The Infinitely Surprising Career Of A Mathematician
We’ve all heard about CRISPR, the groundbreaking gene-editing tool, or LIGO and gravitational waves, the latest frontier in astronomy. But what about the cutting-edge research in math?
Ask anyone what a scientist looks like and expect the cliched answer: someone in a lab coat, looking at a specimen under a microscope. But what does a mathematician look like? How do they do research? What does it even take to be a mathematician in the first place?
Mathematicians Rebecca Goldin, Eugenia Cheng, and Emily Riehl join Ira to give us a peek into their abstract, complicated, and beautiful world. They’ll tell us about studying higher dimensions that you can’t even see, coming up with a new way of defining what mathematical proofs look like, and what it’s like to be women in math.
SciFri continued the conversation with Goldin, Riehl, and Cheng—discussing their favorite mathematical puzzles, tips for young women entering the field, and more.
Dr. Eugenia Cheng is Scientist in Residence at the School of the Art Institute of Chicago and author of several books, including Beyond Infinity: An Expedition to the Outer Limits of Mathematics (Basic Books, 2017) and The Art of Logic in an Illogical World (Basic Books, 2018).
Rebecca Goldin is the director of the STATS project with the Sense About Science organization. She’s also a professor of mathematical sciences at George Mason University. She’s based in Fairfax, Virginia.
Emily Riehl is an assistant professor of the Department of Mathematics at Johns Hopkins University. She’s based in Baltimore, Maryland.
IRA FLATOW: This is Science Friday. I’m Ira Flatow. Later in the hour, we’ll talk about the global influence of internet states like Facebook and Google. But first, we know scientists study weird things, fish in the deep ocean and galaxies far, far away, sometimes rocks from other solar systems, or things that are so microscopic, they could fit a couple of million of them on the head of a pin.
But can you imagine studying something that’s not even a real physical thing, something that you can’t see or hear or feel? And imagine trying to do that while people tell you that you can’t do it because you’re a woman. Joining me now to talk about all of these topics are three mathematicians.
Rebecca Goldin is a professor in the Department of Mathematical Sciences at George Mason University in Fairfax, Virginia. She’s also the director of STATS, an organization aimed at improving statistical literacy. Welcome to Science Friday.
REBECCA GOLDIN: Thank you.
IRA FLATOW: Welcome. And Eugenia Cheng is a scientist in residence at the Chicago School of the Art Institute of Chicago in Chicago. Welcome to Science Friday.
EUGENIA CHENG: Hi. Thanks for having me back. It’s great to be here.
IRA FLATOW: Nice to have you back. Emily Riehl is assistant professor in the Department of Mathematics at Johns Hopkins and she’s joining us today from WGLT in Normal. Illinois. Welcome to the show, Emily.
EMILY RIEHL: Thank you.
IRA FLATOW: Rebecca, let me ask you first. I want to bring up something that we said at the top of this show, which is that from a mathematician’s point of view, a donut and a coffee cup are the same thing. How is that?
REBECCA GOLDIN: Yeah, well, so a lot of times, mathematicians like to study the way things that can be equivalent if you mush them around or deform them. So if you take a coffee cup, you can imagine that it’s got exactly one hole in it, and that’s where you put your hand to grab onto your coffee. And if you mush that around, you can kind of morph it into a donut. So people in the field of topology would call those things equivalent. And there’s a lot of attempts to kind of study different spaces by keeping track of things like how many holes it has.
IRA FLATOW: Our audience doesn’t get a lot of chances to talk to real mathematicians, so I want to open this up and give out the phone number. If you want to talk to a mathematician about what’s really interesting, 844-724-8255. 844-SCI-TALK. You can also tweet us @scifri.
And Rebecca, I know that one of the things you study is geometry and the structure of higher dimensions. What does that mean exactly? How do you visualize higher dimensions?
REBECCA GOLDIN: Great. Yeah, that’s an awesome question. And actually, people often think that you have to see it in some kind of physical world. But just like when we study numbers and we talk about things like infinity, we don’t always have a visual idea of how it actually looks. But to give a really kind of simple example of the kind of thing that I think is super fun and ends up being in very high dimensions, you can imagine questions like how you would intersect lines and planes.
So imagine that you have in three dimensional space, that’s our normal what we live in space. And you just took four lines and the lines are not parallel. And they don’t intersect with each other. And so they’re just kind of sitting there askew. And you say, how many other lines intersect all four of those?
And if you try to do that by hand, you might be able to get somewhere. But if you start ramping that question up and asking, OK, but let’s assume that the lines live in a plane and the planes intersect in some other way. And you start putting additional constraints on things, very quickly, you get to very high dimensional questions. And they’re just a ton of fun. Very beautiful mathematics there.
IRA FLATOW: My math teacher, my geometry teacher, used to call things in math elegant. Solutions–
REBECCA GOLDIN: Yeah.
IRA FLATOW: –they were elegant. And we took his word for it. Eugenia, you and Emily are in the same math field. You’re both category theorists. What does that mean? Do you have an example to help us envision what that means?
EUGENIA CHENG: Yeah. I like to call category theory the mathematics of mathematics. And to understand that, first I have to explain what mathematics is. You see, I don’t think that mathematics is just about numbers and equations, although that may be the impression you get from classes in school, which is, to me, sad, because math is about so much more than that.
I think math is about understanding how things work very deeply. And we make analogies between different situations and say, what can we understand about these two cookies, for example, that is also going to be true about these two apples or these two people these two other things? And that analogy turns into the number two.
And category theory actually does that for mathematics itself. So it says, what about this branch of math can we understand that is similar to this other branch of math that’s also similar to this other branch? And what we’re going to do is be really lazy about it, because I don’t want to have to do the same thing over and over again. I don’t know about you, but I hate doing the same thing over and over again. So instead of doing that, we’re going to make a theory that will do it for us. And that’s what category theory is.
IRA FLATOW: Oh, OK. Just for jeopardy of going further into the weeds, I’m going to ask Emily Riehl to tell us about– she specializes in a category theory specialization in something called, what is it?
EMILY RIEHL: Well, actually, I work in infinite dimensional category theory.
IRA FLATOW: Oh, there it is. [LAUGHS]
EMILY RIEHL: And a way to think about what that does is a category provides a template for a mathematical theory. So there are the mathematical objects, which are like the nouns of the theory, and then there are the transformations between those objects, which are the verbs.
But as mathematics becomes more complicated, we need sort of a more robust linguistic template to describe the objects that mathematicians like Rebecca care about. So we might need pronouns, adjectives, adverbs, prepositions, conjunctions, interjections, and so on. And so that’s where the infinite dimensions come in. We have not only the objects and the transformations, but there might be transformations between transformations, like the homotopy that turns a donut into an infinite dimensional plane with a hole punctured in it.
EUGENIA CHENG: And if I can add to that, because I have to admit I’m also an infinite dimensional category theorist, you picked three mathematicians and two of them are infinite dimensional category theorists. But really, as Emily says very well, it’s all about having more nuance so that we can talk about things with greater and greater subtlety. And that’s something that we both believe in and I’m sure that all mathematicians believe in.
Because things aren’t just right and wrong. Unfortunately, in school math, things are often right and wrong and they’re often wrong. But there are so many ways in which things can be the same and not the same, as Rebecca said, that a coffee cup can be considered to be the same as a donut.
And just like we can consider relationships between people but we can also compare relationships and say, well, whose relationship is better? But then we can say, well, maybe this relationship is better because they have more fun. But this other relationship is better because they don’t argue very much. And then we could compare the ways of comparing and say, well, which is better? Is it better to have more fun or is it better to avoid arguing? And this is another way that we get many dimensions.
IRA FLATOW: You know, you just explained why Lewis Carroll was a mathematician, right? I mean, Alice in– you just had a scene out of Alice in Wonderland that you just described.
EUGENIA CHENG: Possibly something like that. And the wonderful thing about Alice in Wonderland is that anything is possible because it’s happening inside someone’s imagined imagination. And that’s a wonderful thing about math as well, that on the one hand, you might think it makes it difficult that we can’t necessarily see and touch things because they’re not physically real. But the great thing is that we’re not constrained by physical reality either. We’re only constrained by our own imagination. And so if you have a huge imagination, that means you have a huge capacity for thinking about mathematics.
IRA FLATOW: So that means that if things that you describe may have no consequence in reality. They may not describe nature or reality at all. But it just mathematically works and it’s beautiful. Would that be fair?
REBECCA GOLDIN: In some sense, I think you’re really asking a philosophical question there, right? Because I think many mathematicians feel like they’re really discovering something that is. And it is under the context of some base set of assumptions. And of course category theorists are very, very concerned with those assumptions. They’re extremely important.
But a lot of times, once you sort of get into the weeds of something, you’re going to make some assumptions. Once you make those assumptions, there’s a tremendous amount of very beautiful mathematics that kind of fall out from the assumptions and from your agreed upon language, let’s say.
And many mathematicians feel like they’re really discovering things, rather than inventing them. So that’s a little bit of a philosophical thing. Is it an invention or is it discovery? And most of the things, even in very basic mathematics, that we talk about, it’s not that we have a concrete thing to say.
If I said, what’s a number? You wouldn’t really have an answer to that question, except that you can count things. But then what would be the number pi? Or what would be a negative number? We don’t really have a concrete object. But we very easily, our minds are kind of set up to understand math in a much broader sense than just it has to be physically there and physically present.
And the consequences are very real. I mean, you couldn’t put a man on the moon– or a woman on the moon– if you weren’t able to be able to do calculations that involve things like real numbers, which we don’t have a concrete thing to talk about. We just have actually our minds to get our heads around it.
IRA FLATOW: Well, all of us who saw and read Missing Figures will know exactly what you’re talking about.
EUGENIA CHENG: Hidden Figures.
IRA FLATOW: Hidden Figures. I’m sorry. Yeah.
EUGENIA CHENG: Yes.
REBECCA GOLDIN: Hidden Figures, yeah.
EUGENIA CHENG: The great thing about the interaction between math and reality is that you not start out with a particular aim in mind. You might not have a specific application. But if you do some beautiful and profound mathematics, then often, some unexpected application will come later that mathematicians were often not expecting.
And this can happen 10 years later. It can happen 100 years later, 300 years later. For example, the number theory from hundreds of years ago is now at the basis of internet cryptography. Maybe thousands of years later. The platonic solids, the icosahedron from 2000 years ago didn’t appear– we weren’t– we didn’t find examples in nature until the 1950s.
And so focusing on direct applications in life is not necessarily the best thing to do. But focusing on something fundamental and beautiful that’s not necessarily real, just like thinking about fiction and what that can–
IRA FLATOW: But–
EUGENIA CHENG: –teach us about our lives.
IRA FLATOW: –let me just interrupt. But you can describe a passage in fiction and have people say, aha, I know what you’re talking about. But when you tell people what you’re talking about, how many can really understand why you see beauty there?
EUGENIA CHENG: I say everyone can. What does everyone else think?
IRA FLATOW: Rebecca, no?
REBECCA GOLDIN: Well, I definitely think that it depends on what kind of level you’re talking about when you say it. So I think that almost every single person I’ve ever talked to, I can find an interesting mathematical question that they can explore and see the beauty in.
But of course it’s also true that we get very specialized and then we talk to other people who are also very specialized and I don’t see that as particularly different than what happens in any technical field. There are some questions that are truly very interesting that, say, Emily would find really interesting what I have to say about something but someone else might not. And that’s OK because she’s a highly trained mathematician. It’s not– there’s a conversation we had there.
IRA FLATOW: Right, but–
REBECCA GOLDIN: But I do think that there’s access to everyone at some level, depending on your background.
IRA FLATOW: Well, you know, you’re right. And I can see because my switchboard has lit up like–
EUGENIA CHENG: Great.
IRA FLATOW: –it hasn’t. And they all want to talk about math, so you really have hit home on talking about mathematics. Our number, if there’s still room, on 844-724-8255. Or you could try tweeting us. We watch the Twitter all the time @scifri. We’ll come back with– take a lot of your phone calls. This has really sparked interest. Stay with us. We’ll be right back after the break.
This is Science Friday. I’m Ira Flatow. We’re talking this hour about mathematics. And it has sparked some great interest in our listeners. Let me quickly go through our guests. Rebecca Goldin, Eugenia Cheng, Emily Riehl, all professional mathematicians, I guess you get paid for that instead of just doing the crossword puzzle. Let’s go to the phones. I’ll give out the number if there’s room, 844-724-8255. Also, you can reach us on Twitter @scifri. Let’s go to the first call from Bruce in Huntsville, Alabama. Hi, Bruce.
BRUCE: Hello, hello.
IRA FLATOW: Hi, there.
BRUCE: My question is do mathematics exist without human beings or a consciousness to think of them?
IRA FLATOW: Wow. [LAUGHS] Talking about philosophy. Does mathematics exist without people?
EUGENIA CHENG: So here’s what I think. I think, like what Rebecca said, some mathematicians think they invent math and some people think they discover it. What I think is that I discover mathematical concepts and I invent language for thinking about it. So the philosophical question becomes, do thoughts exist, do concepts, do ideas exist without humans existing?
I think that the language that we invent for communicating mathematics to other people definitely does not exist without us. But those ideas, do they exist without us? I don’t know.
IRA FLATOW: Wow. Well, let me say if Rebecca or Emily wants to chime in on that. You, well?
EMILY RIEHL: I think one thing that I’m appreciating as I get further on in my career is how important human communities are to the mathematics that’s being developed. So if a sort of very charismatic lecturer or a good expositor can have a huge influence over a field by making other young mathematicians excited and drawing people in, and so then a lot of energy happens focusing on particular problems and questions, then you could very easily imagine the development having been different.
IRA FLATOW: Let’s go to Homer in Woodland, California. Hi, Homer. Welcome to Science Friday
HOMER: Hello. Thank you for taking my call. I’ve been blind since birth and one of your guests was talking about how if you have a big imagination, you can pretty much do anything. And that’s me. That’s why I decided to call–
EUGENIA CHENG: Wonderful.
HOMER: –because– and I’m attempting to write a book. I’m a sci fi enthusiast. So when you mentioned higher dimensions, it’s about a kid who travels to higher dimensions. And basically I’m just using my own imagination. So–
EUGENIA CHENG: That’s wonderful.
HOMER: I don’t know what to base it on. As far as I know, third dimension is length, width, and height, but fourth dimension I’ve heard is time. I don’t know if that’s true or not. But then where do you go from there? I mean what do we know about higher dimensions or what we can do?
IRA FLATOW: All right, let’s see if we get some hints for you. Good luck, Homer. Yeah.
REBECCA GOLDIN: Those are great questions. And I should add that there are, in fact, blind mathematicians. So it’s certainly not impossible to do very high level mathematics if you’re blind. There’s, as far as looking at higher dimensions, one of the ways to think about it, a lot of people like to think of space and time as having– those being those four dimensions that we can think about. But any time you keep track of a bunch of things, you’re really dealing in high dimension.
So if I wanted to keep track of people’s hair color and their eye color and their address and some other information, then I’m really– maybe their income and also their phone number, that would be the kind of thing that maybe a Realty people are interested in keeping track of that kind of information. And that’s already a bunch of dimensions, one dimension for each piece of information that you carry about somebody.
So there’s a kind of way in which what mathematics does with dimension is really just keep track of things. And if you keep track of a lot of things, you’re actually keeping track of a lot of dimensions.
IRA FLATOW: Well, you know, high dimensions have been in the news in physics, which takes mathematicians to figure it out for them, especially string theory, talking about big dimensions. Or many, we’re talking about 12 a dozen or more high dimensions there. Do you understand what’s going on there, because you’re all dimensional mathematicians?
EUGENIA CHENG: There’s sort of a joke in infinite dimensional category theory that once you go beyond three, it basically might as well be infinity because it’s so difficult beyond that. One, two, three, infinity. It is hard to understand. But it’s a great question when you say, do we really understand it? And I think one reason that many people have put off math is that they think they don’t understand it. But none of us really understands it, honestly. We
We’re just trying to understand it more all the time. And being confused doesn’t mean that we’re not good at it. I think a lot of people are put off because they feel confused and they go, oh, I’m no good at math. But actually, being confused and caring about it is what matters. Often, the people who think they understand it, they really don’t.
EMILY RIEHL: If I might–
IRA FLATOW: Yes, go go ahead.
EMILY RIEHL: –sorry, quickly add one practical suggestion, one way to imagine what four or five dimensions might look like from the perspective of three dimensions is to imagine what three dimensions would look like from the perspective of one or two dimensions. So this is essentially the move that Edwin Abbott makes in his book Flatland, which is a wonderful novel.
IRA FLATOW: Yeah.
EUGENIA CHENG: Another way is to imagine escaping. So you can escape someone who’s chasing you in three dimensions by time traveling. And then you can escape someone, if they have a time traveling machine as well, then you can imagine, what machine could you use to escape that person? That would be the fifth dimension.
IRA FLATOW: I have a tweet coming in from Dylan who touches on something that really bugs me. And that is, could you ask your experts what is the utility of zero? Now, when I watch baseball scores– I’m a big baseball fan– and I watch the scores all the time, I ask– zero is a number. People do not– they say we’re at the bottom of the innings there’s no score. Of course there is a score. It’s zero zero, right? Is it– and he says, is it odd for me that we have a representation for nothing? Zero has been a big problem in math for centuries, hasn’t it?
EUGENIA CHENG: Yeah, there was actually a very long history between when they thought of numbers and when they came up with zero. And the way I like to think about zero is, yeah, zero isn’t that interesting, but you’d really miss it if it was gone. And I tell my students that it’s just like some people. They’re not very interesting but they can be really important. Sometimes the boring people are really important. And zero is a bit like that.
IRA FLATOW: You’d know if they were gone. [LAUGHS] Let me ask you a question that has been– I’ve talked about over the years. And I’ll do it this way. I was once asked to create a panel of women physicists, and so I approached every notable woman physicist that I knew and I asked them to sit on this panel.
And not one of them said that they would, because they said we don’t want to be known famous as women physicists. We are physicists regardless of our gender. We are physicists who happen to be women. Do you feel the same way about women mathematicians? I mean, you must have faced the problem of being one woman mathematician in a field of many men mathematicians.
EUGENIA CHENG: Of course. I’m happy to jump in, but I would like to see if everyone else would like to speak first.
REBECCA GOLDIN: Well, I’ll say something about that. I think that this is probably something that, in part, was the specific women that you spoke with. I don’t think that everybody feels uniformly the same about this question. But I think that many women have kind of common experiences as they kind of progress through their careers, both at the early times and then as they kind of go through. Things come up in different kind of ways in different stages of their career. And I think, at least speaking for myself, being female within mathematics has definitely played a role for how it’s come out, whether that’s good or bad.
And so if somebody kind of identifies you as a female in the field, of course you don’t want that to be the only thing about you that is viable. There’s 50% of our population is female. Hopefully people would be interested in hearing also about my mathematics or my ideas or other kinds of things.
But I don’t think it’s irrelevant, either. If it were irrelevant, we wouldn’t have such a shortage of women in mathematics. We wouldn’t have such a difference in achievement levels that we kind of see in society amongst those people who do get higher degrees in mathematics. And so I think it’s a very real issue that has social consequences.
As Emily was talking about earlier in the program, if you can’t have a community, you really don’t have mathematics as we know it. So if the community becomes one in which there are very few women or in which women are discouraged or in which women don’t kind of get to the same place as men, then I think it is an issue. And so it’s hard to both acknowledge it’s an issue and refuse to kind of recognize yourself as part of that conversation, whether it’s you’re male and you’re part of the conversation or you’re female and part of the conversation.
EUGENIA CHENG: Yes, I agree. And when I was younger and I was just starting out, I really also didn’t want to draw attention to the fact that I was a woman. And I didn’t want to give anyone the opportunity to say that I wasn’t good enough because I was a woman.
And then as I became more advanced and I became more secure and I got a permanent job and I was respected in the community, I became more active about it. And as the situation hasn’t improved, I think, enough, that women are still very under-represented, I realize that we need to do more and do more actively and I wanted to take more responsibility for putting myself out there.
If I complain that the images of women, if the images of men in mathematics as presented by the media are largely older white men, then I need to put myself forward to help dispel those images. And so I realized eventually that I needed to do something more active and make myself visible. And I was very inspired, actually, by mathematicians like Emily, who works in my field, coming and being much more active and vocal about those issues.
IRA FLATOW: Emily, you’re a mathematician but you’re also a sportswoman. You played rugby, right? Is that different from being a woman in math, different than or similar, being a woman in sports?
EMILY RIEHL: Well, so I had just come back from a sabbatical in Sydney where one of my main collaborators lives. And there, I’d have kind of a funny experience of going to the Center for Australian Category Theory for a seminar and I would be the only woman out of about 15 mathematicians at all levels. And then I’d go directly from that to training for Australian rules football where there would be 50 women of all ages. So it is quite a transition.
But at this point in my career, I am mostly attentive to how under-representation along gender axes– but other axes as well– affects my students. So when I teach a large multivariable calculus course to 350 incoming students at Johns Hopkins, I start with a comic, an XKCD comic by Randall Munroe entitled “How it works.”
And what the comic is is it’s two stick figures at a chalkboard. One’s drawing an integral and the other walks by and says, wow, you suck at math. But then in an identical panel right next to it, the person with the chalk as a female and the caption is now, wow, girls suck at math. And I use this comic to explain how it’s harder for students who feel like they stand out in the sea of faces in the classroom to ask a question and then to really engage with the mathematics in a way that I think makes it easiest to learn.
IRA FLATOW: Mm-hmm. And are there any other stereotypes that you face as mathematicians, women mathematician?
EMILY RIEHL: I don’t think all–
EUGENIA CHENG: One of the–
EMILY RIEHL: Sorry
EUGENIA CHENG: Oh, no. Go on.
EMILY RIEHL: I don’t think all the stereotyping happens along gender lines. So for instance, there’s– one of my– one of the people I’m inspired by is John Urschel who was a guard for the Baltimore Ravens but recently retired from professional football to focus full time on his PhD in applied mathematics at MIT, so–
IRA FLATOW: Wow.
EUGENIA CHENG: Yeah, so I agree that it’s not just about gender. And I’ve been proposing that we should change the words we use about gender so that instead of thinking about masculine and feminine behavior, we should use non-agenda prescriptive words that are descriptive of character traits instead. So I’ve been proposing ingresssive and congressive to replace masculine and feminine. And the idea is that ingressive is about going into things and not really worrying too much and congressive is about bringing things together in congress.
And mathematics is ultimately a very congressive pursuit. We’re try to understand things and we collaborate a lot together. Yet, mathematics is presented ingressively and it’s tested ingressively. There are tests. There are competitions. It’s about right and wrong. There’s problem solving competitions, competitive atmospheres to get into PhD places and to get promotions when, in the end, the math, certainly, that we do is about shedding light on situations and making connections between situations. And so if people are put off by the ingressive characteristics of mathematics, then they’ll never get to the part where it becomes beautifully congressive.
IRA FLATOW: This is Science–
REBECCA GOLDIN: You can see she’s clearly a category theorist.
IRA FLATOW: This is Science Friday from PRI, Public Radio International. I’m Ira Flatow talking mathematics. Let me just follow that point a little more. So you’re saying that women, because they are more inclusive, if they’re congressive, they’re better– might be better mathematicians or better at solving a problem with other mathematicians?
EUGENIA CHENG: I’m thinking that congressive people are better in certain ways. For example, congressive people are more likely to underestimate their own abilities and seek to improve a lot. And over the 20 years I’ve been teaching undergraduates, I’ve noticed that the female students will often think they’re doing terribly when they’re doing fine. And the male students often think they’re doing fine when they’re doing terribly.
IRA FLATOW: Wow. We have–
REBECCA GOLDIN: So there are lots of other kind of pieces to that story as well. I love this discussion, this conversation. And I think also, there’s another feature or bias or division that you might say that that really has to do with young versus old people. So there’s this kind of idea in mathematics that you peak when you’re young and you have to be very young to do mathematics. So if you’re not showing some kind of brilliant sparky shiny something by the time you’re 14, you’re just not all that good. And no one is going to invest in you.
And I think that is something that’s really quite pernicious because people often come to mathematics a little bit later or, as was also mentioned earlier on your show, that they’re in school mathematics. It’s not very interesting to them and they’re not very invested in doing it very well. And it’s not until they get quite far into the game mathematically that they see something really beautiful, something beyond calculus,
EUGENIA CHENG: Yes.
REBECCA GOLDIN: –something that really kind of–
EUGENIA CHENG: Exactly.
REBECCA GOLDIN: –gets them to fall in love. And that kind of story, by then, you’ve fallen in love and now you’re, say, 21. You’re basically an old maid. I mean, that’s, [LAUGHS] I think, a really incorrect assumption about how mathematics is learned, how it grows on people, and how they become mathematicians. But it is quite a pervasive viewpoint.
EUGENIA CHENG: And the idea of a math prodigy can contribute to people thinking that you have to be born with that ability and then it’s the opposite of the growth mindset. It’s the fixed mindset where you think you’ve either got it or you haven’t. Whereas no one thinks about biology prodigies . You don’t say, oh, that was a child prodigy in biology. And if you can’t– if you’re not brilliant into biology by the time you’re 11, then it’s all over.
IRA FLATOW: Well, let me– we have about a minute left, but let me wrap this up by asking, we were talking about romanticizing math, and I’m curious what mythological creatures come to your mind when you think of math.
EMILY RIEHL: So I kind of think of math as a Phoenix in that we still use theorems today that were first proven millennia ago. The truths that were discovered are then used. But the way that we talk about the mathematical ideas of centuries past is completely different. It’s completely unrecognizable, I think, because we’ve consolidated our understanding. We’ve invented new mathematical universes to explore.
IRA FLATOW: Well–
EUGENIA CHENG: That’s a lovely image.
IRA FLATOW: Yeah.
EUGENIA CHENG: I’ve described it. In my book, Beyond Infinity I describe infinity as a Loch Ness monster because it’s a creature. And what we– I feel like I’m doing as a mathematician is I go off into the undergrowth or the jungle or the nature and I wander around looking for strange creatures or just traces of strange creatures. And whether they exist or not doesn’t really matter. But in the process of looking for them, we understand more about ourselves and the world around us.
IRA FLATOW: Quickly, Rebecca, you got one?
REBECCA GOLDIN: That’s great. So I think we’re choosing large, scary creatures. I would choose a dragon. But for me, it’s about sort of this huge untamable scary thing that I just have to have somehow. I want it for my pet but I can’t have it.
IRA FLATOW: I’m sorry, I’m going to have to– we’ll come back. There’s such a great interest in this, I– who knew? Rebecca Goldin, professor, Department of Math Science at George Mason University. Eugenia Cheng is at School of Art Institute of Chicago. And Emily Riehl sits as a professor in the Department of Math at Johns Hopkins.
Great discussion on math. Well, such interest, we’ll have to come back and bring them back on to talk more about it. Stay with us. We’ll be right back after this. . I’m Ira Flatow. This is Science Friday from. PRI.