Do you cringe at the very mention of mathematics? Have you ever thought you might not be "good enough" to do math or science? Special guest Saramoira Shields talks to us about how to tackle our math phobia & realize our own mathematical potential.
ABOUT OUR GUEST:
Saramoira Shields describes herself as a bit of a generalist. Her background is colorful and diverse, including experience in theoretical mathematics, robotics, engineering, film production, artificial intelligence, and more. Her great passion for STEM has led her to various science outreach events, from NASA socials to online engagement with curious minds. Currently, Saramoira works on spacecraft design over at the Space Systems Design Studio at Cornell University.
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Hope you enjoy.
SARAMOIRA SHIELDS: Oh yeah, no problem!
SYNAPSE: I actually wanted to talk to you because I first found out about the stuff that you do through a YouTube video you did a while back, like a few years back. ...About math and fear and some of the experiences that you get by telling people that you study math on purpose, for fun.
SARAMOIRA: Right, right!
SYNAPSE: And I kind of wanted to start it off with that. So what kind of motivated you to record that video and put that out there?
SARAMOIRA: Well, you know, I was - [laughter] To be perfectly honest, it was late and I was procrastinating on something else because I was a student. But I had gone back to school, so I was an older student. And you know, older students tend to be opinionated about what they’re seeing - [laughter] - from other students in classes. And I kept getting these, “Oh, you’re brilliant! You’re studying math, ahhh!” And then you know, people would kinda back away slowly.
And as someone who has worked in the real world and you know, done a lot of other things and then come back to it, it really just drove home for me that I’m like - no, no, this is not about geniuses. This is not about amazing brains and untouchable smart people, you know? That’s not - nothing in the world - is it really about that.
You get where you want to go just by working really, really hard. And some people have a lot of things in their way that they have to work past, and some people have less things in their way that they have to work past. And sometimes you get curveballs thrown at you, and sometimes you’re working against a lot of preconceived notions about you and all of that...
But that doesn’t - that’s not something that’s, like, structurally in your brain. You know? That’s not something that’s about math and whether or not you can do it. That’s about the world you live in and what those problems are.
I was getting frustrated hearing from my friends, “Oh, I could never do that.” And I’m like, you’re some of the smartest people I know! You’re driven and focused and you’re doing all sorts of crazy stuff! I had a friend who was producing a film tell me that. I was like, “You’re producing a film! That doesn’t make any sense!”
And so yeah, I just sort of - late one night, was like, you know what? I’m just gonna get this out because I’m kind of tired of making the same arguments over and over again to everyone I know. I’ll just make a little video, stick it on YouTube, and then I can point people to it. Just like a little pep talk, you know? Stop saying that you’re stupid or that you’re gonna beat yourself up over the fact that you’ve had a hard time in your math classes or the fact that you hated your math classes...or whatever it was.
You know, just name that. I’d rather have someone tell me they hate math because they find it boring and not applicable to their lives than to have someone be like, ‘Oh I’m not - I’m not smart enough for that.’ That’s - I don’t think that’s the right argument, right? I think we’re all on some level smart enough for these things, but if you trick yourself into thinking that you’re not, you’re not actually getting at the problem. Because a lot of people do really struggle with math, but those problems are generally not because they’re not smart enough. It’s because something else is happening. And um, it could be something like dysgraphia or dyslexia or something like that, and that’s different than saying, I’m not built to do math. That’s actually a different problem. And it’s not true. That just means that you have to do it differently.
And you have to know that. And you have to fight for that. And if you haven’t have the preparation, you didn’t have good classes...Well then, you gotta work with that problem. That’s a different problem than you not being smart enough. That’s a background problem, right? So I just wanted to throw it out there and just be like, okay, I can point people to this and kinda get them out of their fear brain and start looking at what their actual problem is. Because people can solve problems...and being afraid of math is a problem that you can solve. But it’s very particular to each person.
So that’s why I did it. I did not expect that, you know, more than maybe some people in my classes would see this video [laughter]. I just sort of showed it to a bunch of people and was like, alright, I’ll have it in my back pocket for when my friends are like, ‘Hey, I can’t do this!’
It went a bit further than I thought it would, which you know, I have no problem with if it’s helping people around the world. That’s great! I want that. I want people to check themselves and check their fear and really get at what the problem is.
SYNAPSE: Absolutely. Everybody has their own set of obstacles that they have to maneuver around. It’s a different life experience for everybody. It’s not like you give, like, 20 students one textbook, and they all just [snaps fingers] absorb it.
SARAMOIRA: Exactly, exactly. And you know, I think a lot of people - I mean, I can only really speak to the American education system - but a lot of the people I know and myself growing up, you get this sort of sense of this linear: ‘You either know the facts or you don’t know the facts. And if you know the facts, you’re a smart kid. And if you don’t know the facts, then you’re not a smart kid. And that’s just that, right?’ I really rail against that, I think that that is...wrong. It’s a wrong attitude, you know? [laughter]
That’s not what learning is. Unfortunately, I think that’s a lot of what people think learning is or are taught what learning is when they’re young. And it’s not that. It’s all about, do you have the drive to learn the things that are important to you, right? And there’s a lot of people who have to conquer a lot of math fear or science subject fear in order to do what it is that they want to do with their lives. And stubborness is rewarded [laughter], you know? Like putting your foot down and saying, ‘No, I got to know this stuff.’
If this way that I’m learning it isn’t working, I gotta find some other way. I gotta convince my teacher that I wanna know it, and they gotta work with me. Or whatever it is.
I mean, you know, that’s one piece of it. I’m not going to - I hesitate to basically be like, oh it’s just bootstrap - just get yourself in there and just lean in. Like, no, there’s definitely some - you know, if your problem is you’re dealing with a teacher who’s holding you down or holding you back or giving up on you - you gotta solve that problem, right?
Or if the problem is you’re dealing with an undiagnosed learning disability or learning difference, then you gotta solve that problem. Right? If you’re dealing with money issues - we have a big problem with poverty in education. And if you’re dealing with that - that is a huge problem that also needs to be addressed. I mean, these things can get very complicated.
But don’t, don’t, don’t ever chalk it up to you’re not good enough. Right? If you really have the drive and want to know, then you should be demanding the support for that. You should really fight for it. And that can get kind of exhausting for people. But I think it’s a healthier mindset.
If you’re dealing with some real struggles in learning, then acknowledge that. And be like, ‘You know what? I’m working really hard because I’m dealing with some real struggles. Or like, I’m dealing with the fact that the school I went to for high school didn’t have the right classes for me to be prepared for my major or something like that. And that happens a lot! And I think a lot of people don’t know - and they have this linear idea - if you’re not on the train where final stop is like, math PhD, or biology, or space or whatever...by the time you’re like....10. [laughter] ...Then you’re never going to get on the train! And I think they have this idea, and...Yeah, that’s just not true.
And there’s lots of people at various points in learning about a topic who will be coming in later on and going, “Oh, god, I have all this background I’ve got to catch up on or I’ve gotta do something different”. And a lot of those people are actually really good to have in those communities because they are are approaching it from a different side. Or you know, if you’re dealing with a standard learning disability, right?
I have tutored a lot of kids with dyslexia and that sort of became a thing that I would do - I would tutor specifically kids with dyslexia. And I didn’t know until I was much older that part of the reason I was so good at it was because I have dyslexia.
SYNAPSE: Oh wow.
SARAMOIRA: But I have a specific type of dyslexia - learning disability, whatever you want to call it. And you know, I can rail for days about how I don’t think it’s an actual disability. It’s a difference in the brain that isn’t well matched to like, taking timed tests and doing all that kind of stuff. But I didn’t know that until I was put into those impossible sort of situations that are impossible for people with those forms of learning disability. And then I was like, “No, this is actually really impossible. What’s going on? [laughter] ...Something is different. [laughter] What is it? Why can’t I do this thing that it seems like everybody else doesn’t have a problem with, right?” And yeah, that is a different problem to be solved. Do I think that means I can’t do mathematics or do optimization or science or anything - No. No! That’s ridiculous. There’s a ton of stuff that I’m really good at that, that like you never get tested on for college, right, that’s all very important for doing stuff. Did it make me feel like I couldn’t do anythi -- Yes. [laughter] Yes, it did.
And actually, I’ve never actually had the chance to talk about this...I was first dealing with dyslexia - I have a specific type where my reading speed is very, very slow. So I can do oral exams all day, right? But you give me a pencil and a piece of paper, and you expect me to write stuff out? It’s gonna be a mess. [laughter] Especially if you time it, that’s just terrible.
And the week where my video was going viral was the week where I was discovering that I have this problem.
SYNAPSE: Oh wow.
SARAMOIRA: And I was like, I’m gonna fail this class that I’m in. I just took the hardest exam of my life, and it was a take-home exam. And I was like, I didn’t have enough time to finish it. I had stayed up for like 24 hours trying to just write out this thing. And everybody else didn’t seem to have as much of a problem. And I was just like [gasps] oh no...I might not be able to graduate with a degree in mathematics, ahhh. I was - I was feeling really bad. And I had to watch my own video, you know? [laughter]
SYNAPSE: [laughter] Give yourself a pep talk?
SARAMOIRA: Right, and it took a while actually, it took a while...I think that video came out in 2013. A little while ago. And I didn’t get diagnosed until 2015. And that was after I had gone to disability services at my university, and I was like, “I am not going to graduate. I have two classes that I have to take and I have tried to take them...multiple times.” And there are these classes where it’s like 70% of the course grade, or 60% or whatever it is, is based on like, two exams that are timed.
SARAMOIRA: Right? And so I’m just never going to pass these classes. And I’m just like bawling, right? [laughter]
SYNAPSE: Aww.. [chuckles]
SARAMOIRA: And I finally got referred to be tested...
And that happens! That happens a lot with people. There’s a lot of people who don’t even know that they have something different until they’re older. Or they don’t know what it is until they’re older, right? They don’t have a name for it until they’re older. There’s a lot of stuff that we just haven’t known about brains and learning, and we’re still learning about it.
So, yeah… Don’t put the blame on yourself [laughter]. You know? ...If the struggle is happening. The struggle can be real, and you can still be smart enough to be doing what you’re doing.
SYNAPSE: Yeah. I also like that you refer to doing math, for instance, like doing anything in your life, as a skill because that’s what it really is. I mean, it takes practice, it takes dedication, it’s not something that you’re just good at right out of the womb.
SARAMOIRA: Right! Yeah, exactly. And you know, math is one of those things for me, too - I really strongly feel that about math because... When you’re not someone who works in mathematics or really studies it deeply, you tend to think that math is all about computing things, and actually mathematics is like a field of study that has all these subfields. It has subjects of its own, right? And so there are subjects of mathematics that make me feel like most people feel when they’re doing math. [laughter] I just feel terrible, I’m like I can never understand this! High level algebra? Like the high level stuff, like college and beyond …. Eugh.
SARAMOIRA: Eugh! Like I do not like it. It’s incredibly abstract, and it really hits that little - that point for me that’s really hard where you have to write everything out and not mess up the symbols, and it’s just like - ‘Ugh, this is tedious and boring and stupid, and I feel stupid. [laughter] And you just spin up in your brain like uggghhh. Well, algebra may not be for me [chuckles]. But there’s all this other math that is for me. And I do have to know some algebra and [raspberry noises]. That’s how I feel about learning it. But I can excel in other subjects of mathematics, you know, because there are other subjects that are just completely different.
In a certain sense, it’s kind of like saying, “Oh well, I really struggle with physics, so I can’t do biology.”
….What? [laughter] Like, nope!
I don’t think everyone needs to love mathematics and love every subject of mathematics, you know?
SARAMOIRA: But like, you know, give yourself some credit, you’re learning some hard stuff! And I’d rather have you say, “Hey, I don’t like this, and I don’t really want to spend the time to wrap my head around it, I’d rather spend the time on something else.”
Okay! That’s fine! But don’t beat yourself up over like, “Oh, I can’t. I’m never going to do this thing that I want to do because I can’t.”
That’s - mmm. You’re much less likely to do the things that you want to do if you don’t try to do them in the first place. It’s hard to remember especially when you’re in it, but that’s really what I was trying to drive at for people.
Don’t compare yourself to others, just compare yourself to yourself. Keep plowing through, and you never know, you might stumble into a whole field after that that seems easy to you. And then you’re like, “Oh, I do belong here.” You know?
But yeah, it’s like - you’re going through hell, keep going, right? [laughter] Don’t stay there. That’s the sort of mental state I see a lot of people get into. Especially with anything science or math related. They get into that, “Oh, I’ve given up.” And uh, no, no...that’s - mmm.
It’s really personal. And a lot of teachers, even good teachers...Even if you have a very motivated teacher who wants everyone to succeed and is trying all the different ways of doing that. It’s a very personal process. Learning is a very personal process.
And you know, you may not be able to get what you need from a certain teacher. That’s not the same problem as not being able to do it, right? [laughter] You know, that’s a different problem. It’s sort of like a ‘take ownership’ thing. Take ownership of your own methods and the ways that you have found to work for you. Don’t beat yourself up too much if you don’t do exactly what other kids can do, or what other people in your research group can do. That’s why there are different people in your research group. That’s why there are different people working on different things all at the same time.
SYNAPSE: Yeah, speaking of research, too...I think a lot of people - when they think of the word or hear the word research - they think of beakers and goggles [laughter] and people doing weird chemistry experiments with crazy hair. What exactly does math research entail?
SARAMOIRA: Well, you can kind of split math - the term math - you can kinda split it up into two things. The first thing is what’s called ‘pure math’...or you know, people like to call it ‘pure math’, and other people…hate that. [laughter] We’ll call it pure math versus applied math.
So pure math is basically theoretical math. It’s the really abstract like, you know, I’m thinking really hard and classifying millions of types of things and I’m trying to get the idea and structure of something that doesn’t really necessarily solve a real world problem...yet, right? But doing it in this very abstract, very overarching sense.
It’s a lot like theoretical physics. I think a lot of people think that physicists are people who are blowing things up or something, right? [laughter] But a lot of theoretical physicists are just people who think really hard! They’re reading really, really dense papers with a lot of math in them, and they’re just trying to understand a concept.
So there’s that branch. That’s theoretical math, or pure math. And there’s the applied math branch. That’s where you get people who are like, “I’m trying to model the growth cycles of a certain canopy in the rainforest over decades, using various types of data that I’m getting from other people, and I’m trying to predict patterns of behavior…” Or something like that, right?
That’s one type of applied mathematics. And then when you’re doing stuff like that, you’re doing a lot of thinking and a lot of calculating and a lot of the math-y looking stuff, but you also have to think very hard and work with people who are out in the field getting data for you. And trying to see what the patterns are. So if you’re doing applied things, you could be going out and having adventures and then coming back and doing some math on it, right? If you’re doing applied mathematics for robotics research, say, you might be working in a lab with robots where you’re trying to map out behaviors.
So basically, you go into work and you break stuff every day. [laughter] And then after some chunk of time, maybe months, maybe even years, you figure something out! And then you get to publish a little paper about your applied math problem.
But it really depends on what type of math you’re talking about, what type of research you’re looking at.
Often times you’ll find, if you’re someone who’s doing theoretical math, the theory that you’re working on, these ideas that you’re working on are suddenly applicable to something - and then there’s this whole applied side to the things that you’ve been working on. You’ll see that a lot, sort of repackaging these things, and going, “Oh right, okay, this - yeah, we proved this. This is a true thing that just is theoretically true in these sort of abstract ways, but then I didn’t know that these people over here who are trying to solve this real-world problem could solve it using our theoretical model.’ And so you get a lot of that, going back and forth. But a lot of it - a lot of it’s thinking. [laughter] A lot of it’s doing that kind of stuff...and trying stuff. There’s a lot of like, I’m like writing down my notes and I’m trying out some things, or maybe building a little model. Even if you’re doing theoretical stuff, if you’re doing any kind of geometric theoretical stuff. You can visualize it by building a little tactile model or something that you’re looking at.
And then you go, “Oh, I got it! Ah! I have an idea!” And then you do a thing and you’re working it out and you’re like, “This is great, I totally solved it! I totally solved it!” And you go to bed and you look at it the next morning and you look at it and you go, “This isn’t solved.” [laughter] “I didn’t solve it at all. No, I’ve made all the mistakes. This is terrible.” [laughter] And then you’re like, okay back to square one. I’m going to try this again! [laughter]
So it’s a lot of throwing things at a problem and trying to take them to a logical conclusion.
But yeah, on a day to day basis, the type of math that I like to do - what I find fun is more theoretical. And a lot of that’s just sort of like, oh this is an interesting little problem, I’m gonna think about it a bunch, and I’m gonna just sort of draw some random little doodles and pictures and things and then you know, have some tea [laughter]. Pet my cat. [laughter] Write something up on a chalkboard and be like, Hmm.
But there are mathematicians out there who are measuring like rock formations and things, so that they can get a good sense of data that they need for a model that they’re trying to build.
Then they go back to the chalkboards and they go, Hmm. [laughter]
SYNAPSE: A lot of hmm-ing involved, I’m gathering… [laughter]
SARAMOIRA: [laughter] Yes, yes! There’s a ton of that. But I don’t think that’s unique to mathematics - I think that’s true of pretty much any field if you actually want to solve something or do something. There’s a lot of Hmm.
SYNAPSE: [laughter] I’ve never heard that classification of different kinds of math fields, and that makes a lot of sense to me than...I used to talk to some of my TAs back in college who were working in the math department. And I was like, “So what kind of research do you guys do? Because I’m looking for research positions.”
And he was like, “Well, there’s this famous problem that mathematicians around the world are working on, and they’re trying to prove that zero actually equals zero.”
And I was like, “I don’t - I don’t understand, I don’t know if math is for me… [laughter] I don’t know if I could handle that much thought.”
SARAMOIRA: [laughter] Yeah, yeah, wow. That’s a mathematician joke right there. [laughter] I mean, that’s very abstract, right? That’s the very theoretical, sort of categorical, side of mathematics. Where it’s like, “Yes, but are these statements that we’re making actually true?” [laughter] “My understanding is that addition works like this, but is that true?” [laughter]
And I mean...you know, I’m not being facetious there either. There are, for example - An example I’ve used in talks before is that - we understand things like, okay, what’s a triangle?
Well, a triangle has three sides. It’s an enclosed figure. The sides are straight. And what are the facts that we know about triangles? Well, if you took trigonometry, you know all these weird things about cosines and sines that nobody remembers. And if you do have to use them, you end up writing them down on a post-it note and keeping them by your desk because nobody remembers those identities, and that’s fine. [laughter]
But you learn basic things like, okay, it’s got enclosed angles, and the angles all add up to 180 degrees. And there’s a bunch of calculations that you can do to find out angles given certain types of triangles and all this kind of stuff...
Well, there are geometries where triangles exist, have three sides, those sides are straight, they enclose a space inside, and their angles never add up to 180 degrees. Ever. There’s multiple geometries like this.
And so, you do have to be very skeptical of your assumptions when you’re working in mathematics. Because if you’re working in a certain type of space, if you’re building something sort of logically and step-by-step and following those rules - those spaces may behave very differently than your assumption.
So if your assumption is that all triangles have 180 degrees inside of them - well, I can draw you a triangle on a sphere that has straight sides and the angle sum is always gonna be greater than 180 degrees. I can draw you a 270 degree triangle on a sphere. Right? And there’s a hyperbolic triangle - a good way to think of it is sort of the other end of that spectrum. You’ve got this sphere where everything adds up to greater than 180 degrees, right? Well, hyperbolic triangles - straight sides, three angles, enclosed - and those angles always add up to less than 180 degrees. And that is - that is logically sound. And you can do a whole bunch of really cool math in both of those spaces.
But you know, if you’re learning about those spaces and working in those spaces, and you’re not examining every assumption that you’re making - you’re gonna make mistakes, and you’re gonna say things that aren’t true.
So that’s why mathematicians - If you’ve never met a mathematician, you’re just like, “Okay.” [laughter] “These people might not be all there.” [laughter] “They really argue a lot about like, really easy stuff. I don’t understand…” [laughter]
But I think that’s true of any field, that’s the thing… When you’re sufficiently expert at something, you’re gonna look like a magician to anyone who’s not, right?. To sort of borrow from, you know, the “any advanced technology sufficiently advanced looks like magic”. It’s the same thing for people. If you’re sufficiently pro at something, you’re sufficiently prepared to deal with any kind of problem or any kind of situation, you’re gonna look like a wizard to people who don’t have that background. But you know, it always cycles back to - you can’t compare yourself to the person who’s like, “Obviously, no, in this case - these triangles don’t add up to this so we can’t make that assumption because we’re working in a totally different geometry system - “
Well, if you haven’t learned all that stuff, then no, it’s not gonna be obvious to you, right? [laughter]
SARAMOIRA: That’s fine! Most of the time, most of the time I feel completely at sea. I’m just like, “What am I even looking at?” Especially if there’s lots of dense symbols, you know?
I think that also is an intimidation factor for mathematics, for a lot of people. You have these formulas with Greek letters in them and all sorts of crazy - You’re just like, what even is this? [laughter] But the thing you sort of have to keep in mind when you’re looking at stuff like that is a) it is hard. It’s hard to understand a lot of mathematical statements. And the reason why is because one line in a mathematical proof can carry so much information that it takes pages of plain English to explain it. That’s why it hard!
It is a language in a way, but it’s an incredibly dense language. It’s more like - what would...I don’t even know what a good little way of thinking about that is. Because you know, if you’re translating language - spoken language, human communication language - it can be really difficult, especially if you’re using different alphabets and different writing systems and all this kinda stuff. And you’ve got idioms and things that don’t translate well…
But in general, in order to communicate one idea in one language and then communicate the same idea in another language, you’re going to be doing roughly the same stuff. You’re going to be saying roughly the same stuff.
Math is kind of like translating into another language that uses a different writing system, while writing everything in, like, shorthand and then encode. You know? [laughter] Yeah, like shorthand! If you’ve ever seen shorthand, people write out whole speeches where you’re like, ‘Oh yes, this would take 20 pages to write this all out!’ And if you write it in shorthand, it’s like a page, and you’re like...how? What?
It’s all these rules for like, this means this, and this means this - and then you can kind of unpack this whole speech from a much shorter, shorthand version.
That’s what math is kinda like. It’s like translating into another language and then creating a shorthand. So then you’re looking at something that’s shorthand and also in another language. [laughter] So yeah, nobody breezes through that stuff. [laughter] And if somebody is breezing through that stuff, it’s because they already spent the years it takes to understand what that shorthand meant. So you know, you kind of have to keep reminding yourself of that.
SARAMOIRA: Um, yeah! So I don’t use Facebook unfortunately, so I cannot offer that. But I do use Twitter, and my Twitter handle is @mathematigal. Like the word mathematical, except with a ‘g’ instead of a ‘c’. So you can find me there.
You can also just search my name, Saramoira. My first name is pretty unique. So that’s S-A-R-A-M-O-I-R-A. And that’ll get you to mathematigal, as well.
And I have a website, but it’s really just like, this is what Saramoira does. It doesn’t get updated a lot [laughter]. It just shows you where I’m working and what I’ve worked on. And that’s saramoira.com.
And I did, for a while, blog at mathematigal.com. And I haven’t done it for a while, but I do wanna get back into it. So, I have a couple of pieces up that are several years old there, but hopefully I get more up.
And I would announce everything on Twitter. I think Twitter is really the way to go for following anything I do because I check that...obsessively [laughter]. That’s kinda my jam. But yeah.
SYNAPSE: Sweet, awesome! Thank you so much!
SARAMOIRA: Yeah, thank you!
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