Recommendation Reference Info

The programs are the following, but I think they just ask for a PDF upload, so you can reuse the same rec letter.

• PROMYS (math) Due Tues 3/3
• Garcia Center (hands-on material science research) Due Wed 3/4
  • Submission link they told me to share
• YSPA (astrophysics !) Due Mon 3/16

No need to read all this! Just use whatever you find useful. And please let me know if you would like me to share anything else in particular. Thanks again Mrs. R!

1. Love of math

There’s this feeling I get when I finally see why something is true. It’s not quite happiness. More like relief and wonder at the same time. I don’t think most people feel the need to sit there stunned after working through a derivation, and they probably get a lot more done because of that.

It’s really hard for me to treat math as rules to apply. If I see a result and I don’t understand where it came from, I literally can’t move on. It’s an itch that forces me to take apart the rules and rebuild it from definitions. The ideas themselves (structures that we construct and share with one another) are just beautiful, and I think they’re worth understanding purely for their own sake.

But I also love what math does. Inspired by your class, I interned at the statistics department at George Mason University for 8 weeks, getting to work with professors with decades of experience and applying math to problems that actually move the world. It was thoroughly amazing watching the same abstract structures I loved on paper turn out to be exactly what you need to model something real. Math really is unreasonably effective, and getting to experience that happening in front of me, surrounded by people who feel the same way about it, was probably the most exciting 8 weeks of my life.

2. Stubborn (in a good way?)

I still remember that first time when I was handed the rule $\sigma_{X+Y}=\sqrt{\sigma_X^2+\sigma_Y^2}$, and for hours all I felt was rage.

But why?? Where did it come from? I just could not proceed once this happened and spent that evening reading the web, until finally I found a satisfying answer that derived from definitions.

Then there’s a gush of wonder when I realize I’ve now loaded a whole new programming language into my brain and can smoothly compute things in a new realm of thinking.

(I ended up converting that derivation into a flashcard that I still see once in a while today.)

Digging into where the rule came from just made it all the more satisfying when we went over the derivation in RS2 using a concrete example (of dogs) to illustrate.

The same process happens all the time in math and physics, like when I first learned the Central Limit Theorem, this video was what finally gave the satisfying aha moment. That final moment where it clicks is I think a huge part of what makes these subjects so fun.

3. Collaboration

The best part of class, though, was getting to explore each new topic with friends on the whiteboards that you hung up around the room. Comparing approaches after working through a problem and seeing that someone thought about it from a completely different angle was genuinely very fun.

I also really appreciated it the times when you asked us to stand up and explain our solutions to the class. Having to actually teach your thinking to other people forces a kind of clarity that just solving it on paper doesn’t. You can’t make hand-wavy arguments when your peers are waiting attentively for the next step.

In fact, I made time outside of class on the weekends to meet up with some friends and learn statistics together, to keep the discussions going. And honestly the GMU internship was the same impulse of wanting to work with others who love this stuff and be in a room where I could learn from people who’ve been doing this for decades, not just read about it alone.

It’s also why I look forward to varsity math team every week. I stay at school until 9:30 on Thursday nights, not because I have to, but because getting to sit with a really beautiful problem and watch someone pull out a technique I’ve never seen before is one of my favorite parts of the week. And then getting to go represent the school at competitions, especially the team and relay rounds, are just so much fun.