Episode 58 - Susan D'Agostino

09/10/20 • 25 min

Kevin Knudson: Welcome to My Favorite Theorem, a podcast about math and so much more. I'm one of your hosts, Kevin Knudson, professor of mathematics at University of Florida. And here is your other host.
Evelyn Lamb: Hi, I'm Evelyn Lamb. I'm a math and science writer in Salt Lake City, Utah. So how are you, Kevin?
KK: I’m fine. It's it's stay at home time. You know, my wife and son are here and we're sheltered against the coronavirus, and we've not really had any fights or anything. It's been okay.
EL: That’s great!
KK: Yeah, we're pretty good at ignoring each other. So that's pretty good. How about you guys?
EL: Yeah, an essential skill. Oh, things are good. I was just texting with a friend today about how to do an Easter egg hunt for a cat. So I think everyone is staying, you know, really mentally alert right now.
KK: Yeah.
EL: She’s thinking about putting bonito flakes in the little eggs and putting them out in the yard.
KK: That’s a brilliant idea. I mean, we were walking the dog earlier, and I was lamenting how I just sort of feel like I'm drifting and not doing anything. But then, you know, I've cooked a lot, and I'm still working. It's just sort of weird. You know, it's just very.
EL: Yeah, time has no meaning.
KK: Yeah, it's it's been March for weeks, at least. I saw something on Twitter, Somebody said, “How is tomorrow finally March 30,000th?”
EL: Yeah.
KK: That’s exactly what it feels like. Anyway, today, we are pleased to welcome Susan D'Agostino to our show. Susan, why don't you introduce yourself?
Susan D’Agostino: Hi. Thanks so much for having me. I really appreciate being here. I’m a great fan of your show. So yeah, I'm Susan D’Agostino. I'm a writer and a mathematician. I have a forthcoming book, How to Free Your Inner Mathematician, which is coming out from Oxford University Press. Actually, it was just released in the UK last week and the US release will be in late May. And otherwise, I write for publications like Quanta, Scientific American, Financial Times, and others. And I'm currently working on an MA in science writing at Johns Hopkins University.
KK: Yeah, that's pretty cool. In fact, I pre-ordered your book. During the Joint Meetings, I think you tweeted out a discount code. So I took advantage of that.
SD: Yes. And actually, that discount code is still in effect, and it's on my website, which I'll mention later.
EL: Great. So you said you're at Hopkins, but you actually live in New Hampshire?
SD: Exactly. Yes. I'm just pursuing the program part-time, and it's a low-residency program. So I’m a full-time writer, and then just one class a semester. It creates community, and it's a great way to meet other mathematicians and scientists who are interested in writing about the subject for the general public.
EL: Nice. I went to Maine for the first time when I was living in Providence last semester and drove through New Hampshire, which I don't think is actually my first time in New Hampshire, but might have been. We did stop at one of the liquor stores there off the highway, which seems like a big thing in New Hampshire because I guess they don't have sales tax.
SD: No sales tax, no income tax, “Live Free or Die.” Yeah, and you probably test right around where I live because I live in New Hampshire has a very short seacoast, about 18 miles, depending on how you measure it. We live right on the seacoast.
EL: Oh yeah, we did pass right there. Wonderful. Yeah, the coast is very beautiful out there.
SD: I love it. Absolutely love it. I'm feeling very lucky because there's lots of room to oo outside these days. So, yeah, just taking walks every day.
EL: Wonderful.
KK: So you used to be a math professor, correct?
SD: Yes.
KK: And you just decided that wasn't for you anymore?
SD: Yeah, well, you know, life is short. There's a lot to do. And I love teaching. I had tenure and everything. And I did it for a decade. And then I thought, “You know, if I don't write the books I have in mind soon, then maybe they won't get done.” I've got my first one out already, only two years into this career pivot to writing, and I’m working on my next one. And I always had in mind, in fact, I have a PhD, but I also have an MFA. So I have a terminal degrees both in math and writing. And I always had one foot in the math world and one foot in the writing world, and I realized I didn't want to only live in one. So this is my effort to live fully in both worlds.
KK: That’s awesome.
EL: Yeah. Nice. So the big question we have now of course, is what is your favorite theorem?
SD: Okay, great. My favorite theorem is the Jordan curve theorem.
KK: Nice.
SD: Yeah. It’s a statement about simple closed curves in a 2-d space. So before I talk about what the Jordan curve theorem is, let's just make sure we're abundantly clear about what a simple closed curve is.
E...

Previous Episode

Episode 57 - Annalisa Crannell

Evelyn Lamb: Welcome to My Favorite Theorem, joining forces today with Talk Math With Your Friends. I'm Evelyn Lamb. I co-host this podcast. I'm a freelance math and science writer in Salt Lake City, Utah. And this is your other host.
Kevin Knudson: Hi, I'm Kevin Knudson, professor of mathematics at the University of Florida, where it is boiling hot today, and I’m very happy to be in this—how would they put this on on TV?—crossover event, right?
EL: Yeah.
KK: So like, I think last night on NBC, on Wednesday nights, there are all these shows that take place in Chicago: Chicago Med and Chicago PD and Chicago Fire, Chicago Uber, who knows what. Anyway, sometimes they'll just merge them all into one three-hour super show, right? So here we go. This is the math version of this, right?
EL: Yes. And I realized today that our very first episode of My Favorite Theorem, we published that in late July 2017. So this is our early third birthday! And we're so glad that people came to join us! And we are very happy today to have our guest Annalisa Crannell with us. Hi, Annalisa. Can you introduce yourself and tell us a little bit about yourself?
Annalisa Crannell: So hi, my name is Annalisa Crannell. I profess mathematics at Franklin and Marshall College, which is in south-central, southeastern Pennsylvania. It's a small liberal arts college. I got my PhD working in differential equations, partial differential equations, nonlinear differential equations, switched into discrete dynamical systems, topological dynamical systems, but for the past 10 or 15 years have been really thinking hard about projective geometry applied to perspective art.
KK: That’s quite the Odyssey.
AC: Yeah, I was really influenced by by Paul Halmos saying that one of the marks of a really good mathematician is that they can change fields. And so yeah, I feel like I'm trying to enjoy so many different aspects of what this profession allows us to do.
EL: And a fun story, at least it was fun for me, is that one time you were here in Utah giving a talk at BYU, which is down the street. And we went to an art gallery and you pulled out your chopsticks and showed me how you use your chopsticks to help you know where to stand to best appreciate art, and it was just so amazing to me that that was this thing that you could do. So that was that was a lot of fun. And I think it just, to me, sums up the Annalisa experience.
AC: Thank you. Yeah, summing, I guess, is a good thing for mathematicians. I think everybody should carry chopsticks with them. I mean, it's great. It's frugal. It helps you avoid to trash, but it also helps you do really cool mathematics. So what's what's not to love about them?
EL: Yeah. So what is your favorite theorem?
AC: So if you had asked me about five years ago, I would have said the intermediate value theorem. But today, I am going to say no, Desargues’ theorem. So Desargues’ theorem first came into human knowledge in the 1640s. And it's a theorem that sounds like it's sort of about planar geometry, but I really think of it as being about perspective. So is this when I'm supposed to tell you what the theorem says?
KK: Yes, please.
EL: Yeah. Okay, should we all get out our—so this is one, I feel like I always need like a piece of paper. (I’m trying to hold it up, but I’ve got a Zoom background.) But I got my piece of paper out so I can hopefully follow along at home.
AC: Yeah. If you had a piece of paper or a chalkboard right behind you, you could imagine that you would have a triangle, like, standing up on a glass pane. And then on one side of this glass pane would be maybe a magician or somebody holding a light. Maybe your granddaughter drew the magician. (Okay, for people in the podcast, I'm showing a picture that my granddaughter drew on the chalkboard.) If this light shines on the triangle, then it casts a shadow, and the shadow is also a triangle. And so we say those two triangles are perspective from a point, the point is the light source. And we say that because the individual corners, the corresponding corners, are colinear with the light source. So A and the shadow of A are collinear with a light. B and the shadow of B are colinear with a light. But it turns out that those shadows, the triangle and its shadow, are also perspective from a line. And what that means is that if you think not about the points on the triangles, but the three lines on the triangles, and you really think of them as lines, not line segments, so going on forever, then the corresponding lines will also intersect along a line. And you can think of that second line, which we call the axis, as the intersection between the plane of glass that's sitting up in the air and the ground. So the interesting thing to me about Desargues’ theorem is that it pretends like it's a theorem about planar geometry, because this theorem holds when the two triangles are both in the same plane, in...

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Episode 59 - Daniel Litt

Kevin Knudson: Welcome to My Favorite Theorem, a math podcast and so much more. I'm Kevin Knudson, professor of mathematics at the University of Florida. Here is your other host.
Evelyn Lamb: Hi, I'm Evelyn Lamb. I'm a math and science writer in Salt Lake City, Utah. I have left the county two times since this all happened. We don't have a car, so when I leave my home, it is either on feet or bicycle, which is your feet moving in a different way. But I have biked out of our county now into two different other counties. So it's very exciting.
KK: Fantastic. Well, I do have a car. I bought gas yesterday for the first time since May 26, I think. And yesterday was June 30.
EL: Yes.
KK: And I've gotten two haircuts, but it looks like you've gotten none.
EL: Yes. That’s correct. I’m probably the shaggiest. I've been in a while. My I normally this time of year is buzzcut city, which I do at home anyway. But I don't know.
KK: I will say I’m letting it get a little longer actually. I know I said I got a haircut, but you know, Ellen likes it longer somehow. So here we go. This is where we are. My son's been home for three months, and we haven't killed each other. It's all right.
EL: Great. Yeah, everything's doing as well as can be expected, I suppose. If you're listening to this in the future, and somehow, everything is under control by the time we publish this, which seems unlikely, we are recording this during the 2020 COVID-19 pandemic, right, which—I guess it still stays COVID-19 even though it's 2020 now, to represent the way time has not moved forward.
KK: Right. Time has no meaning. And you know, Florida now is of course becoming a real hotspot, and cases are spiking. And I'm just staying home and, and I have four brands of gin, so I'm okay.
EL: Yeah. Anyway!
KK: Anyway, let's talk math. So we're pleased today to welcome Daniel Litt. Daniel, would you please introduce yourself?
Daniel Litt: Hey, thank you so much. It's really nice to be here. I'm Daniel Litt. I'm an assistant professor at the University of Georgia in Athens, Georgia, likewise, a COVID-19 hotspot. I also have not gotten gas, but I think I've beat your record, Kevin. I haven't gotten gas since the pandemic began.
KK: Wow. That’s pretty remarkable.
DL: I’ve driven, maybe the farthest away I've driven from home is about a 15-minute drive, but those are few and far between.
KK: Sure.
DL: So yeah, I'm really excited to be here and talk about math with both of you.
KK: Cool. All right. So I mean, this podcast is—actually, let’s talk about you first. So you just moved to Athens, correct?
DL: I started a year ago.
KK: A year ago, okay. But you just bought your house.
DL: That’s right. Yeah. So I actually live in northeast Atlanta, because my wife works at the CDC, which is a pretty cool place to work right now.
KK: Oh!
EL: Oh wow.
KK: All right. Is she an epidemiologist?
DL: She does evaluation science, so at least part of what she was doing was seeing how the CDC’s interventions and deployers, how effective they were being help them to understand that.
KK: Very cool. Well, now it would be an interesting time to work there. I'm sure it's always interesting, but especially now. Yeah. All right. Cool. All right. So this podcast is called my favorite theorem. And you've told us what it is, but we can't wait for you to tell our listeners. So what is your favorite theorem?
DL: Yeah, so my favorite theorem is Dirichlet’s theorem on primes in arithmetic progressions. So maybe let me explain what that says.
KK: Please do.
EL: Yes, that would be great.
DL: Yeah. So a prime number is a positive integer, like 1, 2, 3, 4, etc, which is only divisible by one and by itself. So 2 is a prime, 3 is a prime, 5 is a prime, 7, 11, etc. Twelve is not a prime because it's 3 times 4. And part of what Dirichlet’s theorem on primes in arithmetic progressions tries to answer, part of the question it answered, is how are primes distributed? So there is a general principle of mathematics that says that if you have a bunch of objects, they're usually distributed in as random a way as possible. And Dirichlet’s theorem is one way of capturing that for primes. So it says if you look at an arithmetic progressions—that’s, like 2, 5, 8, 11, 14, etc. So there I started at 2 and I increased by 3 every time. Another example would be 3, 6,9, 12, 15, etc—there I started at 3 and increased by 3 every time. So Dirichlet’s theorem says that if you have one of those arithmetic progressions, and it's possible for infinitely many primes to show up in it, then they do. So let me give you an example. So for 3, 6, 9, 12, etc, all of those numbers are divisible by 3. So it's only possible for one prime to show up there, namely 3.
EL: Right.
DL: But if you have an arithmetic progression, so a bunch of numbers which differ by all the same amount,...