34th Annual UMBC McNair & Undergraduate Research National Conference

I am T^2 mathematics scholar at the University of Texas at Arlington striving to be a mathematics professor at an 4 year institution.Mathematics has been the constant thread running through my personal and academic life. My fascination lies in its ability to reveal hidden structures and patterns, which can be distilled into theorems that withstand the test of time. I am inspired by the contributions of mathematicians such as Euler, Pythagoras, and Johann Bernoulli, whose work continues to shape modern mathematics. We still use theorems established by those amazing mathematicians today, so it leads me to have the ambition to establish a theorem/formula that can have a positive impact on society. As an undergraduate at the University of Texas at Arlington, I found myself increasingly drawn to pure mathematics, where the focus is on the underlying properties and theories rather than immediate applications.
My research journey began when I joined the McNair Scholars Program in January 2024. At the time, I had no fixed area of specialization, but with the guidance of Department Chair Dr. Su, I was introduced to Dr. David A. Jorgensen, who recognized my enthusiasm for abstract mathematics. I knew before that I wanted to take math to the next level; I wanted to come up with the Trujillo Theorem. He shared with me the idea that prime numbers could be factored using matrices and quickly discovered a formula to factor any prime number. At the time, I had no idea what matrix factorization was. This insight became the foundation for my own research into using matrices to factor irreducible polynomials in summer of 2024, work that ultimately led to the proof of the Trujillo Theorem 2024 and the T² in 2024 in my work An Alternate Way of Factoring Mathematical Objects and The Mystery Behind Free Resolutions. In the summer of 2025, Inside Free Resolutions: Exploring the Limits of Polynomial Factorizations (2025) led to the creation of Trujillo 2025 and an alternate proof for Trujillo 2024.My time as a tutor at both the Academic Success Center and the Learning Resource Center has been equally formative. Working with students from a wide range of majors, many pursuing challenging careers in STEM, I have learned how critical it is to make mathematics accessible. I never want mathematics to be the barrier that keeps a student from becoming an engineer, astronaut, therapist, etc. This perspective is deeply personal for me. As a scholar on the autism spectrum, I once struggled socially and academically, but I was fortunate to have special education teachers who believed in me and built my confidence. Today, when I help a student overcome a difficult concept, I often see in them the same uncertainty I once felt. It brings me happiness that I can be in the role of my special ed teachers at the higher level. The joy of guiding them toward understanding is one of the most powerful motivators in my career path .Beyond the classroom, my life has been shaped by a commitment to discipline and perseverance. In January 2025, I reached a milestone of losing 150 pounds, a transformation achieved through consistent running, strength training, and mindful eating. Running has become both a passion and a discipline. I typically run 30 to 50 miles per week and have completed marathons such as The Cowtown Marathon and the Irving Marathon. The qualities required for long-distance running, such as patience, focus, resilience, and the ability to push through challenges, are the same qualities that sustain me in mathematical research, where progress often comes through sustained effort and incremental breakthroughs. Grad school is a marathon, not a sprint. I strive to inspire students that no matter how hard it gets, mental toughness and a strong spirit will be needed to achieve their ambitions and dreams. My motto Two Years Two Months Two Medals that means I ran two marathons within 2 months of my two year anniversary of weight loss one medal to remember each year by. Trujillo theorem 24’ and 25’ to represent milestones in my research journey, two tutoring jobs to fill with love and joy.