Affirmations by Paige B. '24

“My name is Paige, and I’m a bit of an optimist. Or at least, I try to be. …
Beyond being an optimist, I’m a mathematician. Or at least, I try to be.”

– my blogger bio, circa summer 2023

In one of the very few blog posts I wrote before MIT, I wrote:

I am good at math.

I was terrified of putting this thought out into the world. Hell, I followed the sentence up with a number of caveats all to the effect of: Yes, I do know there are people who are immensely better than I am at math in every possible category of “betterness.” (Does such an objective ranking of “betterness” exist? Would such a ranking even be useful for any real purpose? I don’t think so, though this isn’t the point; I wrote it when I was 17. I digress.) But regardless, I typed the thought, hit post, and put it out into the world.

I am good at math.

When I read this sentence now, I wonder what value, if any, such a statement has. I’ve discussed this blogpost idea with a number of other mathematics graduate students, nearly all of whom agree: making such a statement isn’t wrong, but they would never say it themselves. At this point in my life, I think I agree. When I try to be as objective as I can (a lost cause, as a subjective being), the sentence just feels… braggy. Unhelpful. Unnecessary.

Unnecessary?

Yes.
No good can come from putting
Such a thought
Out into the world.

Is that true?

I think so.
Nearly every time I’ve heard this phrase,
it’s been from someone trying to make others
feel bad about themselves.

Then why did you post it all those years ago?

…

Listen, I didn’t believe that sentence was true when I made that blog post 5 years ago. When I was 17, all I knew was that I didn’t know anything. I didn’t know what college would be like. I didn’t know if I was prepared for how hard MIT would be. I didn’t know if I could even remotely be someone good at math.

But I knew that I wanted to be. I wanted to have this utter confidence to walk into my first class and sit in the front row like the nerd I am. I wanted to not carry this fear of being seen as dumb in homework sessions. I wanted to believe that I was someone who could feel good at something.

In this way, I wrote out the sentence

I am good at math

not as a declaration, but an affirmation.

At 17, I didn’t know much, but I knew MIT would be really hard. I also knew that MIT would only get harder if I didn’t believe in myself. If I didn’t let myself try my best for fear of failing. If I didn’t let myself be seen as dumb in homework sessions. So… I faked it.

And would you say that was “unnecessary?”

Listen, I don’t love your tone Mr. Italics.
…
But no, I wouldn’t say that was “unnecessary.”
In fact, I found that “faking it” worked.

a) My first year I went straight into my meeting with my academic advisor and (essentially) said “These are the classes I want to take. I think I have the prerequisites. It’ll be hard, but I want to try. Give me a shot and you’ll see—I will try my goddamn best.” And there was a moment when, frankly, I didn’t know how he’d respond. There was some part of me that thought he’d turn around and say “That sounds absurd, take these classes instead” or “Who do you think you’re kidding” or something to that effect. But he didn’t. 

He gave me a shot, approved my classes, and (essentially) said

Give it your best.

At the end of that semester, I went back to him with grades I was proud of, and a new absurd class schedule to attempt in the spring. He later became my academic advisor for the rest of undergrad, and he even wrote one of my letters of recommendation to graduate school.

b) That fear of being seen as dumb? Well, that went straight out the window when I went to my first office hour and terribly mispronounced a mathematician’s name to the professor (Dirichlet, if you’re interested—the mathematician whose name I butchered, not the professor). From that point on, I just stopped caring about making a fool of myself. I just… decided to accept that the best learning happens when you open yourself up to the opportunity of being seen as an idiot.

And, much to my shock, I made friends in that process.

My PSET⁠01 problem set group and I made a pact: if we spent an hour or two before office hours carefully refining our “foolish” questions into something reasonable to ask an MIT professor, I’d volunteer to ask whatever questions emerged. What resulted was a series of office hours, week after week, of my friends and I going and asking the questions we needed to ask to learn the material and pass the class.

What’s shocking about this to me, is that this just felt right. I knew how I learned best (e.g. asking potentially dumb questions in office hours), and others responded well to that. I was able to exist in this space in a way that I needed to. In a way that best supported my mental health, and gave me the opportunity to learn and get better at math. In a way that allowed me to be me. I guess I was just shocked that this wasn’t seen as a foolish, isolating, endeavor.

Hell, I made friends in that process. Friends who learned that we liked/didn’t like pure math together. Friends who were open to conversations about pedagogy and education and mathematical communication. Friends who lifted each other up; who made each other feel like we were, or at the very least could be, 

Good at math.

That wasn’t easy to find, but “faking it” sure helped.

I clung to that affirmation whenever I found myself struggling in my classes. I’d tell myself– my classmates– my friends: “Right now you’re learning something new, and that’s hard to do, but that doesn’t mean you can’t do it.”

I used that affirmation to push back against toxic norms in math. When someone would say that a question was “easy” or “trivial” or “obvious” I’d respond: “Well clearly it’s not, because someone’s asking the question in the first place. And even if there is a simple explanation, that’d be a better response than calling the question ‘easy.’”

I needed that affirmation to make it through MIT. So no, I guess I wouldn’t (subjectively) say that it was “unnecessary.”

What about now?

What do you mean?

You’re not 17 anymore.
You’re 22.
Hell, you’re in grad school
Hell, you’re gonna be a math PhD student at MIT in less than 8 months.
And sure, you don’t have shit figured out, but
Does it feel unnecessary for you now?

…
Objectively-

Stop trying to be objective, it’s a lost cause-

Yeah,
I don’t think I need the affirmation anymore.
I mean, what good does it do?
At this point
…
At this point,
Everyone knows that everyone’s just trying their best.
Shouldn’t that be enough?

I don’t know,
Is that enough?

…
No.
It doesn’t feel like it.
…

For one thing, it feels lonely as hell. Sure, idealistically, everyone should just know that everyone’s just trying their best. But that doesn’t inherently stop the feelings of inadequacy, either due to internal or external reasons. That doesn’t magically create the space you need to exist in the ways you need to exist. That doesn’t stop you from constantly asking yourself if you’re even remotely good at this.

Sometimes it just feels like people are taking chances on me, and I don’t know why. At what point in high school was I able to convince someone that I should be admitted to MIT? At what point in undergrad did I become someone who could get paid to research pure math? At what point did I stop faking it? Did I ever?

And these questions just repeat in a loop in my brain. Sometimes, it feels like the loop never stops. But sometimes, there’s a brief silence. A glimpse of clarity. A moment of feeling like I could be a goddamn mathematician.

Not because I resolved some massive open problem, or because I feel like an Expert™ in some topic. Not because I feel like I am

Good at math,

but because I can feel small ways in which, by “faking it,”

I’ve gotten better.

The moments when I needed that affirmation in undergrad were often associated with questions of sustainability. Moments where I couldn’t help but feel like “Listen, I know that learning new things is hard, but at what point is it too hard? Am I trying too hard? At what point does it get easier? Does it ever?” But I held out hope that one day things, perhaps small and insignificant things, would feel easier.

It wasn’t easy to hold out hope. I felt like I was being too optimistic—too naive—to know better. As if, I was too young to understand just how brutal mathematics can be. As if, I was lying to myself by using idealistic pedagogical beliefs along the lines of “Practice makes better.” As if, it was an inescapable fact of the world that life was meant to always be exactly this hard, and that no one else felt the same.

But, as I said, there have been brief moments where I don’t feel this way. Where, for a moment, my optimism doesn’t feel like blatant naivety.

Like, this last summer when I worked at MathROOTS for the first time (a mathematics summer camp run by MIT’s math department for high schoolers). At this camp, there were moments where I just knew how to exist within this (mentorship? educational? social?) space. Where years and years of being interested in education and thinking about math communication came to fruition.

I don’t want to go terribly into the weeds with the dozen or so moments that made me feel this way at the camp, but I will give one specific mundane example. There was one night where another mentor and I were giving feedback on the practice problems students had turned in. After you finish giving feedback, you’re supposed to put the papers in alphabetical order. And my friend, an amazing colleague and educator, started going through the papers one at a time to do so. Looking for papers with a last name starting with A… then with B… and so on. And I have spent years alphabetizing papers for teachers—hell, I used to do so in my second grade class during recess. So, I politely asked my friend for the papers, and quickly alphabetized them in one hand (if you’re interested, using an insertion sort algorithm).

And it’s dumb. This moment shouldn’t matter. And yet, I couldn’t drop this feeling of just utter exhilaration. Like, it was something I was good at, or at the very least it was something I had gotten better at.

After the exhilaration wore off, my first thought was: I am good at this.

This was immediately followed-up with: You shouldn’t think such things. You shouldn’t think such things because it makes you an ass. You shouldn’t think such things because it’s important to be humble. You shouldn’t think such things because it’s taboo. You should just be happy that you are trying your best, and everyone knows that everyone is just trying their best, so such thoughts shouldn’t be thought in the first place.

So is it enough?

No, it’s not.
That’s not how my brain works.
I try to find moments of happiness
when and where I can.
To ignore such moments of utter glee
“because it’s taboo”…

It’s invalidating.
You worked hard.
You’ve gotten better.
You didn’t think you ever would.

Did I really?
Did I really think
That things would never get better?
That I could never get better?

Constantly.

Okay,
but now I know that isn’t true.
Objectively-

I swear to god-

Objectively,
I know this isn’t true anymore.
Shouldn’t that be enough?

I don’t know.
Is that enough?

…
No.
…
Why isn’t it enough?

Sometimes, I worry that I’m working too hard.⁠02 <i>“Am I trying too hard?”</i>

I’ve thought this time and time again since I’ve started graduate school. And let me be clear, I have loved graduate school so far. But I would be remiss to point out that it has taken work to love graduate school. I have three amazing advisors, all of whom care deeply about education and mentorship and beautiful mathematics. Hell, if they didn’t, I wouldn’t want to be their student. Hell, if I didn’t care deeply about those things either, I don’t know if they’d even want me to be their student.

But because I care about those things, I know what I need to be able to exist in this space in the ways that I need to. I know, at least somewhat, how I like to learn, and collaborate, and exist. And yet, when I started graduate school, I thought that I’d have to throw all that out the window.

When I imagined what graduate school would be like, I pictured reading papers til the sun rises. I imagined attempting to solve problem after problem only to be told that such exercises were “trivial.” I thought I’d have to take on toxic mindsets regarding math I had long since dismissed because they didn’t make me happy.

And I won’t go so far as to say that this isn’t some people’s graduate school experience. I am certain there are mentorship horror stories echoed by thousands of students from around the world. But I knew that I didn’t want that. I didn’t want to passively take on the role of “hardened and unfeeling and purely objective mathematician” (a role, thatI am nearly certain, doesn’t exist in actuality).

But it’s hard to dismiss this nagging feeling that, at times, such a role would be easier.

Would it be?

Wouldn’t it be?
Wouldn’t it just be easier
To always do what others want you to do?
To work until you can work no longer?
Isn’t that what graduate advisors want?

Do you really think that?
Is that how you’d advise your students?
Is that a mindset you’d encourage?
Is that the world you want to live in?

No.

Then why would you think that’s the world
Your advisors want for you?

…

Why would you even want to be “a good”
Mathematician,
Educator,
Friend,
In a hypothetical world
So unchanging,
So static,
So unfeeling,
So… hard?

I wouldn’t want to be!
That’s the whole point!
I have to feel like the world isn’t static,
I have to believe
That optimism isn’t the same as being naive.
I have to believe that all this work was for something.

What if,
The “something” this work was for,
Was to be a practicing optimist?
To be someone who thinks that
The world can change?
Someone who believes that
People are worth changing for?

…

Last semester, I put in a lot of work into learning to love graduate school. To learn that it was okay for me to exist in this space in the ways that I most need to. Which meant, talking to my advisors about such questions. Giving them the opportunity to prove me wrong. To prove that it’s not naive to have such conflicting feelings about the road of academia I chose to go down. And, to my (perhaps, in this way, naive) surprise, they did prove me wrong.

I told them how, sometimes, it feels like I’m hurting my career in moments where I focus on my mental health. In moments where I prioritize advocacy and education work. In moments where I put myself first. To which they (essentially) said “Is it really hurting your career to do what you need to do? To put energy into the things you care about? To exist in the ways you need to exist?” And, for the first time in a long time, I didn’t feel so naive.

In one of the few blog posts I make before I return to MIT, I will type the thought, hit post, and put it out into the world.

I am not naive.

Do you really believe that?

I don’t know.
I know that I want to.
But I am 22,
And while I don’t know much,
I know MIT will be really hard.
And it’ll only be made harder if I believe otherwise.

Are you scared to return to MIT?

No.
I’m not.
Or at least, I don’t want to be.
And I think,
For now,
That has to be enough.