9:59:59.000,9:59:59.000 The world is awash[br]with divisive arguments, 9:59:59.000,9:59:59.000 conflict, fake news, 9:59:59.000,9:59:59.000 victimhood, 9:59:59.000,9:59:59.000 exploitation, prejudice,[br]bigotry, blame, shouting, 9:59:59.000,9:59:59.000 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.