An unexpected tool for understanding inequality: abstract math | Eugenia Cheng

94,256 views ・ 2019-04-09

TED


Please double-click on the English subtitles below to play the video.

00:13
The world is awash with divisive arguments,
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conflict,
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fake news,
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victimhood,
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exploitation, prejudice, bigotry, blame, shouting
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and minuscule attention spans.
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It can sometimes seem that we are doomed to take sides,
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be stuck in echo chambers
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and never agree again.
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It can sometimes seem like a race to the bottom,
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where everyone is calling out somebody else's privilege
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and vying to show that they are the most hard-done-by person
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in the conversation.
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How can we make sense
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in a world that doesn't?
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I have a tool for understanding this confusing world of ours,
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a tool that you might not expect:
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abstract mathematics.
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I am a pure mathematician.
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Traditionally, pure maths is like the theory of maths,
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where applied maths is applied to real problems like building bridges
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and flying planes
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and controlling traffic flow.
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But I'm going to talk about a way that pure maths applies directly
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to our daily lives
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as a way of thinking.
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I don't solve quadratic equations to help me with my daily life,
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but I do use mathematical thinking to help me understand arguments
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and to empathize with other people.
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And so pure maths helps me with the entire human world.
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But before I talk about the entire human world,
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I need to talk about something that you might think of
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as irrelevant schools maths:
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factors of numbers.
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We're going to start by thinking about the factors of 30.
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Now, if this makes you shudder with bad memories of school maths lessons,
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I sympathize, because I found school maths lessons boring, too.
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But I'm pretty sure we are going to take this in a direction
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that is very different from what happened at school.
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So what are the factors of 30?
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Well, they're the numbers that go into 30.
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Maybe you can remember them. We'll work them out.
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It's one, two, three,
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five, six,
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10, 15 and 30.
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It's not very interesting.
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It's a bunch of numbers in a straight line.
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We can make it more interesting
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by thinking about which of these numbers are also factors of each other
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and drawing a picture, a bit like a family tree,
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to show those relationships.
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So 30 is going to be at the top like a kind of great-grandparent.
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Six, 10 and 15 go into 30.
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Five goes into 10 and 15.
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Two goes into six and 10.
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Three goes into six and 15.
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And one goes into two, three and five.
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So now we see that 10 is not divisible by three,
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but that this is the corners of a cube,
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which is, I think, a bit more interesting
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than a bunch of numbers in a straight line.
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We can see something more here. There's a hierarchy going on.
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At the bottom level is the number one,
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then there's the numbers two, three and five,
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and nothing goes into those except one and themselves.
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You might remember this means they're prime.
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At the next level up, we have six, 10 and 15,
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and each of those is a product of two prime factors.
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So six is two times three,
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10 is two times five,
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15 is three times five.
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And then at the top, we have 30,
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which is a product of three prime numbers --
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two times three times five.
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So I could redraw this diagram using those numbers instead.
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We see that we've got two, three and five at the top,
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we have pairs of numbers at the next level,
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and we have single elements at the next level
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and then the empty set at the bottom.
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And each of those arrows shows losing one of your numbers in the set.
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Now maybe it can be clear
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that it doesn't really matter what those numbers are.
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In fact, it doesn't matter what they are.
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So we could replace them with something like A, B and C instead,
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and we get the same picture.
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So now this has become very abstract.
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The numbers have turned into letters.
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But there is a point to this abstraction,
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which is that it now suddenly becomes very widely applicable,
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because A, B and C could be anything.
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For example, they could be three types of privilege:
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rich, white and male.
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So then at the next level, we have rich white people.
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Here we have rich male people.
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Here we have white male people.
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Then we have rich, white and male.
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And finally, people with none of those types of privilege.
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And I'm going to put back in the rest of the adjectives for emphasis.
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So here we have rich, white non-male people,
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to remind us that there are nonbinary people we need to include.
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Here we have rich, nonwhite male people.
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Here we have non-rich, white male people,
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rich, nonwhite, non-male,
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non-rich, white, non-male
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and non-rich, nonwhite, male.
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And at the bottom, with the least privilege,
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non-rich, nonwhite, non-male people.
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We have gone from a diagram of factors of 30
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to a diagram of interaction of different types of privilege.
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And there are many things we can learn from this diagram, I think.
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The first is that each arrow represents a direct loss of one type of privilege.
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Sometimes people mistakenly think that white privilege means
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all white people are better off than all nonwhite people.
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Some people point at superrich black sports stars and say,
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"See? They're really rich. White privilege doesn't exist."
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But that's not what the theory of white privilege says.
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It says that if that superrich sports star had all the same characteristics
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but they were also white,
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we would expect them to be better off in society.
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There is something else we can understand from this diagram
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if we look along a row.
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If we look along the second-to-top row, where people have two types of privilege,
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we might be able to see that they're not all particularly equal.
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For example, rich white women are probably much better off in society
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than poor white men,
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and rich black men are probably somewhere in between.
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So it's really more skewed like this,
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and the same on the bottom level.
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But we can actually take it further
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and look at the interactions between those two middle levels.
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Because rich, nonwhite non-men might well be better off in society
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than poor white men.
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Think about some extreme examples, like Michelle Obama,
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Oprah Winfrey.
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They're definitely better off than poor, white, unemployed homeless men.
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So actually, the diagram is more skewed like this.
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And that tension exists
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between the layers of privilege in the diagram
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and the absolute privilege that people experience in society.
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And this has helped me to understand why some poor white men
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are so angry in society at the moment.
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Because they are considered to be high up in this cuboid of privilege,
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but in terms of absolute privilege, they don't actually feel the effect of it.
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And I believe that understanding the root of that anger
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is much more productive than just being angry at them in return.
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Seeing these abstract structures can also help us switch contexts
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and see that different people are at the top in different contexts.
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In our original diagram,
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rich white men were at the top,
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but if we restricted our attention to non-men,
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we would see that they are here,
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and now the rich, white non-men are at the top.
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So we could move to a whole context of women,
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and our three types of privilege could now be rich, white and cisgendered.
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Remember that "cisgendered" means that your gender identity does match
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the gender you were assigned at birth.
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So now we see that rich, white cis women occupy the analogous situation
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that rich white men did in broader society.
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And this has helped me understand why there is so much anger
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towards rich white women,
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especially in some parts of the feminist movement at the moment,
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because perhaps they're prone to seeing themselves as underprivileged
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relative to white men,
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and they forget how overprivileged they are relative to nonwhite women.
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We can all use these abstract structures to help us pivot between situations
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in which we are more privileged and less privileged.
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We are all more privileged than somebody
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and less privileged than somebody else.
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For example, I know and I feel that as an Asian person,
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I am less privileged than white people
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because of white privilege.
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But I also understand
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that I am probably among the most privileged of nonwhite people,
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and this helps me pivot between those two contexts.
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And in terms of wealth,
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I don't think I'm super rich.
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I'm not as rich as the kind of people who don't have to work.
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But I am doing fine,
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and that's a much better situation to be in
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than people who are really struggling,
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maybe are unemployed or working at minimum wage.
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I perform these pivots in my head
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to help me understand experiences from other people's points of view,
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which brings me to this possibly surprising conclusion:
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that abstract mathematics is highly relevant to our daily lives
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and can even help us to understand and empathize with other people.
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My wish is that everybody would try to understand other people more
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and work with them together,
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rather than competing with them
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and trying to show that they're wrong.
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And I believe that abstract mathematical thinking
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can help us achieve that.
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Thank you.
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(Applause)
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