Evelyn Lamb: Welcome to My Favorite Theorem. I'm your host Evelyn lamb. I'm a freelance math and science writer based in Salt Lake City. Today I am by myself because I'm on location. I am in Washington DC right now for the Science Writers conference. That's the conference for the National Association of Science Writers and I'm really happy to be joined by Yen Duong, who is a also a science writer with a math background. So yeah, can you tell us a little bit about yourself?
Yen Duong: Yeah, so I am in Charlotte, North Carolina, and I work part time for North Carolina Health News. And the rest of my time, I am a freelance math and science writer like you.
YD: And I just finished the AAAS Mass Media Fellowship this summer, and before that I got my Ph.D. at UIC in geometric group theory.
EL: Yeah, and the AAAS fellowship is the one, the way I started doing science writing as well. A lot of people, when you come to conferences like these, you find out a lot of people who are more senior in the field have also gone through this. So it's really great. The application deadline, I believe is in January. So we'll try to air this at a time when people can look into that and apply for it. But yeah, it's a great program that brings grad students in science, you know, math and other sciences, into newsrooms to learn a little bit about how the news gets made and how to report on science for a broader audience. So it was a great experience for me. It sounds like it was a great experience for you.
YD: Yeah, it's fantastic. It's 10 weeks, I think this coming year, the stipend will be $6,000. So that's great. It is paid. And for me, at least it jump started the rest of my career as a math and science writer.
EL: Yeah, definitely. And it’s nice to hear that it's being paid a little more. I lived in New York City for less than that. And that was difficult. Okay, so do you want to tell us about your favorite theorem?
YD: I've been listening to this podcast for a while. And it's like, okay, I'll do a really fancy one to be really impressive. And people will think I'm fancy. But I decided not to do that. Because I'm not that fancy. And I think it's silly to be that pretentious. So I'm going with one of the first theorems I learned, like as an undergrad, which was Ramsey theory, that the Ramsey number of R(3,3) equals six.
EL: Okay, great. So, yeah, tell us what a Ramsey number is.
YD: Okay, so this is from graph theory. And the idea of saying, R(3,3)=6, I’ll just do the whole spiel.
EL: Yeah, yeah. And please use your hands a lot. It's really helpful for the podcast medium when you’re—Yeah, I know. Like Ramsey theory. I’m, like, moving my hands all around to show you what everything is.
YD: I will attempt to not pen and paper and start drawing things. Luckily, we don't have any available, right now. Yeah. So the idea is that, let's say that you are trying to put together a committee of three people. And you either want all three people to pairwise know each other and have worked together before, or you want all three people to be relative strangers. What you don't want is one person in the middle and everyone talks to them. And then the other two people don't talk to each other. That's a bad committee. Yeah. So the question is, how many people do you need to look at to guarantee that you can find such a committee?
EL: Right, so how big is your pool going to be of people you're choosing?
YD: Exactly. So like, if I look at three people? Well, that's not great, because it's me, you and someone in the next room. And there you go. We don’t have a good committee. And if I look at 100 people, like okay, I'm pretty sure I can find this with 100 people. So what Ramsey theory does is use graph theory to answer this question. And so like I said, the giveaway was that the number is 6, and something that I really love about this theorem is that you can teach it to literal—I think I taught it to 10 year olds the summer.
YD: And it's just a really nice basic introduction to, in my opinion, the fun parts of math. These kids who are like, “Ugh, I have to memorize equations, and I hate doing this.” And then I start drawing pictures and I explain the pigeonhole principle, and like, “Oh, I get it, like, I can do this.” I’m like, “Yes, you can! Everyone can do math!”
EL: Yay. Yeah. So the, the proof for that is, is kind of like you, you take a hexagon, right? Or the vertices of a hexagon and try to build—what do you do to denote whether you have friends or strangers?
YD: So graph theory is when you have vertices, which are dots, and edges, which are lines in between dots, and you use it to describe data and information systems. So in this case, we can make each person a dot, so we'll put six dots on a piece of paper. I do not have paper. I am using my hands. So we’ll have six dots on a piece of paper, and we’ll draw a blue line for friends, and we can draw a red line for strangers. So now our question becomes, how many dots do I need to make either a red triangle or blue triangle. So if you have six dots, let's look at one person, and that person will be me. And I look out at this crowd of five people. So for at least three of those people, I will have the same color line going to them. So they might all be strangers, so I'll have five red lines, or one might be a stranger and four friends—one red and four blue—but in that case, I have three, at least three, blue ones. So I can just assume that one of them is blue. So we'll just say, “Okay, I’ve got three blue lines going out.” So now I look at those three friends of mine. And I look at the relationships that they have with each other. This is really hard without pen and paper.
EL: Yeah, but luckily, our listeners have all gotten out of pens, two colors of pens, and they are driving this at home. So it's fine.
YD: Excellent. Good job, listeners! So now you've got your three dots. And you've got three blue lines coming out of them to one common dot. So you've got four dots on your piece of paper. So if in between any of those three dots, I draw a blue line, we’ve got our blue triangle, and we're done. We've got our committee.
YD: Therefore, if I want to make this a proof, I'd better draw red lines. Yeah, I should draw a red line. Yeah. So now I've got three dots. And I've got red lines. But now I have red lines between all three of them. And there's my committee. So that's it. That's the entire proof. You can do it in a podcast in a few minutes. You can teach it to 10 year olds. You can teach it to 60 year olds. And I love it because it's like the gateway drug of mathematics proofs.
EL: Yeah, it’s really fun. And yeah, you can just sit down at home and do this. And—spoiler alert: to do this for four, to get a committee of four people, it's a little harder to sit down at home and do this, right? Do you—I should have looked up
YD: Oh, the Erdos quote, right? Is that what you're talking about?
EL: Well, well, I you can do four. Yeah, there's an Erdos quote about I think getting to six. Or five.
YD: So the Erdos quote is, paraphrased: if aliens come to the earth, and they tell us that they're going to destroy us unless we calculate R(5,5), then we should get all of the greatest minds in the world together and try to calculate it and solve it. But if the aliens say that we should try to compute R(6,6), then we should just try to destroy the aliens first.
EL: Yeah, so I think R(4,4) is like something like 18. Like, it's doable. I mean, by a computer, I think, not by a person, unless you really like drawing very large graphs. But yeah, it's kind of amazing. The Ramsey numbers just grow so fast. And we've been saying R(3,3) or R(4,4), having the same number twice in those. There are also Ramsey numbers, right, where it’s not symmetric.
YD: Like R(2,3) or R(2,4), Okay, so well two is maybe not the greatest number for this. But yeah, you can do things where you say, Oh, I'm going to have either a complete—so I'll either have a triangle of red, or I'll have four dots in blue, and they'll all be connected to each other with blue lines, a complete graph on four dots or however many dots.
EL: Yeah. So they don't have to be the same number. Although, you know, usually the same number is sort of a nicer one to look at. So how did you learn this theorem?
YD: Let's see. So I learned this through—I’ll just tag another great program—Budapest semesters in mathematics.
YD: From a combinatorics professor. So BSM is when college students in the U.S. and Canada can go to Budapest for a semester and learn math from people there and they hang out with all these others. It’s a nice study abroad program for math. So that's when I first learned it. But since then, I think I've taught it to just like a hundred people, hundreds of people. I tell it to people in coffee shops, I break it out at cocktail parties, it's just like, my like, math is fun, I promise! little theorem. I think I've blogged about it.
EL: So watch out. If you're in a room with Yen, you will likely be told about this theorem.
YD: Yeah, that's my cocktail party theorem, that and Cantor’s diagonalization.
EL: Yeah, well, and cocktail parties are a place where people often like, describe this theorem. Like, if you're having a party, and and you want to make sure that any [ed. note: Evelyn stated this wrong; there shouldn’t have been an “any”] three people are mutual acquaintances, or mutual strangers, although the committee one actually makes a lot more sense. Because like, who thinks through a cocktail party that way? It's just a little contrived, like, “Oh, I must make sure the graph theory of my cocktail party is correct.” Like, I know a lot of mathematicians, and I go to a lot of their parties, but even I have never been to a party where someone did that. So on this podcast, we also like to ask you to pair your theorem with something. And why have you chosen for R(3,3)?
YD: I thought really hard about it, by the way.
EL: Yes. This is a hard part.
YD: Yeah. So I decided on broccoli with cheese sauce.
EL: Okay. Tell us why.
YD: Because it is the gateway vegetable, just like this theorem is the gateway theorem.
YD: Yeah. Like, my kids sometimes eat broccoli with cheese sauce. And it's sort of like trying to introduce them to the wonderful world of Brussels sprouts and carrots and delicious things. I feel like the cheese sauce is sort of this veneer of applicability that I threw on with the committee thing.
EL: Oh, very nice. Yeah.
YD: Even with the situation of the committee, like no one has ever tried to make a committee of three people who’ve all worked together or three people who didn’t. But, you know, it makes it more palatable than just plain broccoli.
EL: Yeah, okay. Well, and honestly, I could kind of see that, right. Because, like, it can be really that third wheel feeling when you’re hanging out with two people who know each other better than, you know either of them or something. Yeah. So actually, I feel, yeah, if you were making a committee for something, I could see why you might want to do this. I feel like a lot of people are not so thoughtful about making their committees that they would actually be like, “Will the social dynamics of this committee be conducive to…?”
YD: This is why my husband and I don't host cocktail parties, because my way of doing it is like, let's just invite everyone we know. And he's like, no, but what if someone feels left out? And then he gets stuck in the graph theory of our cocktail party and then it doesn't happen.
EL: And he's not even a mathematician, right?
EL: Should have been, turns out.
YD: Yes, that's true. Stupid computers.
EL: Yeah. So when you make broccoli with cheese sauce, how do you make it. Are you a broccoli steamer? Do you roast it?
YD: We're definitely, if it's going to have cheese sauce on it, you’ve got to steam it. But generally, we're more roasters because I prefer it rested with garlic and olive oil.
YD: So delicious. Broccoli with cheese sauce is really a last resort. It's like, man, the kids have not eaten anything green in like a week
EL: They need a vitamin.
YD: Let’s give them some broccoli.
EL: So one of our favorite recipes is roasted broccoli with this raisin vinaigrette thing. You put vinegar and raisins, and maybe some garlic, A couple other things in a blender.
YD: Wait, so you blend the raisins?
EL: Yeah, you make a gloppy sauce out of the raisins and everything. And I don't think you plump them first or anything. I mean, usually I kind of get in a hurry, and I’ll put them all in, the ingredients, and then go do something else, and then come back. So maybe they plump a little from the vinegar. But yeah, it makes like a pasty kind of thing. It kind of looks like olive tapenade. And I have actually accidentally mistaken the leftover sauce in the fridge for olive tapenade and have been a bit disappointed. You know, if you're expecting olives, and you’re eating raisins instead, you’re just not as happy. But yeah, it's a really good recipe. If you want to expand your broccoli horizons, maybe not as kid friendly.
YD: Actually, my kids do love raisins. So maybe if I put raisins on top of broccoli, they would like it more.
EL: Yeah, I think there's some cumin in it too, something? And we're talking about recipes, because both of us like to cook a lot. And in fact Yen's blog is called Baking and Math. And it's not like baking with math. Like, there's baking, and there's math.
YD: Yeah, it’s a disjoint union. It doesn’t make that much sense, but I'm still a big fan of it. And it's actually how we met.
YD: Yeah. Because you found me on the internet.
EL: Yeah, I found you on the internet. And it was when I was writing for the AMS Blog on Math Blogs. And I was like, this is a cool blog. And yeah, then we became internet friends. And then I realized a couple of years later like, I feel like I know this person, but we've never actually met. We met at Cornell, at the Cornell topology festival, and I was like, “Wow, you're tall!” I just realized I always think people are either shorter than I think or taller that I think unless they're exactly my height because I think my
YD: You expect everyone to be your height?
EL: Yeah, my default, the blank slate version is like, “Oh, this person is the same height as I am.” So yeah, I was like oh, you're taller than I am. And I expected you to be exactly my height because I have no imagination
YD: I’m trying to think if I was surprised by, maybe, no, I don't think you had blue hair, maybe you did? No.
EL: No, I probably had blond hair at that point, yeah.
YD: I remember we did acro yoga when we first met. That's a good thing to do when you first meet someone.
YD: It was very scary. It wasn't leap of faith, but so is meeting a stranger on the internet.
EL: Yeah. But luckily we’re both great people.
YD: Yeah. I also signed up for that conference because you tweeted that you were going to go, and I though, “Oh, I might as well sign up and then I can meet you.”
EL: I should have asked for a commission from the festival, although they probably paid for your travel, so it'd be like a reverse commission. So people can find your writing at your blog Baking and Math. They can find you on Twitter, you’re yenergy. And where here can they find your your science and health writing?
YD: So I post a lot of my clips on my website, my professional website, so that's yenduong.com, and then I also write for North Carolina Health News if you're interested in exactly what it sounds like, North Carolina health news.
EL: Yeah I'm sure a lot of people are I read them and I'm not in North Carolina, but I have a body, so I am interested in health news.
EL: So thanks a lot for joining me.
YD: Thanks for having me. It was super fun. Fun fact for podcast listeners: Evelyn and I did not know where to look during this conversation. We couldn’t tell, should we look at each other or at the recording device?
EL: Yeah, so we did some of both. All right. Bye.