is a scientific component to baking that is different from other types of cooking where it's actually some scientific reaction that's going on that makes something happen.
So when you mix eggs and sugar, you're not just mixing them, you're actually causing a chemical reaction to happen that changes their physical structure or something like that, which I find really amazing. And so in that sense, it is science somewhat, but it's also an art because there is some leeway in all those things that you do. And the way in which you combine them can make different things happen.
So for example, baking cakes is scientific but if it were not creative, then there would only be one kind of cake in the world. And imagine how sad that would be.
CODY GOUGH: That'd be depressing.
EUGENIA CHENG: [LAUGHS]
CODY GOUGH: Very, very sad. If you had to give a recommendation, where people can start learning how to think more mathematically and more logically? Do they pick up one of your books? Do they start somewhere else? What's the best way to get around that?
EUGENIA CHENG: It sounds like I'm just unashamedly self-publicizing, but really, the reason why I started writing books for general audiences was that people ask me this question a lot. And I didn't know any books that I really felt I could wholeheartedly recommend. I think that the landscape for popular math books has really improved a lot in the last few years. But there were books that I had read and enjoyed but a lot of them, especially for non-mathematical types, they're really just not that accessible.
And I wanted to write something that I could wholeheartedly recommend not just to really bright teenagers who are probably going to become mathematicians, but to people who never really got on with math and slightly regret it because I meet a lot of people, 10 years ago they said, oh I can't do math. And now, people are more likely to say, oh I kind of wish that I knew what was going on and I regret that-- well, I liked math up to a certain point, up to algebra, but then I couldn't do calculus or something. And I kind of regret it.
And I wanted to reach those people, people who would previously not have dreamt of picking up a popular math book. And that's why-- who was it who said that if you don't see the book that you want to read, then you have to write it?
ASHLEY HAMER: This quote is widely attributed to author Toni Morrison, though it's unclear when she came up with it. The most clear record of her saying it was in October 2013 when she tweeted the line. It went like this, "if there's a book you want to read but it hasn't been written yet, then you must write it."
EUGENIA CHENG: And so I realized that if there wasn't a book that I could wholeheartedly recommend in that way, then I should just write it. So I did.
CODY GOUGH: Well, thank you for writing it. And How to Bake Pi, really, it's a good book. So [LAUGHS] we'll wrap up with a final segment called the Curiosity Challenge. And I'll give you a break for a second and I'll ask you a question that we've written about on curiosity.com. Maybe teach you something, maybe just show off even more knowledge that you already have. So my question for you is, do you know why do crackers have holes in them?
EUGENIA CHENG: Why do crackers have holes in them? I do not know why crackers have holes in them. I'm not even sure I knew that crackers had holes in them.
CODY GOUGH: [LAUGHS] Yeah, most crackers-- almost all crackers--
EUGENIA CHENG: Or they're part of the baking process. Is it something to do with how they need to aerate when they're baking?
CODY GOUGH: It is indeed, yes. I'll give you partial credit for that. To make crackers is you mix water, flour, wheat flour, yeast to special enzymes together, let it sit for about 16 hours. And while it sits, the enzymes break the starch, and the flour into simple sugars. You're probably familiar with lots of this from your baking career. And the yeast gobbles down the sugars and belches out carbon dioxide gas. And that fills the dough with gas bubbles that make it rise.
So in the first 10 minutes of baking that dough, a phenomenon called oven spring that makes the yeast speed up the respiration and it kind of belches out a puff of carbon dioxide. And yeah, you need to let off some steam that way. So you can actually still see if you get like a pack of saltine crackers where the cracker rose in the form of browned bubbles between the holes, and that's kind of where that was. But with the right number of holes, the rising doesn't get out of control and you get that flat crispy final product per se.
EUGENIA CHENG: Oh, well, that's wonderful.
CODY GOUGH: So just a little random fast fact. You can read more about that on curiosity.com. Now, you've got a zinger for me.
EUGENIA CHENG: What is the alcohol content of Angostura Bitters?
CODY GOUGH: Angostura Bitters? Bitters. I'm going to say 0.5% alcohol.
EUGENIA CHENG: So the answer is 44.7.
CODY GOUGH: Are you serious?
EUGENIA CHENG: And I know this because I was trying to buy some in Manhattan where you can't buy liquor in a normal store, right? And I know that Angostura Bitters has quite a high alcohol content. So I thought I'd better go to a liquor store to buy it. And I went to a liquor store and I asked if they had Bitters and they looked at me like I was a total idiot, which happens a lot when I'm in Manhattan somehow.
And they said, no, you have to buy it in a grocery store. And I kind of went, oh, OK. And so I thought maybe I was wrong about that alcohol content. So lo, I went to the nearest grocery store and found it. And it is 44.7% alcohol, which is pretty much like whiskey.
CODY GOUGH: Yeah.
EUGENIA CHENG: And but you have to buy it in a normal grocery store in Manhattan. Of course, here in Chicago you buy it in a liquor store normally.
CODY GOUGH: Yeah, of course. Of course. Have you written any recipes that feature that?
EUGENIA CHENG: No, I just like it in drinks.
CODY GOUGH: Oh, there you go. Yeah, it's delicious. Well again, thank you so much for joining me. I've been with Dr. Eugenia Cheng. We'll have links in the show notes to all of your publications and keep an eye out for the next one, The Art of Logic in an Illogical World. I really appreciate you spending some time with me.
EUGENIA CHENG: Thanks very much for having me.
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ASHLEY HAMER: Looks like all of this adds up to the extra credit question. If you've got a question you'd like answered on the podcast, send it in along with your name to podcast@curiosity.com. We've got an Olympics-themed question this week from Linda Fichtenbaum who writes, why don't figure skaters spot when they turn? Don't they get dizzy? The answer after this.
CODY GOUGH: Have you ever been listening to the Curiosity podcast and wanted to share a clip on Facebook or Twitter? Now you can, thanks to gretta.com, that's G-R-E-T-T-A. You can stream our podcast on gretta.com/curiosity and their podcast player will follow along with a written transcript of each episode while you listen.
When you hear a clip you want to share, just find it and click Share. Gretta will build you a video for you to share with your friends so that you can help spread the word about our podcast. Again, that's gretta.com/curiosity. And drop us a line to let us know what you think of this super cool new service.
ASHLEY HAMER: I'm back with the extra credit answer. Linda Fichtenbaum asked how figure skaters avoid getting dizzy without spotting when they spin. By spotting, Linda is referring to the trick that dancers use to avoid getting dizzy. As your body turns, you keep your head and eyes focused on one spot for as long as possible. Then whip your head around to keep it stuck to that spot for the next turn.
But figure skaters spin way too fast to afford this luxury. Instead, they just have to practice spinning and spinning and spinning until their brains get used to the sensation. There are also some other tricks they use. Your vestibular system, which keeps track of balance is most sensitive to changes in speed. You'll be a lot less dizzy if you've come out of a spin gradually than if you stop all at once.
Skaters are also taught to come out of a spin with their eyes locked on a landmark, which isn't too different than a dancer's spotting. And just in case all else fails, most figure skating routines choreograph a slow graceful move at the end of a spin just to help skaters get their bearings and avoid any disasters. Thanks for asking.
CODY GOUGH: That is all for this week. And hopefully, next week Ashley won't have the flu.
ASHLEY HAMER: Yeah.
CODY GOUGH: I think you sound great, though.
ASHLEY HAMER: Well, thank you. I feel there's a nice gruffness to my voice.
CODY GOUGH: [LAUGHS] Well, we'll be back next week with another gruff episode. Thanks so much for listening. I'm Cody Gough.
ASHLEY HAMER: And I'm Ashley Hamer.
[THEME MUSIC]
SPEAKER: On the Westwood One Podcast Network.