0:00:01.446,0:00:07.082 The world is awash[br]with divisive arguments, 0:00:07.082,0:00:10.825 conflict, fake news, 0:00:10.825,0:00:13.281 victimhood, 0:00:13.281,0:00:18.871 exploitation, prejudice,[br]bigotry, blame, shouting, 0:00:18.871,0:00:21.999 and minuscule attention spans. 9:59:59.000,9:59:59.000 It can sometimes seem 9:59:59.000,9:59:59.000 that we are doomed to take sides, 9:59:59.000,9:59:59.000 be stuck in echo chambers, 9:59:59.000,9:59:59.000 and never agree again. 9:59:59.000,9:59:59.000 It can sometimes seem[br]like a race to the bottom, 9:59:59.000,9:59:59.000 where everyone is calling out[br]somebody else's privilege 9:59:59.000,9:59:59.000 and vying to show that they 9:59:59.000,9:59:59.000 are the most hard-done-by person[br]in the conversation. 9:59:59.000,9:59:59.000 How can we make sense 9:59:59.000,9:59:59.000 in a world that doesn't? 9:59:59.000,9:59:59.000 I have a tool for understanding[br]this confusing world of ours, 9:59:59.000,9:59:59.000 a tool that you might not expect: 9:59:59.000,9:59:59.000 abstract mathematics. 9:59:59.000,9:59:59.000 I am a pure mathematician. 9:59:59.000,9:59:59.000 Traditionally, pure maths[br]is like the theory of maths, 9:59:59.000,9:59:59.000 where applied maths is applied[br]to real problems like building bridges 9:59:59.000,9:59:59.000 and flying planes 9:59:59.000,9:59:59.000 and controlling traffic flow. 9:59:59.000,9:59:59.000 But I'm going to talk about a way[br]that pure maths applies directly 9:59:59.000,9:59:59.000 to our a daily lives as a way of thinking. 9:59:59.000,9:59:59.000 I don't solve quadratic equations[br]to help me with my daily life, 9:59:59.000,9:59:59.000 but I do use mathematical thinking[br]to help me understand arguments 9:59:59.000,9:59:59.000 and to empathize with other people. 9:59:59.000,9:59:59.000 And so pure maths helps me[br]with the entire human world. 9:59:59.000,9:59:59.000 But before I talk about[br]the entire human world, 9:59:59.000,9:59:59.000 I need to talk about something[br]that you might think of 9:59:59.000,9:59:59.000 as irrelevant schools maths: 9:59:59.000,9:59:59.000 factors of numbers. 9:59:59.000,9:59:59.000 We're going to start by thinking[br]about the factors of 30. 9:59:59.000,9:59:59.000 Now, if this makes you shudder[br]with bad memories of school maths lessons, 9:59:59.000,9:59:59.000 I sympathize, 9:59:59.000,9:59:59.000 because I found school[br]maths lessons boring too. 9:59:59.000,9:59:59.000 But I'm pretty sure we are going[br]to take this in a direction 9:59:59.000,9:59:59.000 that is very different[br]from what happened at school. 9:59:59.000,9:59:59.000 So what are the factors of 30? 9:59:59.000,9:59:59.000 Maybe you can remember them.[br]We'll work them out. 9:59:59.000,9:59:59.000 It's one, two, three, 9:59:59.000,9:59:59.000 five, six, 9:59:59.000,9:59:59.000 10, 15, and 30. 9:59:59.000,9:59:59.000 It's not very interesting. 9:59:59.000,9:59:59.000 It's a bunch of numbers[br]in a straight line. 9:59:59.000,9:59:59.000 We can make it more interesting[br]by thinking about which of these numbers 9:59:59.000,9:59:59.000 are also factors of each other[br]and drawing a picture, 9:59:59.000,9:59:59.000 a bit like a family tree 9:59:59.000,9:59:59.000 to show those relationships. 9:59:59.000,9:59:59.000 So 30 is going to be at the top[br]like a kind of great grandparent. 9:59:59.000,9:59:59.000 Six, 10, and 15 go into 30. 9:59:59.000,9:59:59.000 Five goes into 10 and 15. 9:59:59.000,9:59:59.000 Two goes in six and 10. 9:59:59.000,9:59:59.000 Three goes into six and 15. 9:59:59.000,9:59:59.000 And one goes into two, three, and five. 9:59:59.000,9:59:59.000 So now we see that 10[br]is not divisible by three, 9:59:59.000,9:59:59.000 but that is this the corners of a cube, 9:59:59.000,9:59:59.000 which is I think a bit more interesting 9:59:59.000,9:59:59.000 than a bunch of numbers[br]in a straight line. 9:59:59.000,9:59:59.000 We can see something more here.[br]There's a hierarchy going on. 9:59:59.000,9:59:59.000 At the bottom level is the number one, 9:59:59.000,9:59:59.000 then there's the numbers[br]two, three, and five, 9:59:59.000,9:59:59.000 and nothing goes into those[br]except one and themselves. 9:59:59.000,9:59:59.000 You might remember[br]this means they're prime. 9:59:59.000,9:59:59.000 At the next level up,[br]we have six, 10, and 15, 9:59:59.000,9:59:59.000 and each of those is a product[br]of two prime factors. 9:59:59.000,9:59:59.000 So six is two times three, 9:59:59.000,9:59:59.000 10 is two times five, 9:59:59.000,9:59:59.000 15 is three times five, 9:59:59.000,9:59:59.000 and then at the top, we have 30, 9:59:59.000,9:59:59.000 which is a product of three prime numbers, 9:59:59.000,9:59:59.000 two times three times five. 9:59:59.000,9:59:59.000 So I could redraw this diagram[br]using those numbers instead. 9:59:59.000,9:59:59.000 So we see that we've got[br]two, three, and five at the top, 9:59:59.000,9:59:59.000 we have pairs of numbers[br]at the next level, 9:59:59.000,9:59:59.000 and we have single elements[br]at the next level, 9:59:59.000,9:59:59.000 and then the empty set at the bottom. 9:59:59.000,9:59:59.000 And each of those arrows shows[br]losing one of your numbers in the set. 9:59:59.000,9:59:59.000 Now maybe it can be clear 9:59:59.000,9:59:59.000 that it doesn't really matter[br]what those numbers are. 9:59:59.000,9:59:59.000 In fact it doesn't matter what they are. 9:59:59.000,9:59:59.000 So we could replace them with[br]something like A, B, and C instead 9:59:59.000,9:59:59.000 and we get the same picture. 9:59:59.000,9:59:59.000 So now this has become very abstract. 9:59:59.000,9:59:59.000 The numbers have turned into letters. 9:59:59.000,9:59:59.000 But there is a point to this abstraction, 9:59:59.000,9:59:59.000 which is that it now suddenly[br]becomes very widely applicable, 9:59:59.000,9:59:59.000 because A, B, and C could be anything. 9:59:59.000,9:59:59.000 For example, they could be[br]three types of privilege: 9:59:59.000,9:59:59.000 rich, white, and male. 9:59:59.000,9:59:59.000 So then at the next level,[br]we have rich white people. 9:59:59.000,9:59:59.000 Here we have rich male people. 9:59:59.000,9:59:59.000 Here we have white male people. 9:59:59.000,9:59:59.000 Then we have rich, white, and male. 9:59:59.000,9:59:59.000 And finally people with[br]none of those types of privilege. 9:59:59.000,9:59:59.000 And I'm going to put back in[br]the rest of the adjectives for emphasis. 9:59:59.000,9:59:59.000 So here we have rich white[br]non-male people, 9:59:59.000,9:59:59.000 to remind us that there are[br]non-binary people we need to include. 9:59:59.000,9:59:59.000 Here we have rich non-white male people. 9:59:59.000,9:59:59.000 Here we have non-rich white male people, 9:59:59.000,9:59:59.000 rich non-white non-male, 9:59:59.000,9:59:59.000 non-rich white non-male, 9:59:59.000,9:59:59.000 and non-rich, non-white male, 9:59:59.000,9:59:59.000 and, and at the bottom[br]with the least privilege, 9:59:59.000,9:59:59.000 non-rich, not-white, non-male people. 9:59:59.000,9:59:59.000 We have gone from a diagram[br]of factors of 30 9:59:59.000,9:59:59.000 to a diagram of interaction[br]of different types of privilege, 9:59:59.000,9:59:59.000 and there are many things[br]we can learn from this diagram, I think. 9:59:59.000,9:59:59.000 The first is that each arrow represents[br]a direct loss of one type of privilege. 9:59:59.000,9:59:59.000 Sometimes people mistakenly think[br]that white privilege means 9:59:59.000,9:59:59.000 all white people are better off[br]than all non-white people. 9:59:59.000,9:59:59.000 Some people point at superrich[br]black sports stars and say, 9:59:59.000,9:59:59.000 "See? They're really rich.[br]White privilege doesn't exist." 9:59:59.000,9:59:59.000 But that's not what the theory[br]of white privilege says. 9:59:59.000,9:59:59.000 It says that if that superrich sports star[br]had all the same characteristics 9:59:59.000,9:59:59.000 but they were also white, 9:59:59.000,9:59:59.000 we would expect them[br]to be better off in society. 9:59:59.000,9:59:59.000 There is something else[br]we can understand from this diagram 9:59:59.000,9:59:59.000 if we look along a row. 9:59:59.000,9:59:59.000 If we look along the second-to-top row,[br]where people have two types of privilege, 9:59:59.000,9:59:59.000 we might be able to see 9:59:59.000,9:59:59.000 that they're not all particularly equal. 9:59:59.000,9:59:59.000 For example, rich white women 9:59:59.000,9:59:59.000 are probably much better off in society 9:59:59.000,9:59:59.000 than poor white men, 9:59:59.000,9:59:59.000 and rich black men are probably[br]somewhere in between. 9:59:59.000,9:59:59.000 So it's really more skewed like this, 9:59:59.000,9:59:59.000 and the same on the bottom level. 9:59:59.000,9:59:59.000 But we can actually take it further 9:59:59.000,9:59:59.000 and look at the interactions[br]between those two middle levels, 9:59:59.000,9:59:59.000 because rich non-white non-men[br]might well be better off in society 9:59:59.000,9:59:59.000 than poor white men. 9:59:59.000,9:59:59.000 Think about some extreme examples,[br]like Michelle Obama, Oprah Winfrey. 9:59:59.000,9:59:59.000 They're definitely better off[br]than poor white unemployed homeless men. 9:59:59.000,9:59:59.000 So actually the diagram[br]is more skewed like this. 9:59:59.000,9:59:59.000 And that tension exists 9:59:59.000,9:59:59.000 between the layers[br]of privilege in the diagram 9:59:59.000,9:59:59.000 and the absolute privilege[br]that people experience in society. 9:59:59.000,9:59:59.000 And this has helped me to understand[br]why some poor white men 9:59:59.000,9:59:59.000 are so angry in society at the moment, 9:59:59.000,9:59:59.000 because they are considered to be high up[br]in this cuboid of privilege, 9:59:59.000,9:59:59.000 but in terms of absolute privilege,[br]they don't actually feel the effect of it. 9:59:59.000,9:59:59.000 And I believe that understanding[br]the root of that anger 9:59:59.000,9:59:59.000 is much more productive[br]than just being angry at them in return. 9:59:59.000,9:59:59.000 Seeing these abstract structures 9:59:59.000,9:59:59.000 can also help us switch contexts 9:59:59.000,9:59:59.000 and see that different people[br]are at the top in different contexts. 9:59:59.000,9:59:59.000 In our original diagram, 9:59:59.000,9:59:59.000 rich white men were at the top, 9:59:59.000,9:59:59.000 but if we restricted[br]our attention to non-men, 9:59:59.000,9:59:59.000 we would see that they are here, 9:59:59.000,9:59:59.000 and now the rich white[br]non-men are at the top. 9:59:59.000,9:59:59.000 So we could move to[br]a whole context of women, 9:59:59.000,9:59:59.000 and our three types of privilege[br]could now be rich, white, and cisgendered. 9:59:59.000,9:59:59.000 Remember that cisgendered means[br]that your gender identity does match 9:59:59.000,9:59:59.000 the gender you were assigned at birth. 9:59:59.000,9:59:59.000 So now we see that rich white cis women[br]occupy the analogous situation 9:59:59.000,9:59:59.000 that rich white men did[br]in broader society, 9:59:59.000,9:59:59.000 and this has helped me understand[br]why there is so much anger 9:59:59.000,9:59:59.000 towards rich white women, 9:59:59.000,9:59:59.000 especially in some parts[br]of the feminist movement at the moment, 9:59:59.000,9:59:59.000 because perhaps they're prone[br]to seeing themselves as underprivileged 9:59:59.000,9:59:59.000 relative to white men, 9:59:59.000,9:59:59.000 and they forget how overprivileged[br]they are relative to non-white women. 9:59:59.000,9:59:59.000 We can all use these abstract structures[br]to help us pivot between situations 9:59:59.000,9:59:59.000 in which we are more privileged[br]and less privileged. 9:59:59.000,9:59:59.000 We are all more privileged than somebody 9:59:59.000,9:59:59.000 and less privileged than somebody else. 9:59:59.000,9:59:59.000 For example, I know and I feel 9:59:59.000,9:59:59.000 that as an Asian person, 9:59:59.000,9:59:59.000 I am less privileged than white people[br]because of white privilege, 9:59:59.000,9:59:59.000 but I also understand that I am probably 9:59:59.000,9:59:59.000 among the most privileged[br]of non-white people, 9:59:59.000,9:59:59.000 and this helps me pivot[br]between those two contexts. 9:59:59.000,9:59:59.000 And in terms of wealth, 9:59:59.000,9:59:59.000 I don't think I'm superrich. 9:59:59.000,9:59:59.000 I'm not as rich as the kind of people[br]who don't have to work, 9:59:59.000,9:59:59.000 but I am doing fine, 9:59:59.000,9:59:59.000 and that's a much better[br]situation to be in 9:59:59.000,9:59:59.000 than people who are really struggling, 9:59:59.000,9:59:59.000 maybe are unemployed[br]or working at minimum wage. 9:59:59.000,9:59:59.000 I perform these pivots in my head 9:59:59.000,9:59:59.000 to help me understand experiences[br]from other people's points of view, 9:59:59.000,9:59:59.000 which brings me to this[br]possibly surprising conclusion: 9:59:59.000,9:59:59.000 that abstract mathematics 9:59:59.000,9:59:59.000 is highly relevant to our daily lives 9:59:59.000,9:59:59.000 and can even help us to understand[br]and empathize with other people. 9:59:59.000,9:59:59.000 My wish is that everybody would try[br]to understand other people more 9:59:59.000,9:59:59.000 and work with them together, 9:59:59.000,9:59:59.000 rather than competing with them 9:59:59.000,9:59:59.000 and trying to show that they're wrong. 9:59:59.000,9:59:59.000 And I believe that abstract[br]mathematical thinking 9:59:59.000,9:59:59.000 can help us achieve that. 9:59:59.000,9:59:59.000 Thank you. 9:59:59.000,9:59:59.000 (Applause)