To me, math is more than solving problems or trying to get the right answer; math is the way you think. Math has strict criteria that one must meet in order to get the problem correct, you are either right or wrong. But how you get to this correct answer changes immensely from person to person, from idea to idea. That is what I think makes math so special. It is not simple memorization or understanding the deeper thoughts of an author we can only speculate about. It is a critical thinking, challenging problem that forces you to understand the world around you in different, unique ways, to problem-solve and push through adversity. This is what I think makes math help people. In a day and age with AI and everyone on social media, thinking critically has fallen to the back burner in our lives. Taking people’s words on social media and not doing our own research plagues our society with misinformation and followers. We live in the most information-rich time in all of human existence, and we often waste our resources by blindly trusting others’ words and looking to others for solutions. Math develops not only the skills necessary to work out large, complex problems, but also gives different ways of thinking. After all, 2×2 = 2+2. There are multiple ways to reach the same truth, and math teaches us to explore those paths instead of accepting the first answer we see. Math also teaches patience and discipline in a way that few other subjects can. When solving a difficult problem, there is no shortcut that guarantees success every time. You have to sit with the problem, break it apart, and try different approaches until something works. This process builds resilience because failure is a natural part of learning math. Getting an answer wrong is not the end, but instead a step toward understanding why it was wrong. Over time, this creates a mindset where challenges are not avoided but faced directly. This kind of thinking carries over into real life, where problems are rarely solved instantly and often require persistence and effort. Math trains people to stay focused, think clearly, and keep working even when the solution is not obvious at first. In addition, math helps people develop independence in their thinking. Unlike many situations where answers are given or opinions are shared, math requires you to prove things for yourself. You cannot rely on someone else’s reasoning without understanding it, because the logic has to make sense step by step. This builds confidence in your own ability to think and analyze information. In a world where people are constantly influenced by others, this skill becomes extremely important. Math teaches you to question, to verify, and to understand rather than just accept. This independence of thought is what allows people to make better decisions, avoid misinformation, and form their own conclusions based on reasoning instead of influence.

“No one can be compelled to do wrong. For if a person does what is right, even under compulsion, he does not sin; and if he does what is wrong, then he does so willingly. Therefore, every sin is voluntary, and no one is forced to sin.” — On Free Choice of the Will by Augustine of Hippo Augustine’s claim that no one can be forced to do wrong does not mean he ignores outside pressure. Instead, he is changing how we understand responsibility. He argues that wrongdoing always comes from the individual, not from the situation. In this passage, he makes a very direct claim: if you do something wrong, then you chose to do it. Even if there is pressure, fear, or consequences, the final decision still belongs to the person. This creates a world where responsibility cannot be shifted onto anything external. At a deeper level, Augustine is trying to protect the idea that humans are morally accountable for their actions. However, this idea depends on a strong assumption about human nature, especially the belief that people can always separate their will from the pressures around them. Augustine believes that people never truly lose their ability to choose. He argues that even under compulsion, a person’s action still reflects their will. If someone is forced into doing something good, the action is still good. But if someone does something wrong, then it must come from within them. This shows that Augustine draws a clear line between influence and control. Outside forces can push a person, but they cannot make the final decision for them. This idea makes responsibility unavoidable. No matter what situation someone is in, they are still the source of their actions. At the same time, this also means that Augustine is setting a very high standard for human freedom. He assumes that the will is always strong enough to resist pressure, which may not always reflect how people actually think and act in real life. This idea becomes more complicated in extreme situations where every option leads to harm. For example, imagine a man is threatened and told to commit a sinful act or his family will be harmed. If he gives in, Augustine would say he still chose to do wrong. But if he refuses and his family suffers, then his inaction also leads to harm. In that case, every choice has serious moral consequences. This raises an important question: is doing nothing also a kind of decision? If so, then the man may be responsible either way. This shows a possible weakness in Augustine’s argument, because it assumes that the will is completely free even when all options are limited. In real situations, people are often forced to choose between two wrong outcomes, and Augustine’s idea does not fully explain how responsibility works in those cases. At the same time, Augustine’s argument is powerful because it challenges common excuses. People often justify their actions by saying they had no choice or that anyone else would have done the same thing. Augustine rejects this completely. He believes that even in the hardest situations, no one is physically forcing you to act. The final step, the action itself, always comes from your own will. For example, if someone is pressured to harm another person to save their own family, Augustine would still argue that the act of harming someone is their decision. The pressure may explain why they did it, but it does not remove responsibility. This idea makes his argument very strict, but also very clear. He is building a system where responsibility cannot be avoided by blaming circumstances or other people. Another major challenge I bring to Augustine’s idea comes from his belief in an all-powerful and all-knowing God. If God already knows every decision a person will make, then it raises the question of whether those decisions are truly free. If every action is already known ahead of time, it can seem like there is no real choice at all. This connects back to the idea of being forced. If your actions are already set, then you are not really choosing them, you are just following a path that has already been determined. This creates a tension in Augustine’s argument. He wants to say that humans are fully responsible for their actions, but at the same time, his belief in God’s omniscience makes free will harder to defend. In the end, Augustine’s passage is not just about whether people can be forced to do wrong. It is about defining responsibility as something that always comes from within. His argument is strong because it makes accountability clear and direct, but it also struggles with real-life situations and deeper questions about whether true free will actually exists. Augustine held the strong belief that you control your decisions, and responsibility is always passed to the person committing the actions. He strives to create a system that holds people responsible and creates a clear-cut right and wrong, easing the burden of judging sinful actions. This worldview does come with caveats that can change depending on a person’s perspective. Augustine’s view is creative and very clear in theory; however, in practical application, his ideas fall under the scrutiny of moral gray areas and the conscious beliefs of the everyday person. In the end, his argument succeeds in defining responsibility, but falls under the scrutiny of complexity in real human decisions.

As I approach graduation, I have a clear vision for my future. I plan to pursue a degree in physics or engineering, with the goal of one day contributing to research at places like CERN. I am driven by a desire to better understand the fundamental laws of the universe and to work on technologies that push the boundaries of what is possible. This path did not develop overnight. It grew through hands-on experiences in high school that allowed me to explore, build, and think like an engineer. One of the most impactful parts of my high school experience was taking engineering courses where I learned to use AutoCAD and other design systems. These classes gave me the opportunity to turn ideas into real, tangible objects. I learned how to design precise models, think in three dimensions, and understand how small details can affect the success of a project. This was not just theoretical learning. It was practical, problem-solving work that required patience, creativity, and attention to detail. Beyond design, I gained experience working with large CNC machines and 3D printers. Using this equipment showed me how digital concepts become physical reality. I worked on projects that required careful planning, troubleshooting, and iteration. When something failed, I had to go back, adjust my design, and try again. That process taught me resilience and reinforced the idea that progress comes from persistence. These experiences made engineering feel real and exciting, and they pushed me to think bigger about what I could achieve. At the same time, my AP Physics C class deepened my understanding of the science behind what I was building. It connected the hands-on engineering work with the underlying principles of motion, energy, and forces. Instead of seeing physics as just equations, I began to see it as a powerful tool for explaining and predicting how the world works. Combined with my engineering experience, this class strengthened my interest in pursuing physics at a higher level and inspired me to aim for ambitious goals like working in advanced research environments. Looking back, the most valuable part of my high school experience was how tailored it became to my interests. By combining engineering classes, hands-on projects, and advanced physics, I was able to create a path that prepared me for my future goals. These experiences did more than teach me technical skills. They showed me what I am capable of and gave me the confidence to pursue challenging opportunities. As I move forward, I plan to continue building on this foundation and work toward a career where I can contribute to meaningful scientific and technological advancements.

Growing up, the hardest challenge I have faced was not academic or technical, but personal. My mom’s struggle with alcoholism created an unstable environment that often felt unpredictable and overwhelming. There were moments when I felt powerless, unsure of how to help or even how to process what was happening around me. Home, which is supposed to be a place of consistency, sometimes felt uncertain. In the middle of that, I had to learn how to stay focused, grounded, and motivated, even when things felt out of my control. During that time, I found something unexpected that helped me cope: physics. What started as curiosity quickly became something much deeper. When I studied physics, I entered a world governed by logic, structure, and rules that did not change depending on circumstances. Equations always had answers. Systems behaved in predictable ways. In contrast to the instability I experienced at home, physics gave me a sense of order and clarity. It became more than just an academic interest. It became a place where I could think clearly and regain control of my thoughts. As my interest grew, I set an ambitious goal for myself: to build a desktop fusion reactor. At first, it felt almost impossible, especially given my situation. I did not have easy access to mentors, advanced equipment, or financial resources. On top of that, balancing school with the emotional weight of my home life made it even harder to stay consistent. But instead of giving up, I approached the challenge the same way I approached my circumstances. I broke it down into smaller, manageable steps. I taught myself the necessary concepts through books, research, and experimentation. I stayed disciplined, even on days when motivation was difficult to find. Along the way, I faced constant setbacks. Designs failed, parts did not work, and I often had to rethink my approach. At the same time, I was learning how to handle stress and uncertainty in my personal life. What helped me push through both was the same mindset: persistence and problem-solving. I learned to treat failures not as reasons to stop, but as opportunities to adjust and improve. Whether I was troubleshooting a circuit or navigating a difficult situation at home, I focused on what I could control, one step at a time. Through that experience, I achieved something much greater than completing a technical project. I built resilience. I learned how to channel hardship into growth and how to use my passion for STEM as both a tool and an outlet. Physics gave me more than knowledge; it gave me stability, purpose, and a way forward. It showed me that even in uncertain circumstances, I have the ability to create something meaningful. That is why I am committed to pursuing a STEAM degree, so I can continue turning challenges into opportunities and use what I build to make a difference beyond myself.

When I was younger, I did not think of school as something that would shape my future. It was simply a place I had to go every day. I completed assignments, took tests, and moved from class to class without thinking very deeply about what I was learning or why it mattered. Education felt routine rather than meaningful. That perspective began to change in eighth grade because of one teacher, my language arts teacher, Mr. Knoll. He taught with a level of passion that I had never seen before. It was clear that he truly cared about the ideas behind the material he was teaching, not just the assignments or grades. One day he introduced our class to the film Dead Poets Society. Watching that movie changed the way I thought about education. It showed learning as something alive and meaningful, something that could shape how you see the world. Mr. Knoll’s enthusiasm was contagious, and for the first time I began to see education not as a set of tasks but as something that could inspire curiosity. That shift in perspective stayed with me as I moved into high school. I started reading more on my own, asking deeper questions in class, and taking my education more seriously. What began as curiosity gradually turned into motivation. But during my sophomore year, my life outside of school changed in ways I did not expect. My mother began struggling with alcoholism, and the stability of my home slowly became uncertain. There were nights when things were chaotic and mornings when I had to walk into school trying to focus while my mind was still thinking about what had happened at home. It was emotionally difficult and sometimes distracting, but it also forced me to think about what direction I wanted my life to take. During that time, education became more than just something I was required to do. It became something that gave me purpose and focus. Instead of allowing the challenges at home to pull me away from my goals, I began channeling my energy into learning. I became especially drawn to science and physics. My curiosity about physics began after watching a video about CERN and theoretical physicist Michio Kaku discussing the structure of the universe. The idea that humans could study the fundamental laws that govern the universe fascinated me. I started reading physics books, watching lectures, and exploring topics far beyond what I was learning in my classes. That curiosity eventually pushed me to pursue opportunities beyond my classroom. I attended a physics and cosmology workshop through the University of California, Berkeley, where I explored ideas about cosmology and the origins of the universe alongside other students who shared the same curiosity. Being part of that program helped me realize how exciting it is to pursue scientific questions that do not yet have clear answers. I also completed an internship connected with the University of Colorado Boulder, where I was able to observe and participate in real scientific research. Seeing scientists analyze data, test ideas, and work through difficult problems gave me a clearer picture of what pursuing physics could look like as a career. Outside of these experiences, I also spent time exploring science independently. One of my most challenging personal projects was building a small desktop fusion reactor, which required learning complex concepts and working through repeated failures before making progress. That process taught me patience and persistence. At the same time, I stayed involved in my school community. I have played varsity soccer for three years, which taught me discipline and teamwork. I am also a member of the National Honor Society and have been working on creating a nonprofit tutoring initiative that provides free math support to students. I am also developing a program that would help high school students gain funding and materials for science experiments so that curiosity and exploration are not limited by financial barriers. Looking back, the moment in eighth grade when Mr. Knoll introduced my class to Dead Poets Society feels like the beginning of a much larger journey. His passion for teaching helped me realize that education is not just about completing assignments or earning grades. It is about discovering what inspires you and finding a direction for your life. As I faced challenges in my personal life, that perspective became even more meaningful. Education gave me something to hold onto and something to build toward. I believe that learning can be a path to independence, transformation, and purpose. Through my education, I hope not only to pursue scientific discovery but also to help create opportunities for other students to find the same sense of possibility that inspired me.

Calculus is important in the STEM field not only because of the mathematical tools it provides, but because of the way it teaches people to think. At its core, calculus is about understanding change, patterns, and relationships between variables. These ideas are essential in nearly every area of science, engineering, and technology. But beyond the formulas and equations, calculus trains the mind to approach problems logically and carefully. It pushes students to ask questions, break complex ideas into smaller pieces, and understand why a solution works rather than simply accepting that it does. In a world where information moves quickly and is often accepted without deeper thought, this type of reasoning has become incredibly valuable. One of the most important lessons calculus teaches is that answers do not appear out of nowhere. Every result comes from a clear chain of reasoning. When solving a calculus problem, you cannot simply memorize an answer and expect it to work in every situation. You have to understand the steps that lead there: why a derivative represents a rate of change, why an integral represents accumulation, and how these ideas apply to real systems. Each step builds on the one before it. If something goes wrong, you have to go back, analyze your thinking, and understand exactly where the mistake occurred. This process builds a habit of careful reasoning and attention to detail, which are essential skills not only in science but in solving real-world problems. This mindset is especially important today. We live in a time where information spreads faster than ever before, and not all of it is accurate. Fake news, manipulated images, and increasingly realistic AI-generated content have begun to erode the level of critical thinking that people apply to what they see and hear. It has become easier than ever to accept something as true without questioning the evidence behind it. In that kind of environment, the habits of thought developed through STEM education become incredibly important. Learning calculus is not just about solving equations; it is about developing the discipline to question assumptions, analyze evidence, and understand the reasoning behind conclusions. STEM education encourages people to move beyond simply accepting statements and instead ask deeper questions. Why does this result occur? What assumptions are being made? How can we test whether an idea is correct? Calculus plays a central role in this process because it provides the mathematical language used to describe how the world changes over time. It allows scientists and engineers to model motion, energy, growth, and countless other systems that shape our universe. Without calculus, many of the technologies and scientific discoveries that define modern society would not exist. For these reasons, I believe calculus is important not only because of the technical knowledge it provides but because of the mindset it develops. It teaches persistence, logical reasoning, and curiosity. It encourages people to go beyond simply knowing an answer and instead understand the process that leads to that answer. In a world where misinformation spreads easily and complex problems require thoughtful solutions, this way of thinking is more necessary than ever. Calculus, and STEM more broadly, helps build a generation of people who do not just accept information, but who question, analyze, and truly understand the world around them.

During my sophomore year of high school, something happened that completely changed how I understood the world around me. My mother began struggling with alcoholism, and what had once felt like a stable and predictable home slowly became uncertain. Growing up, you hear about issues like addiction in school. You learn about them in health classes or discussions about social problems, and they feel like distant examples used to teach a lesson. I remember thinking about those topics academically, the same way you think about many things in school. You understand they exist, but you never imagine that one day they might affect your own family. When my mother’s alcoholism began to affect our home, that distance disappeared. Something I had only heard about in a classroom became part of my everyday life. That realization alone was difficult. It forced me to confront the difference between understanding a problem intellectually and living through it personally. At first it was confusing and emotionally exhausting in ways that are difficult to fully explain. Home had always been a place where I could relax after school, but it slowly became unpredictable. There were nights when things felt chaotic and mornings when I had to go to school and try to focus on classes while my mind was still thinking about what had happened the night before. I would sit in class listening to lectures, taking notes, and trying to focus, while part of my mind was somewhere else entirely. It would have been easy to fall behind or let those challenges slowly take over my motivation. Eventually I realized something important: life does not pause when things become difficult. School continues. Responsibilities continue. Your goals are still there. At some point I understood that I had a choice. I could allow the situation to slowly pull my focus away from the things I cared about, or I could find something that grounded me and helped me keep moving forward. For me, that grounding force became science, especially physics. My curiosity about physics started earlier when I watched a video about CERN and physicist Michio Kaku discussing the structure of the universe. That moment sparked a deep curiosity that kept growing. I began reading physics books, watching lectures, and trying to understand ideas that went far beyond what I was learning in class. When things at home became difficult, physics became more than just an academic interest. It became a place where I could focus and think clearly. Working through difficult physics problems or learning about new concepts gave me a sense of purpose and direction when other parts of life felt uncertain. Instead of feeling stuck in the challenges around me, I focused on understanding something much larger than myself: the laws that govern the universe. That curiosity eventually pushed me to pursue opportunities beyond my high school classroom. I had the opportunity to attend a physics and cosmology workshop through the University of California, Berkeley, where I explored ideas about cosmology and the origins of the universe alongside other students who shared the same curiosity. Being part of that program made me realize how much there still is to discover about the universe and how exciting it is to be involved in that search for knowledge. I also completed an internship connected with the University of Colorado Boulder, where I was able to observe and participate in real scientific research. Seeing how scientists approach unanswered questions and analyze complex problems showed me what pursuing physics as a career actually looks like. Outside of these programs, I spent time experimenting and building projects on my own, including constructing a small desktop fusion reactor. That project required learning many concepts independently and working through repeated failures before things began to function properly. The process taught me patience, persistence, and the importance of continuing to learn even when progress is slow. Alongside my academic interests, I have also stayed deeply involved in other parts of my life. I have played varsity soccer for three years, and the discipline required to train, compete, and work with a team taught me resilience and consistency. Even on difficult days, you still show up and put in the work. I am also a member of the National Honor Society and have been working to create a nonprofit tutoring initiative that provides free math support to students who may not have access to academic resources. In addition, I am developing an initiative focused on helping high school students gain funding and materials for science experiments so that curiosity and exploration are not limited by financial barriers. Looking back now, the challenges that began during my sophomore year changed me in ways I did not expect. Living through something that I had once only heard about in school forced me to develop resilience, empathy, and perspective. It showed me that real life is often more complicated than the examples we discuss in classrooms. But it also taught me that difficult circumstances do not have to determine your future. Instead, they can strengthen your determination to pursue something meaningful. My experiences with research, my internship at CU Boulder, and my participation in the UC Berkeley cosmology workshop all grew from the same curiosity and determination that helped me continue moving forward even during the most difficult moments of my high school experience. Those experiences remind me that even when life becomes complicated and uncertain, it is still possible to keep learning, keep building, and keep searching for answers about the universe and the world around us.