ROSS '23 Group Photo.

Introduction

I had the privilege of being part of the ROSS Program during the summer of 2023. I thoroughly enjoyed my time there, and I'd like to share my reflections on the experience.

Prologue

My thoughts are inspired by Arnold Ross's Prologue. I've included excerpts from the prologue throughout this post.

Reflections

It is an extraordinary gift to be allowed to fully immerse oneself in a subject of interest for an extended period of time. For this, I am grateful to have had the opportunity to do so at ROSS, where I was able to explore mathematics in a way that I had never done before.

Think deeply of simple things.

My exposure to mathematics has primarily revolved around competition math. While competition math undoubtedly has its merits, it often emphasizes rapid problem-solving, intricate techniques, and the pursuit of "flashy" solutions. At ROSS, I discovered a different dimension of mathematical exploration – one that celebrated the elegance and depth present in seemingly simple concepts.

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Claim. $1 \neq 0$

Proof. By multiplicative closure$(\forall a,b \in \mathbf{Z}^+), \ ab \in \mathbf{Z}^+$ of $\mathbf{Z}$, we have that $1 \cdot 1 = 1$. FTSOC, assume $1 = 0$. Then, $1 \cdot 1 = 0 \cdot 1$. From the one$\forall a \in \mathbf{Z}$, $a \cdot 1 = a$ property of $\mathbf{Z}$, we have $0 \cdot 1 = 0$, so $1 \cdot 1 = 0$. By nontriviality$0 \not\in \mathbf{Z}^+$, multiplicative closure of $\mathbf{Z}^+$ is violated. Thus, $1 \neq 0$.

$\square$

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I vividly recall the first day of the program, where our counselor, Paco, tasked us with the proving that $1 \neq 0$. While it may seem "obvious", stating the intricacies of a proof was by no means trivial. I think this serves as an excellent icebreaker for the program, emphasizing the significance of attention to detail and embracing a spirit of curiosity and exploration.

The gold on "them there hills" is not always buried deep. Much of it is within easy reach. Some of it is right on the surface to be picked up by any searcher with a keen eye for detail and an eagerness to explore.

From my journey at ROSS 23, I've come to realize that the gold isn't always buried deep. Much of it lies within easy reach, with some even resting right on the surface. Embarking with a companion on the journey proves even more rewarding, as their fresh perspective often uncover gleams in unforeseen corners. Profound thoughts can manifest in simplicity, and genuine insights often flourish through shared exploration.

$\square$

The ROSS Dunning-Kruger Curve

Not to scale!

My Progress

I started off at the peak of Mount Stupid, and I'm now somewhere in the Slope of Enlightenment.

Not to scale (again)!

Dorm Lectures

My favorite dorm lecture was the one on Infinite Galois theory 🔥

Infinite Galois Theory

Galois's Duel (Reenactment)

Group Theory

I also really enjoyed the introductry lectures on Group Theory by Paco. It inspired me to learn more about the subject, and I'm currently reading through Dummit and Foote.

Thank you Paco!

My gratitude

Wait, I'm not done yet! I'd like to thank the following people for making my ROSS experience so memorable:

• My counselor, Paco:, for being an amazing counselor and friend. Our conversations were a delightful mix of serious mathematical advice and your infectious humor. Thanks for not only guiding me through the program but also for adding a generous dose of laughter to the journey.
• Family 11, A Welcoming Group: Family 11, my fellow participants, you made each day at ROSS memorable. The shared laughter, late-night discussions, and collaborative problem-solving sessions created bonds that I'll cherish. Our diverse perspectives and mutual support enhanced the learning environment, and I'm grateful for the friendships we forged.
• Mr. Pollack, Inspiring Number Theory Lectures: Mr. Pollack, your engaging number theory lectures ignited a passion for the subject that I hadn't fully explored before. Your dedication to teaching and the clarity with which you explained intricate concepts left a lasting impression on me. Your guidance has sparked a new direction in my mathematical journey.
• Mr. All and the ROSS Staff: Lastly, a heartfelt thank you to Mr. All and the entire ROSS staff for orchestrating this remarkable program. Your dedication, attention to detail, and commitment to fostering a nurturing learning environment were evident in every aspect of the program. Your efforts allowed us to fully immerse ourselves in the world of mathematics.

Thank you, ROSS, for an extraordinary summer that will resonate with me for years to come.