**Peter Haine**

#### Graduate Student, 2016-2021

Research: Homotopy theory, algebraic K-theory, higher category theory

Growing up in rural northern New Hampshire, I was always pretty different from everyone else. Whether it be because I was one of a couple of Latinx kids in an almost completely White town, or because I always really loved learning in a place where education was not valued, or any of a number of other reasons. I attended MIT for my undergraduate studies starting in 2012, and now I’m entering my final year of grad school in math at MIT. Coming to MIT as an undergrad was, in many ways, coming to a paradise. However, there were also a lot of ways in which it was difficult for me.

Soon after starting undergrad at MIT, I realized that I was utterly unprepared for almost all of my classes. While it seemed that my classmates were well-prepared from taking AP science classes and participating in STEM-related extracurriculars at colleges near them, I didn’t have those sorts of opportunities. I was always interested in math and science and took advantage of what was available in my community; however, my high school was in the lowest-funded school district in the state and only about 60% of graduates from my school went onto post-secondary education (including community college and associate's degree programs). The school didn’t have enough money for paper or whiteboard markers to last the year, never mind AP science classes. The nearest college was a few hours’ drive away, so it wasn’t feasible to take classes or do programs there. I think some of my MIT classmates quickly caught onto how underprepared I was. People would ask me things like how it was possible for someone “like me” to get into MIT, or if admissions had made a mistake.

I found my math classes incredibly intellectually stimulating and challenging. They were also challenging in some ways I didn’t expect. I had never heard of math competitions, math camps, Art of Problem Solving, or any of the many high school math programs that exist. I found that many of my classmates already knew each other from participating in these programs, and were often quite dismissive of people who didn’t have the same type of background. Certain people would taunt me by saying how “stupid” I was for not being able to start problem sets the night before they were due, or for carefully working out my solutions on pen and paper before typing them up. Another example that has stuck with me over the years is how, during my first year of undergrad, one classmate used to always say things to me like “You don’t already know number theory, how do you *ever* expect to become a mathematician”. When I did take an elementary number theory class the spring of my first year, I worked really hard and got 100% on all of the problem sets, but completely froze on the exams. I did so poorly on the exams that I got a C in the class (a first for me), and really did think that I could never become a mathematician.

Since I felt like I was so much worse at other subjects, it seemed like math was my only option. So I continued doing math, but made an important change: I decided to protect myself by not interacting with these individuals and finding my own way to understand the wonderful math I was learning. I tried to find faculty who I could feel comfortable asking questions to and tried to take classes from them when I could. This was isolating in many ways, but was also something I was used to from back home. Luckily MIT is a big place, and I found many fantastic friends outside of math who value me for who I am rather than what I didn’t achieve in high school.

When it came time to decide what to do after undergrad, I thought that because of my interests in math, teaching, and learning, grad school seemed like a good fit. I did alright in my classes after my first year, but with respect to the standard I was measuring myself against, I didn’t think that someone who was “so far behind” would be accepted to any program. I figured I’d apply, probably not get in, and then teach high school or something.

Despite a lot of practice, I did poorly on the math GRE both times I took it; this cemented my feeling that I wouldn’t get into any graduate programs. I was fortunate to be able to apply to a large number of programs (something my peers also made fun of), with the hope that I might be accepted into at least one of them. When I got accepted into most of the programs I applied to, I realized how the standard I was measuring myself against was inaccurate and distorted. It’s hard to realize this when you get most of your information from your peers. From my experience, I’d like undergrads interested in math to know that, despite what others might think of your background and training, it is possible for you to excel at math as well as pursue math grad school. What I’d incorrectly thought was “so far behind” was actually a very reasonable place to start graduate education.

When it came time to decide whether or not to stay at MIT for grad school, the decision wasn’t so clear. In terms of my mathematical interests, it was the clear winner. On the other hand, I didn’t want to relive the same peer-to-peer interactions from undergrad. There were two things that convinced me to stay. The first was that I had found some excellent faculty mentors at MIT; I’ll highlight two here. The first is Gigliola Staffilani: ever since I met her, she has been a constant source of support and encouragement. If it were not for her support, I’m sure I wouldn’t have made it to grad school. The second is my PhD advisor Clark Barwick (now at the University of Edinburgh). He exposed me to types of math that I found incredibly appealing, was always generous with his time, and encouraged me to work through things at my own pace.

The second reason I decided to stay at MIT was that my interactions with Barwick’s graduate students (through his seminar) indicated to me that the grad community was quite different from the undergrad community. His students were also generous with their time, would often explain to me different aspects of the subjects they were thinking about, and would point me to resources where I could learn more. They were also happy to share their research in an accessible manner.

As an undergrad, I didn’t understand the amazing freedom math grad students have: spending most days thinking about the mathematics they enjoy, discussing math with many wonderful people, and traveling to conferences and workshops. In grad school I’ve had opportunities to spend semesters working with mathematicians in Edinburgh and Berkeley, as well as been able to attend conferences and speak at seminars in Germany and across the US. Coming from a place where many never leave the county or state, I’d never imagined that I’d be able to travel to so many amazing places, never mind that people would pay for my travel!

I’ve also really enjoyed participating in some of the mentoring opportunities that the math department has, such as the Directed Reading Program and running PRIMES Circle. I find it really rewarding to interact with and mentor younger students. Through the PRIMES Circle program, I’ve particularly enjoyed bringing math extracurriculars to students who might otherwise not have them. It is amazing to see how much the high schoolers who participate grow over the course of the program.

In contrast to my undergrad experience, grad school has been a wonderful improvement. I’m grateful for the opportunity to have been part of the MIT math community for so long, and am excited to continue doing math as well as learn from and mentor younger mathematicians.