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Evelyn Lamb: Hello and welcome to My Favorite Theorem, the math podcast with no quiz at the end. I like how we're always besmirching other math podcasts, which as far as I know, also don't have quizzes at the end. I am your host Evelyn lamb. I am 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. Okay, full confession. I don't listen to other podcasts, so I don't know if they have quizzes at the end or not.




EL: Shame. They probably don't. I mean, how would you even administer that?




KK: That’s right. That's right. Yeah. Yeah. We don't need to find this out.




EL: Yeah. Well, we are, we should, we should just get right.




KK: Let’s do it. Yeah.




EL: We are very happy today to invite Daina Taimina onto the show. So Daina, please introduce yourself, tell us a little bit about yourself, and we'll get started.




Daina Taimina: Hello. Thank you for inviting me. And, actually, I didn't prepare much to tell about myself. Because usually, I tell my students, you know, just search for me on the internet. That knows more about me than myself.




EL: Maybe even some of it’s true.




DT: Maybe, yes. Sometimes it's true. Yeah. So well, okay. Well, I was teaching about 20 years, I was teaching mathematics at the University of Latvia. And at about the same time, I was teaching in Cornell, where I, now I have stopped teaching. And I officially count as a retired, so it means I have free time to do whatever I want.




KK: Nice.




DT: Yes. And then sometimes, well, it has been now for 25 years, I have crocheted hyperbolic planes. And I guess that's what people know most. Because sometimes I am introduced on people. “Oh, yeah.” And then this person who is introducing me says, “You know, she's the one with hyperbolic planes.” “Oh, yeah! Yes, yes, I know that!” Okay, I guess that's my other name.




EL: Yeah. And our in your multitalented our listeners can't see it, but when we were saying hi we saw that you have some of your very own paintings in the background on Zoom, where I'm seeing right now, and they look very lovely. So you do art in addition to crochet and math?




DT: Actually, that was before, and I and the reason why I was doing I was doing art, is I signed up for a watercolor lessons because I knew that I'm very bad at art. Because when I was in school, I was told I can do anything but that. And at that time in Cornell, I was teaching students who were very afraid of maths, and most most of them were actually architecture art students or music students, and I really wanted to experience how it is to take some subject where you are told, and you believe all your life, that you are bad and you can’t do it. So I did it. And so yes, that was interesting experience.




EL: Well, and it looks like with some practice, you gained skills. Amazing how that works.




KK: I did that to actually about a year ago. I cannot draw. I'm terrible. So maybe we have the same issues here.




DT: Yes, yes. Yes, exactly.




KK: And I took it I took like a just a two hour drawing workshop online where we draw birds, and I actually drew something that looked like a bird at the end. So you know, it can be done.




DT: Yes, because this is what you what you learn, is that — and then I was explaining to my students, too —I brought in one of my paintings, and I said, it's actually, what I realize is that it was things which I knew. I knew, well, perspective. I knew how to do composition from photography, you know, just like doing some photography. And all I needed was, you know, I did need some technical skills, and that is the same in math. You do need to learn some technical skills, and then you can then you can get on, so it's not that different.




EL: Yeah, that's a great, a great lesson to learn and to help share with your students like, “Hey, we're all learning various things. I have this background, you have this background, but we can all improve in various areas of our lives.”




KK: Yeah.




EL: Well, the name of this podcast is My Favorite Theorem. So, what is your favorite theorem?




DT: Well, as I told you, my favorite theorem is Desargues’ theorem. Yes, and then, well, actually it started with some more ancient theorem, which was Pappus’s theorem. And it was somewhere, I think I was in middle schoo, and I was reading something in a math history, and I read that there is this ancient theorem, where if you are having two lines, and then you choose three points on each of them and those lines are non-parallel. Well, if they parallel than they are, that’s a very simple case. But if you have like two lines at some kind of angle, and then you choose, and then you then you connect in pairs points from these lines, and you always have three points which are on the same line. And I know like I was just like, that's — okay, I'm so old that at that time, there was no Geometry Sketchpad or any of these programs, there was no computer. So I just kept drawing these lines and finding those points, then it was just amazing. And then of course, I was like, “Oh, what else is there?” And that's when I discovered this, this Desargues’ theorem, which said, okay, if two triangles are situated so that three lines joining their corresponding vertices all meet at a single point, then the points of intersection of the two triangles’ corresponding sides, if those intersection points exist, all lie on one line. I couldn't — I read it, and I couldn't believe that. So again, I took a pencil and took a straightedge and I started to draw, like, various ways, and it was really finding these points and having them and, and then later learning that the converse of this Desargues’ theorem is also true, and then that’s a converse, theorem, that's also a dual theorem. So it was just so fascinating. So that was something, like, different from the geometry, you know, like, exactly the geometry we were having going to school, and so that's kind of led to perspective. And yes, I was just like, really it was fascinating.




EL: Yeah, this is one that has come up a few times for me in things I've read, or people I've talked to in the past few years. But yeah, I loved geometry for a long time, and this is not a theorem that I was exposed to, in most of my geometry education.




KK: Yeah.




DT: And it's very interesting that you can you can prove this theorem using another ancient theorem, Menelaus’s theorem — okay, I'm not going to talk about that — but that sounds very algebraic, because that uses uses proportions, and it's totally in Euclidean geometry. But I like the way how Desargues himself saw, and he actually was thinking about it in three dimensions, and then it's simple. When you are cutting, like, a triangular pyramid with two planes, and then it's just totally obvious.




EL: Okay, I'll have to sit down and try to visualize that a little better.




KK: Right, isn't the simplest proof, don't you use three, you have to go into 3d and then it sort of, like you say, sort of becomes obvious?




DT: Exactly, yes, yes. Yes. That's one of those. Yeah, that's one of those cases, and that was so great! You know, you just jump out, and then it's obvious. And then it's also, the other thing is, if you are having — so you know, like you can imagine that you are having a book, or though now you're having a point, and then you are projecting a triangle, and then all you do is, you imagine that those lines, that it stretches, and then all you do is you open it up in one plane. And there's the theorem.




KK: There’s the proof. Yep, I wish our listeners could have just seen that.




DT: I don't know how to describe.




KK: So this actually came up for you in school in Latvia? Like, your instructor actually taught?




DT: No, I believe I was reading something from Martin Gardner, or something outside, but I did have a wonderful geometry teacher.




EL: So you were interested in math very early in your education?




DT: It was just one of my easiest subjects. I was interested more in literature and languages. That's what you are saying, you know, like an art. Math, it’s just something that comes by nothing. It’s just simple, just seeing things.




KK: I mean, well, so Evelyn, maybe you had this experience. I mean, I became a mathematician because I was always good at math, right? It was the thing that I could easily do. And so it's sort of interesting that it was sort of the easy thing you could do, but you liked something else more?




DT: Yes, that’s true. Yeah.




EL: Yeah. I I had sort of a similar experience to you Daina, I think, where I was, you know,“good at math” — good at arithmetic, basically — in elementary school. And I liked the proofs in geometry, although I didn't understand that those were “real math” also. I thought it was just a diversion.




KK: The two-column proofs?




EL: Yeah, I liked the logic part of it. You're working it through, but I thought arithmetic was real math. And so yeah, I wasn't as interested in that. I was more interested in — I really liked science, but I did a lot of music also and stuff. But eventually, it wasn't until college, that I really kind of fell in love with it, and decided to devote my life to it in at least some form.




KK: Including podcasts at this point. So yeah.




DT: Well, you've been successful.




KK: Sure.