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The world is awash
with divisive arguments,

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conflict, 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

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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

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are the most hard-done-by person
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 a daily lives 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,

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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?
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
by thinking about which of these numbers

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are also factors of each other
and drawing a picture,

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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 in 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 is this 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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So 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
non-binary people we need to include.

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Here we have rich non-white male people.

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Here we have non-rich white male people,

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rich non-white non-male,

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non-rich white non-male,

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and non-rich, non-white male,

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and, and at the bottom
with the least privilege,

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non-rich, not-white, 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 non-white 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

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that they're not all particularly equal.

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For example, rich white women

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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 non-white 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, 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

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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 non-white 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

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that as an Asian person,

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I am less privileged than white people
because of white privilege,

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but I also understand that I am probably

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among the most privileged
of non-white 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 superrich.

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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

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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)