The health of town hall, our partners who are set up in the catholic over here at a special guest zeno math powered for hope everyone has had a chance to visit will be set up in the library showing off their cool math games and activities. I so welcome you to tonight very special masking doubleheader with Eugenia Cheng and Amir Alexander. This is part of a big homecoming festival and in helping many of you might be returning to her building for the first time after a couple of years. Weve been remodeling this base and for many more to this might be a First Time Ever at townhall, welcome. This is exactly the type of thing we exist to do. Im so pleased to present these fantastic authors do tonight. We love all of our lecture programs, all of the political talks, all of the arts program if we do here but ive especially fascinated by math, mathematical approaches. Im a reformed college math student and so having the chance to present you Eugenia Cheng and Amir Alexander on a doubleheade doubleheader, this was really great opportunity for the special homecoming festival. Im so pleased to see everyone here tonight and face to our partners. The format is unusual tonight if youve been other townhall because it is doubleheader. We will open with a solo presentation from Eugenia Cheng and then take a short break while we switch the presentation over to Amir Alexander who will come up and give his talk after which we will have a choice of q a. Keep questions in mind from both talks. There is visit beautiful residents tonight where genus talk focuses on its dynamic and then we take this broader historical view of the Historical Development of mathematical thinking with Amir Alexander. Hopefully there will be some residents but both will be happy to answer questions. After that you can pick up a copy of by the book at the book table and will a book signing afterwards and our bar and cafe will be open if door to stick around. The very last thing i will say about townhall is a member supported organization. Thank you so much to the members in a room. Now to introduce eugenia and sick couple words about zeno i would like to welcome julie marl from zeno to the microphone. Thank you so much. [applause] and. Thank you. Im the executive director of zeno and zeno is a seattlebased nonprofit. Our vision is a world where everyone knows they can do math. We achieve this through programming for families of kids ages three to five with a focus on families of color and no income communities. Our is all about making math fun and playful. Because we know theres no such thing as life lived without math and will be based on Math Foundation is key to life opportunity and success. Where so excited to be a Community Partner to townhall for two nights lecture. So dr. Eugenia cheng is scientist and resident at the school of the Art Institute of chicago. She won tenure and pure mathematics at the university of sheffield uk and is now honorary visiting fellow at City University of london. She is prettily top universities of cambridge, chicago and nice and holds a phd and pure mathematics from the university of cambridge. Alongside a research in category theory and her undergraduate teaching, her aim is to rid the world of math phobia. Her first popular math book, how to bake pie was praised by the New York TimesNational Geographic and Scientific American and she was interviewed around the world including on the bbc, npr and the late show with stephen colbert. Our book beyond infinity were shortlisted for the Society InsightInvestment Science book prize 17. She was an early pioneer of math on youtube and reviews have been viewed over 15 million times. Eugenias is also a math columnist for the wall street journal, a concert pianist and founder of the leader student. Please join me in welcoming dr. Eugenia cheng. [applause] thank you very much. First of all, thank you so much to the tunnel for invited me back here to speak on my latest book. Its always very affirming to be invited back somewhere i can, and this is the third time ive been dignified here so that tripoli affirming. Its wonderful to be in saddle and the sun does shine every time i speak at the townhall. So thank you for joining us this evening for a math evening but talk about my latest book the art of logic in an illogical world and the point about the illogical book is this. It can sometimes seem like we are drowning in the current world where the world is awash with divisive this and conflict and fake news, victimhood, exportation, privilege, blame, bigotry, shouting and miniscule attention span. And it can seem we will never agree with each other ever get and where doomed to be stuck in aqua chambers. And just yelling back and forth into nowhere. And is all hope lost, thats the question. And i said no, all hope is not lost. It can seem like that sometimes in this book arose for my teaching art students, and in that fall semester 2016 some things happened, varies things on both sides are galactic, and morning after the election i did what many people did. I got depressed, i cried, i drank and i thought, what can cn you do thats productive . Because i truly believe in doing something rather than sitting around complaining and also believe in looking at your own combination of abilities and tried use them in the best way you can to do something to help the world in a in a way you se. I thought what can i do as a pure mathematician in this political situation . I realized what had been doing all semester was using the principles of mathematical thinking to find greater clarity in those divisive arguments. I i felt i could share that more broadly with everyone who wants to find that clarity, some people of course are not interested but i believe there are people who do want to understand whats going on and understand whats going on all sides of the argument is the first. Im not saying it will solve all the problems but if we dont understand that we cant move forward and thats what about this book. It grew out of the discussion i had with my art students where i teach abstract mathematics. Its not a remedial mathematics. Its not the things they have forgotten from high school. Its how to think him how to use mathematics as a way of thinking. And [laughing] is there someone here who thats a good question. Where is the computer . Does this work . Its on. Thank you. [inaudible] perhaps you could the volume could be turned down because this is just how loud i speak, when im afraid. At least when an interested. When im not interested i speak less loud. Thanks. Ill keep going i suppose until we can find what my next life is. I teach our students and the art students are very interesting students. They are not mathematicians at all. Its my dream job because i want to share what i feel about mathematics with more people and there are myths about math that is just that numbers and equations, that its that everybody can some people are math people and so people are not math people and you get to your tables and cant possibly be a mathematician. Things like that are myths of trying to dispel. Teaching art students at the wonderful place for me to find out more about what put people off math as they work with us and what as it were put them back on math. I believe and im sure if there are any educators in the room you all agree that its really important thank you to tap into what motivates your students in order to motivate them in what youre teaching rather than trying to implode your motivation on top of them. I realize what motivates my students is questions of social and political justice. Thats why this book came out like this. My students in sheffield, food motivated them. Thats when the first book was about math and food. Still doesnt should i get closer to it . Should i go and stand over there . I could get the rest of the top without my slides i like my slides. Thats going to be very competent because i have a lot of transitions but i guess we will try it. I think its that just about numbers, not just that getting the right answer. Its not just about solving problems even. I believe its the framework for agreement on things and that every academic discipline have framework for assessing what should count as good information. In the current world thats what we really need from education because theres tons of information ever. Information is no longer at a premium. I went deciding what counts as good information and pure mathematics has one particular framework based on logic. [laughing] so i believe there have been an oldfashioned traditional view of pure mathematics is but her mathematics applies to applied mathematics. And applied mathematics is useful for science but science is useful for engineering and medicine which is useful for the numerical quantitative parts of the human world and that is a truth and the use of a that was the extent of how my research would ever be useful because my research is so abstract. The thing is this narrow view enables people to declare that they dont need math. People can be glad this exists but they can sit on the ever going to go into any of those fields so i dont need to do it myself. Where as i please. Mathematics is about how to think and that therefore it is about the entire human world, at least the parts of the human world that thinks. Sometimes these days it seems like some of the human world doesnt think very much. So when you way i am going to talk about first of all analogies and what will they put in mathematics. And the interconnectedness of things, then i will talk about how abstract math enables us to see relationships we might didnt see before and that we can use those abstract relationships to pivot between different situations so we can understand more things and we praise they did. And finally i will talk about how this fits in what i believe is intelligence. So first of all, analogies another thing we can say is that pure mathematics is a theory of analogies and heres what i mean by that. Supposing we have two apples and two bananas, then we can say theres something they have in common. If we forget the details about them being apples and bananas we go, they are both two things and this is fundamentally how to come up with the idea of numbers in the first place. Numbers are an abstraction that have something in common. If you teach children how to count, i love helping children with math and you could try to teach medicare you just have to wait until they make that abstraction late and you cant do it for them. They just have to sort of see whats going on. Every time would make another abstraction late in the prices of math education some people dont quite make it. There are various reasons and one is it can seem pointless and another is you just have to wait until you can do. Nobody can do it for you. The other thing is there different ways to do. This is not a completely automatic process. So if, for example, we wanted to this is very exciting. [laughing] if instead of saying two things can we said what this had in common was two fruits that would be true and also an abstraction. However in that case we would not be able to include two chairs in that situation. That is that an example of two fruits so we have to go up one level further to two things in which we can encompass those examples. What im going to argue, one of the things is all the abstraction takes us further away from real life, it enables us to bring informal examples that we could before. Heres a more mathematical example where if we look at one plus two and two plus three, there are examples of a b a people say i was fine with math until the numbers became lessons. Im going to show you what the point is of numbers become letters so we could also say, look at one times two and two times three, but now so now a plus b and a times the all. [applause] thank you very much. Thank you. So they are both examples of a something be and that is a get for the level of abstraction. These levels are abstraction, the both the love of what you would do in elementary school. This level is what might happen we start to meet algebra. This level is what happens if you go to be a math major in university and take abstract algebra, maybe group three. None of these levels is right or wrong. Thats not the point. People think that is about right or wrong. Its not. Its about what might you shedding any particular situation. One of the thinks my phd advisor taught me was the aim isnt to find the most abstract possible approach. The aim is to find a good level of abstraction for what youre trying to do. And what happens the normal life typically is we talk about things being analogous but we dont focus on exactly what is making the analogous. That ambiguity leaves open the possibility of discriminant just basin using Different Levels of abstraction that we are not making clear. Where as in map we are explicit about what level we are using so that we remove that are taken ambiguity. Heres an example how that ambiguity comes in. If we talk about straight marriage and samesex marriage, some people say theres no difference between. The difference is terrible. Whats going on is people using Different Levels of abstraction, so if you think marriage is about an unrelated man and woman, then indeed samesex marriage is not part of the future. Some of us believe really about im an adult in which samesex marriage is a part of that. People disagree because they are using Different Levels of abstraction. The next thing that happens, people who disagree about the upperlevel can hallucinate we have gone further than we have and they get upset and safe the next thing we know we will be allowing any two adults even if they are not unrelated. I have redacted whats going on in case they were chilled and the audience because then we could go further and just say two humans or we could say two living creatures. Or we could say two creatures. [laughing] and the point is that just because some of us have decided we want to go here does not automatically mean we have a shot all the way at the top. But when were not precise way youre using a can open us up to both arguments about this is the same and this isnt the same. Im not saying this approach solves that problem that i think gives us an opportunity to have a slightly clearer and more sensible argument about it. The next and want to talk about is how things become, can be seen as being interconnected. Heres my favorite diagram of interconnectedness and it is an abstraction of the London Underground system. We have forgotten many details about where things are and, in fact, its not geographically accurate that its useful for seeing how stations are connected by which lines that because its not geographically accurate you can end up with slightly hapless tourists tried to take the train from Leicester Square to common garden even though they are only about two minutes walk away. Here is the geographically accurate picture of London Underground which is a different abstraction and its not better or worse. Its probably less useful if youre going to take the train somewhere but its interesting scene where everything is. The point is these are two different abstractions that the limited different aspects of the situation and this is what math does. It abstracts from a situation to see what we can learn from it. Heres an abstraction i find interesting to do a relationship breakdowns. This is what happens when relationships break down that maybe one person i will call them alex feels disrespected and alex is unable to show love. Alex is parker sam feels unloved as result of which sam is unable to show respect so alex feels disrespected. We have a vicious circle that can escalate. I can further abstract and label these arrows as action and these arrows as felix. This doesnt solve the problem but it makes a a start becausee can think about how we could break these arrows because you have to break one to break the circle and you can say is it easy to break an action arrow or a feelings and records maybe we cant control our feelings but maybe we can decide not to act on them. Perhaps when alex feels disrespected they could concentrate on still showing love regardless of that and the situation will not spiral out of control. We reduce it to these two action arrows and argue about who should take responsibility for breaking the arrows. One possible if there is webers more mature should do that. [laughing] we have this vicious circle and this vicious circle at an abstract level is similar to even more tragic things, for example, the situation of Police Violence which one could try and say happens like this, but police feel threatened by black people and so the defend themselves against black people which makes black people feel threatened by the police and so they defend themselves against the police and so the police feel threatened by them. Im not saying this is what happens. Its an overview but it is been shown even when black people dont do anything to defend themselves and did everything theyre supposed to do, theye still Police Violence against them. We can say she would break the action arrows or the feelings arrows . We might argue maybe the police, why do they feel threatened . Could they be trained to feel less threatened . Is been shown they felt less threatened by white people than by black people so maybe we can trained in. We could maybe. Translator take action differently, deescalate rather than escalate things. We could say who should take responsibility . Some people yell and say black people should just obey the law. I would argue its clearly the police where the power in the situation so i think they should be the ones take responsible for changing it. If they dont that doesnt help when did we can find some clarity about what is going on. This is something abstraction can help us with. Another way i used interconnectedness is wind are many factors contributing to the same thing in an interconnected way. There would be a egregious united incident when they need to kick someone off a flight because it was overbooked and the absolute elite and he didnt want to leave so they called security and the got dragged often injured. There were wonderful arguments on the internet going tj shouldve done, if you do what youre told you will not get injured. It really isnt that simple. Whenever someone on unit