Dr. Eugenia Cheng, mathematician, educator, writer, public speaker, and artist, talks about how to simplify and destigmatize advanced math to restore its deeper beauty to the next generation of students.
We listen to music we can’t play. We eat food we can’t cook. Why wouldn't we also think about math concepts we can’t prove or develop, simply for the joy of how they fuel the imagination?
All too often, math phobia deters students from the creative pleasure of numbers.
Dr. Eugenia Cheng joined us to discuss how to overcome math phobia. She’s a mathematician, educator, author of How to Bake Pi, public speaker, columnist, concert pianist, artist, Scientist In Residence at the School of the Art Institute of Chicago and Honorary Visiting Fellow at City, University of London. Her most recent book, Bake Infinite Pie with X + Y, explores the idea of infinity and introduces the thesis that math and science are routes to imagining new ideas.
And there’s not a whiff of math phobia in it.
Addressing Math Phobia
Math is like cooking. Both are a magical process in which something complex (and delicious!) is built from simple things, Eugenia says.
Eugenia’s writing has focused on the excitement, imagination, and creativity that underlies math and numbers.
“Math can help everybody to help themselves,” she says. But math has been wildly misunderstood and misrepresented in recent history.
Unfortunately, most curricula present mathematics without much creativity at all. Those students (and adults!) who’ve felt alienated by math were likely taught math in this way.
Math and creativity are not opposites, she says. There is power and beauty in math. When Eugenia presents math concepts to her art students, she ties math problems to issues her students care about, such as social justice or politics.
Why Math Matters
“Math is about understanding complexity so that it becomes simple,” Eugenia says.
Finding simplicity on the other side of the somewhat formidable complexity of math is like decluttering a house.
Say you’re doing some spring cleaning in your home. You reach a phase in the middle of the process in which your house is actually much messier than it was to begin with. At this point, you might think you are bad at decluttering. But if you persist and make it through the full process, your house becomes clean and peaceful again. And your growth and mastery of the process is evident.
Unfortunately, many of us get stuck in that middle section – in the messy, confusing, overwhelming middle point of learning math, never reaching that payoff for mastering complexity.
Exercising Our Brains
To exercise your body, you might run, bicycle, hike, or garden. But how do you exercise your brain? In the same way that we might run for our physical health, we can embrace math for brain exercise.
“Math is about using our brains well,” Eugenia says.
“Math is about using the brain logically, to find clarity, to find rigor, to be able to express yourself clearly, to make precise arguments, to shine a light through fog. To me, that's what math is about.
“Isn't it beautiful when fog clears away?”
Action Steps for Parents
1 - Separate Worth From Grades
A score on a math test isn’t indicative of anything except an ability to take math tests. There are many ways to be “good” at math, and the ones that matter more in school often matter less in real-life scenarios.
“A wonderful thing that parents can do for children is instill in them the knowledge that they are loved and supported no matter what they do,” Eugenia says. “They can discover what they're good at, at their own pace.”
2 - Work Through Fears of Math
Saying that there’s nothing to be afraid of doesn’t actually help address fear. But like overcoming any fear, the more we understand the subject, the more we can cut through the mystery around it.
If you’re a parent with a fear of math, be honest with yourself about it. Try to demystify math for both yourself and your student by setting out to learn.
3 - Learn Math Together
Don’t be afraid to talk to your children about things you don’t understand. If you don’t immediately grasp a topic, investigate it together with your student.
In this way, you turn math itself into a problem to solve and model the potential that we are always learning and growing.
- New Book: Bake Infinite Pie with X + Y
- Dr. Eugenia Cheng on The Late Show with Stephen Colbert
- Dr. Eugenia Cheng’s Website
This episode was brought to you by Art of Problem Solving, where students train to become the great problem solvers of tomorrow.
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Eugenia Cheng Q&A [1:51]
Eric Olsen: On today's episode, Dr. Eugenia Cheng, mathematician, educator, author, public speaker, columnist, concert pianist, artist, scientist in residents at the School of the Art Institute of Chicago, an honorary visiting fellow at City University of London talks about simplifying, de-stigmatizing and restoring the deeper beauty of advanced mathematics for the next generation of students.
Why is it so important to rid the world, to rid our students of math phobia?
Eugenia Cheng: Well, first I'd like to say it's not the most important thing in the universe. I think it's more important to rid the world of hunger and violence. But, for me, in terms of things I can contribute to the world, that's the thing I feel I can contribute the most right now.
And it's important to me, first of all, because I love math and I think it's been wildly misunderstood and misrepresented. And that makes me sad. But, also I think that it's an injustice to those people who have been made to be afraid of it because it's something that can help them and it's there to help everybody. And it can help everybody to help themselves really. Not to mention, also, it would be better for society because if we have people who are afraid of math, then it spills over into being afraid of science and denying science and not being able to have logical arguments. And I think it's bad for everybody.
How baking gets to the heart of math [3:22]
Eric Olsen: You're a celebrated author, including the wonderful, How to Bake Pie, an Edible Exploration of the Mathematics of Mathematics. How can cooking teach our kids about math beyond just cups to quarts conversions?
Eugenia Cheng: Thank you. It's definitely not just about measuring things, which is also a thing, but it's more about exploring how to put basic ingredients together and use techniques to turn them into something that is not really anything like the thing you started with. It's like a magic trick, except it's not magic. It's kind of real. And math can be mysterious like that because you start with things that are simple and then they get really complicated and that's one of the reasons it can be terrifying, but that's where it's power and its beauty and its joy is to me. Just like baking a cake may seem complicated, but it's so tasty and fun. And that kind of magic process where you take simple things and turn them into something more complex is wonderful to me.
So, partly it's about analogies and finding that way to enjoy the process of taking something simple and basic and doing some things with it to make it into something complicated. That's what I think is at the heart of math.
Are math and creativity opposites? [4:38]
Eric Olsen: And what are your secrets for successfully teaching and engaging art students in math like you do? Students who may potentially self-identify as, "I'm creative, I'm not mathy."
Eugenia Cheng: So, first of all, I try and persuade them that's not a clean dichotomy. That creative isn't the opposite of math’y somehow. And it's just that unfortunately, a lot of math and the curriculum is presented without much opportunity for creativity from the students, which is a real shame because math has tons of creativity in it.
So, first it's very important to me to validate any student who feels that they've been alienated by math, put off math or that the math they saw before wasn't very interesting because maybe it wasn't. And then it's important to me to understand the things that interest them. And for my art students, it's often creativity, being able to have some input and also making it relate to the issues in the world that they care about. It's not things like how fast will this ball roll down a hill if... You know, who cares. So, it is to do with relating it to life. But, I'm very careful about which parts of life and trying to find out what they will care about and tapping into that.
Eric Olsen: Any advice for the parents of female students who you believe may all too often underrate their own mathematical abilities?
Eugenia Cheng: I think it's really important to be aware that if they are underrating their own mathematical abilities, it's probably because somebody else underrated them. And it's not something that they've just invented in their head. It might be because there are some loud people in their class who've told them that they're stupid or it may even be some people in the world who've told them that. Unfortunately, sometimes it is parents themselves who tell their children or who say, oh, I'm no good at math. And so, it's okay if you are no good at math and that kind of thing. And sometimes it's teachers and sometimes it's the school system that labels people as bad at math. If you don't get the maximum score on a test, then these are the people who are good at math and these are the people who are bad at math.
So, I think it's really important to validate that and not just try and get the student to have self-belief coming from nowhere because if they scored low on a test, then it's kind of dishonest to tell them no, but you are good, really. Unless you have some reason for it.
So, in a way, I like people to be sensitive and think that if they did badly in some test, then maybe that's a sign of something because there are other people who do badly in everything and still think they're great at it. That's unfortunate in a whole different direction.
So, I think it's important to say that tests and those standardized tests and tests at school and especially timed tests aren't a good measure of overall intelligence and how good you are at math because there are many ways to be good at math. And that's a very, very narrow one that really doesn't count for that much in the end.
Unfortunately, there's a whole load of hurdles that the current school system makes you jump through and that's one of them, but overall in life, there's much more to it than that.
Eric Olsen: Eugenia, my mommy told me I'm amazing and all evidence to the contrary will not persuade me at this point.
Eugenia Cheng: That's a wonderful thing that parents can do for children is to instill in them the knowledge that they are loved and supported no matter what they do. So, that even if they don't do well in a test at school, there isn't going to be some consequence in their family relationships or that their parents won't love them any less. And they can discover what they're good at at their own pace.
Finding the simplicity on the other side of complexity [8:14]
Eric Olsen: Eugenia, in your work as a pure mathematician, as a category theorist, you play far out in the abstract. Talk about complexity and the simplicity on the other side of complexity. The difference between being reductive with the complex and losing the meaning altogether versus finding the simplicity within the very complex.
Eugenia Cheng: That's a very nuanced difference. And it's a really important one. So, thanks for raising that. I do think that math is about understanding complexity so that it becomes simple because once you've understood how things relate to each other, it's like you can package them up into a neat package that then becomes a single unit. And then you can take a bunch of simple units, single units like that and package them up. And then that becomes a single unit, even though there's a whole lot of complexity inside it. And that involves understanding complex things so that we can treat them as something simple. And I think that to me is what it means to find the simplicity on the other side.
It's a bit like if you really want to tidy your house and declutter, you have to go through a phase in the middle where it's a worse mess, right? You have to kind of get everything out and make a giant mess. And if you're not careful and I admit that I'm not so great at this with decluttering, I'm much better at it in math, but if you're not careful, you get to the phase in the middle where everything is a huge mess and you never make it through the other side of that.
And unfortunately, I think that happens with math in education, somewhat, that everyone finds it complicated and then a lot of people, unfortunately, don't get enough help to get them through to the other side where there's a pill for that complexity. And so, they get just stuck in the part where it's a mess and they're like, well, why am I throwing all these Xs and Ys around? There's nothing in it for me. And that's what I would like to try and change.
Eric Olsen: But, what if my student doesn't want to be a mathematician? Why is math still important?
Math helps you use your brain better [10:12]
Eugenia Cheng: Well, it's a great question because many people don't want to be mathematicians and I'm not claiming that everyone can become a mathematician, just like not everyone can become a 100 meter sprinter. I can run a little bit better than I used to. And that's really all that's important. It's not that I can run or I can't run. It's that I get better at it and that's what I'm going to do. I'm never going to win the Olympics.
And so, not everyone is going to become a research mathematician, but math is still important, I think because it's about using our brains well. And I hope that everybody would like to be able to use their brains well. I think that our brains are the most amazing thing that we have. And so, wouldn't you like to be able to use it well. Like anything that you have, if you can use it well, then you can do things better.
And using it well means many different things. And I think that every academic discipline is about a particular point of view or a particular way of using it well. And with math, it's about using it logically to find clarity, to find rigor, to be able to express yourself clearly, to make precise arguments, to kind of shine light through fog.
And to me, that's what math is about. It's not about calculating answers to things. It's not about getting the right answer. It's not about doing things faster than other people. It's about having a way to shine bright light on situations and clear that fog away. Isn't it beautiful when fog clears away? I don't want to fog shame. Fog can be nice, too. But, when the sun shines, it's a beautiful thing.
Eric Olsen: We have a lot of Pacific Northwest friends in the Art of Problem Solving world. So, I'll apologize for you. Eugenia, finally, any next steps advice for helping the world, for helping our students become less math fearful?
The importance of validating a student’s mathematical fear [12:06]
Eugenia Cheng: I think that it's important to validate where their fear is coming from because if someone is afraid of something and if you just tell them, "Well, there's no need to be afraid of that." That doesn't work. And I know that from my own personal experience because I'm somewhat afraid of dogs. And if people just tell me there's nothing to be afraid of, it really doesn't help. But, what does help me is if they help me to understand dogs because one of the reasons I'm afraid of them is because I'm not really accustomed to them. So, I don't know what they're going to do. And so, I feel like I can't tell if a dog is going to do something dangerous or not. And so, if someone helps me understand the behavior of dogs, then I feel like it's less mysterious.
And so, I think demystifying mathematics, but importantly not passing down your own fear because I think that all fears can be passed down from parents to children. And that the fear of math is definitely one of them. And so, it's really important to try and get over it if you have your own fear is to try and get over it in order not to pass it on.
But, also on the other side of that, if you really love it, then it's also important not to throw that too hard at someone because that could be off putting as well.
Download AoPS’ Raising Problem Solvers Guidebook [13:20]
Eric Olsen: I love that advice for parents. And parents, if you're looking for more help, that's exactly why we created the Raising Problem Solvers Guidebook. It's full of helpful strategies to support and challenge your advanced learners. Curriculum recommendations straight from our Art of Problem Solving families, our stem gift guide, free resource recommendations, and much, much more. Download our Raising Problem Solvers Guidebook for free today.
Eugenia Cheng Rapid Fire [13:57]
Eric Olsen: It's now time for our rapid fire segment called Problem Solved where we ask the guest to solve incredibly complex and difficult education issues in single soundbites. Eugenia, what's one thing about K-12 education you wish you could snap your fingers and problem solved, it's fixed?
What if our kindergarten teachers were paid the most? [14:15]
Eugenia Cheng: Crikey. Well, there's about 15 things, but if there's going to be one that I could just fix, it would be to flip everything around so that kindergarten and early elementary teachers were paid the most and respected the most and had the most funding. And then so that it would then get, instead of people getting paid more as they go up through the education system, they get paid more the earlier they are in the education system because that's the front line of education. That's the most important part of education. It's the most important job that they're doing. And then wouldn't it be great if university professors were paid the least? That's an interesting idea.
Eric Olsen: That’s self-sabotage, Eugenia.
Eugenia Cheng: It’s better for the world, I think.
Eric Olsen: If you could go back and give your kids self-advice on their educational journey, what would it be?
Eugenia Cheng: It would be that to be aware that the people who are loud about being good at things aren't necessarily good at them. They're just loud.
Eric Olsen: What part of education do you think or hope looks the most different 10 years from now?
Eugenia Cheng: I really hope that math education stops having so many times tables in them and a bit later on in that. So, I wish we could get rid of the obsession with times tables and then also get rid of the obsession with calculus. There's this obsession with calculus and calculus is the one litmus test for whether you're a math person or not in high school, AP calculus, but calculus is a really specific and strange part of math, actually. And there are so many other things that could appeal to people in different ways. And so, I'd love to release the stranglehold that calculus has on the consciousness.
Eric Olsen: Richard Rusczyk, our founder, has a great article called Avoiding the Calculus Trap. Specifically talking to that, so for listeners who want to check that out, please do. What's your best advice for parents looking to raise future problem solvers?
Eugenia Cheng: I think it's to go into the problem solving thing together and not be afraid to talk to children about things that you don't understand because that's how you can go into the problem solving thing together. I think that often parents say to me that they don't know how to talk to math about their children because they don't understand it themselves.
On Bake Infinite Pie with X + Y [16:31]
Eugenia Cheng: And my book, Bake Infinite Pie with X Plus Y introduces quite difficult topics. And some people say, 'Oh, but if I don't understand this topic, how can I talk to my child about it?" And I want to say, "That's great. Then you can say to them, well, I don't understand this either. Let's figure out how we can find out more about it." And there are so many resources all around and then you can explore the library and you can look things up on the internet and find videos and show that it's good to think about things you don't understand because that's where you have the potential to grow and become more intelligent.
Eric Olsen: And Eugenia, tell us a little bit more about Bake Infinite Pie with X and Y. Who you wrote it for, where people can find it.
Eugenia Cheng: Thanks. It's for four to eight year old children, officially, and it's a storybook, but it's a storybook involving math concepts around infinity and also baking. And so, it's about two children, X and Y, who are dreaming about infinite pie and they have a mathematical Aunt, Aunt Z. It's illustrated very adorably by Amber Ren.
And what I wanted to do was just create a magical, imaginary, mysterious, curious journey where the children just explore with their Aunt Z these ideas around infinity to show that there aren't clear answers. There's just explorations and dreams that we can go into. And it does introduce concepts that might seem very advanced, like fractals and exponentials and infinity in different directions and convergence sequences. But, the thing is that they're not really difficult ideas to think about. They are difficult ideas to pin down and make rigorous and prove, but that doesn't mean that you have to prove them. Otherwise, you're not allowed to deal with them, just like we're allowed to listen to music, even if we can't play it. Right? And we're allowed to eat food that we don't know how to cook.
And so, I think that we should also be allowed to think about math concepts that we don't know how prove or develop because they spark imagination. So, I really love talking to children about those. I've talked to children about infinity a lot in school visits and they get so excited. I think children are so used to not understanding things, but in a way they're much more used to it than adults. Adults are more likely to freak out. I don't understand this. I can't talk to my children about it.
But, you don't have to understand it. And that's what I keep saying, that you don't have to understand it to talk to children about it. You can also show them that adults don't understand everything either. And what I love saying to children sometimes is, you know what, nobody really understands this. And so, if you want to understand more about it, maybe you could become a mathematician or a scientist and then you could understand something that no one has ever understood before. And then you'll have contributed to pushing forward the boundaries of knowledge of humankind.
Eric Olsen: So excited about the book. Love the advice of humility and vulnerability [00:19:30] for our Problem Solving Parents. And listeners, we'd love to hear your answers as well. So email us at firstname.lastname@example.org with your best advice for raising future problem solvers. And we'll read our favorites on future episodes. Richard, thanks so much for joining us today.
Eugenia Cheng: Thank you.
Episode Summary & Conclusion [19:48]
Eric Olsen: Isn't she fun, folks? I was so thrilled to connect with her. She is the rare mind capable of incredibly complex mathematical thought and research. And also possess the ability to simplify and popularize these thoughts in an extraordinarily practical way. Bringing out and evangelizing not only the value of math, but the beauty within it. I loved hearing her thoughts about the simplicity on the other side of complexity. I loved her advice and suggestions for intellectual vulnerability with our kids. I hope she encouraged you not to be scared to go even deeper and wider with and alongside your kids learning together. And may you continue your journey alongside us raising the great problem solvers of the next generation. See you next week.