Eddie Woo: How Can Math Help Us Understand The Complexity Of The Universe? The world is full of recurring patterns based on math. Math teacher Eddie Woo explains why human beings are naturally drawn to patterns and how we can use math to engage with our complex world.

Eddie Woo: How Can Math Help Us Understand The Complexity Of The Universe?

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EDDIE WOO: I definitely - when I was going through school, I had no joy or delight in mathematics. In fact, I was one of those kids who kind of just - I survived mathematics.


This is Eddie Woo.

WOO: But I certainly didn't ever experience it as a really positive. Like, oh, wow, this is subject to be enjoyed and appreciated. It was really far away from my mind all the way through high school.

RAZ: But, Eddie, he actually ended up becoming the one thing he'd never thought he'd be, a math teacher.

WOO: It's really a testament to how my own teachers changed my own life. I turned up at university with the full intent to become an English and history teacher. I went so far as to have written that on my enrollment form. But it was at university, through some of the educators whom I met there, that I discovered that we don't have enough mathematics teachers and educators in our schools, really, in any level. And when I heard about this, suddenly all these pieces kind of fell into place for me because I realized maybe this is not just about me and my own experience of a subject. This is about something which is shaping our society.

We've got - if we went out on the street today, Guy, and we asked 10 people, do you like mathematics, I think nine of them would tell us no. And that would probably be on a good day. I think on a bad day, 10 would tell us no. We'd have to get further than that to get to the first person who actually likes it. And this is the effect that this shortage of skilled, and passionate and engaged mathematics educators, that's the consequence of that shortage in our culture and society. And I thought, I want to be an educator to make a difference in people's lives. If this is where the need is, I'm going to go down the rabbit hole.


WOO: You know, there's a universal reality and truth to this subject that humanity has been fascinated with for centuries, for millennia. And so I got to sort of stumble upon that, you know, really by accident and realize, wow, there's a reason why mathematicians describe mathematics in these incredible terms. They describe it as elegant, and it has this austere beauty. It was as though, Guy, you and I, we've kind of been born into this world where no one likes music.


WOO: They actually loathe it because it's something they are forced to do when they're young. Everyone really hates this particular style of music, but you have to go through learning how to write the notes and how to memorize the notes in sequence so you can recite them in a time-pressured assessment task. And then, thank goodness, after 13 years of all, compulsory music, we all just escape it, and we're very glad that we survived, having never actually listened to music ourselves.


WOO: That's a terrible way to describe a world. But that's the world we live in because that's how people think of mathematics.


RAZ: Here's more from Eddie Woo on the TED stage.


WOO: I used to believe that math was about rote-learning inscrutable formulas to solve abstract problems that didn't mean anything to me. But at university, I began to see that mathematics is immensely practical and even beautiful. That it's not just about finding answers, but also about learning to ask the right questions. It gradually dawned on me that mathematics is a sense. Mathematics is a sense, just like sight and touch. It's a sense that allows us to perceive realities which would be otherwise intangible to us. Now, I want to show you a mathematical reality that I guarantee you've seen before but perhaps never really perceived. It's been hidden in plain sight your entire life. This is a river delta. It's a beautiful piece of geometry. And when we hear the word geometry, most of us think of triangles and circles. But geometry is the mathematics of all shapes. And this meeting of land and sea has created shapes with an undeniable pattern. It has a mathematically recursive structure. Every part of the river delta, with its twists and turns, is a micro-version of the greater whole. So I want you to see the mathematics in this. But that's not all. There's a mathematical reality woven into the fabric of the universe that you share with winding rivers, towering trees and raging storms. These shapes are examples of what we call fractals, as mathematicians. Fractals get their name from the same place as fractions and fractures. It's a reference to the broken and shattered shapes we find around us in nature. And once you have a sense for fractals, you really do start to see them everywhere - a head of broccoli. The leaves of a fern. Even clouds in the sky. Like the other senses, our mathematical sense can be refined with practice. It's just like developing perfect pitch or a taste for wines. You can learn to perceive the mathematics around you with time and the right guidance.

RAZ: When people ask you a version of, you know, what am I going to do with this - like, when am I ever going to use math, what do you say?

WOO: Yeah. It's - there's such a deep and profound connection between all the mathematics that I learned and that I teach to my students and literally their everyday lives. I think we need to understand that mathematics is so much more than numbers. In fact, you know, if we go back to the - because I'm such an English nerd, I love etymology and where words come from. And if you dig into where the word mathematics comes from, literally, it just means understanding, and that is as broad as the universe that we live in, the cosmos.

You know, biology is the study of living things. Chemistry is the study of substances and materials. Physics is the study of matter and movement. But mathematics is the study of patterns, which are literally everywhere. Now, what does this mean in our everyday lives? Well, we are doing that...

RAZ: Yeah.

WOO: ...Every hour of every day. We are looking out at the world, and we are - I'm just thinking about, OK, when I get in my car and I drive home, you know, I'm sitting in this traffic and thinking about how to get home. I'm thinking about all the paths that I can take. Which one is going to be the fastest and most efficient so I can see my kids sooner? All of that, you're calculating, you're thinking logically in your mind.

It goes to my perception of the world. When I look out at a tree or at a rainbow, I don't just want to, you know, let these pieces of beauty pass me by. What it means to be human is actually to marvel at this universe around us and to say, wow, there's a reason why rainbows are round, why they're - you know when you see a rainbow after rain, it looks like a semicircle, you know, you can see it, you know, hitting the horizon?

RAZ: Yeah, sure.

WOO: But if you're lucky enough and in the right place at the right time, if you're in the sky or on a mountain, you'll actually see that rainbow is not a semicircle, it's a complete full circle. It goes all the way around. That's not a coincidence. That's geometry. That's beautiful. What it means to be human is to appreciate that and say, wow, there's something to wonder at here. And so for me, you know, when do I use mathematics? When do I not use mathematics? The real question is, do I know that I'm doing it when I am?


RAZ: Eddie, I asked a version of this question to Dan Finkel, but what's the danger of a society where people don't engage with math or don't have math competency or literacy? I mean, do you think there are consequences?

WOO: There are really severe consequences, and we've actually seen this in our society today. In so many ways, I could illustrate this. Firstly, can I play a really, really quick game with you guys? Can I play a game with you?

RAZ: Of course. Yeah, I'd love to.



WOO: We're going to go back and forth.


WOO: And we're going to say numbers.


WOO: The goal is, either you or me is going to say the number 23, OK?


WOO: And whoever says the number 23, they're the winner, OK? That's the goal.


WOO: Now, Guy, I'll let you go first. I want you to choose a number between one and four.

RAZ: Three.

WOO: Three. I'm going to add a number to that, and it's always going to be between one and four, OK?


WOO: So I'm going to say - I'm going to add one to that. So you said three, that means I say four. It's your turn now.

RAZ: OK. So I'm going to add a four.

WOO: Ah, I said four. So it's eight now.

RAZ: Yep.

WOO: Yep. I'm going to say two, so 10.

RAZ: And I'm going to say four.

WOO: Fourteen. OK, no worries. I'm going to say four now, so that means we're up to 18.

RAZ: Yeah.


WOO: What would you like to say now, Guy?

RAZ: (Laughter) One?

WOO: (Laughter).

RAZ: I've lost the game.

WOO: Now, I'm going to make a bet. I'm going to bet you laughed because you realized - took you about seven seconds, which is not bad, Guy. Now, I won't give you the full explanation here, but how did I win that? I knew something about patterns underneath that game which you didn't know.

RAZ: Yeah.

WOO: And so I could take advantage of that fact. And, you know, in this case, what's the harm? Aw, I win. No big deal, right? But when you don't know what's going on mathematically underneath something, and increasingly today, Guy, our world is built on and is run by algorithms that have been mathematically designed by people and are hidden from view, you know.

When you're scrolling through your social media feed, you're not thinking that there's mathematics happening underneath there. When you order something online and there's recommended stuff on the side for what - people like you, Guy, have purchased these as well. You're not thinking about there's a formula doing that, but mathematics is underneath all of those things, guiding all of those people's decision-making. And as I've just demonstrated, if you're not aware of that, someone can use that in a really malicious way, and people have used that in really malicious ways.

And so, you know, from a negative point of view, what are the consequences of us having a mathematically-illiterate general population? They're huge. There's people who are having the wool pulled over their eyes, and they don't even know it.


WOO: But at the same time, I think we're missing a part of who we are as human beings. This is what I was sort of getting at in the talk. Can you imagine if we walked around all day with our eyes closed? Can you imagine if we went into the world ignoring our senses? We have our senses because they're a wonderful way to understand and appreciate the world. So not only are there really negative consequences, but there are really positive things that we miss out and that I want people to be able to feel and experience. That, for me, is a really fundamental reason I think mathematics should be something everyone embraces and learns.


RAZ: That's Eddie Woo. He's a high school math teacher in Sydney, Australia. He also has his own channel on YouTube, which, of course, is all about math. You can see Eddie's full talk at ted.com.


RAZ: On the show today, ideas about the beauty of math. Stay with us. I'm Guy Raz, and you're listening to the TED Radio Hour from NPR.


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