This personal statement was part of this student’s successful application to the University of Oxford, King’s College London, University of Warwick, University of Bristol and University of Manchester for Mathematics and Philosophy.
Reflecting on my love of Mathematics over my December holiday, I realised that I view it as a game with rules. Some of the rules are simple like the commutative property of addition, others are more complex such as the quotient rule in calculus. I have always wondered why these rules exist. In search of answers, I came upon Gödel’s First Incompleteness Theorem. I was intrigued that not all true propositions can be proven, which started my journey into epistemology. I initially agreed with foundationalism, as I was familiar with mathematical proofs being written axiomatically. I also realised how we can only define something as an objective reality by relying on prior definitions; thus, all my current knowledge is dependent on prior knowledge, and we need unarguable beliefs to avoid infinite regress. Hence with my foundationalist view, all knowledge is based on these beliefs. Unsatisfied with the fragility of my current epistemological theory, I explored coherentism, which reminded me of my favourite proving technique from A-level Maths: proof by contradiction, as both use the lack of contradictions to justify truths. Trying to support either theory, I noticed I couldn’t justify an epistemological theory from within the system itself, similar to how Gödel’s Second Incompleteness Theorem shows the limitations within formal systems. The thrill of this academic exercise led me to Maths and Philosophy for my future studies.
Curious about the foundational axioms, I researched the axioms in both maths and philosophy, such as the Zermelo-Fraenkel axioms and the three traditional Laws of Thought. What fascinated me was how I managed to prove the statement “if ~~p, then p” using the Law of Excluded Middle, which helped me deconstruct my initial intuitive understanding of double negation. This sparked my interest in propositional calculus, as I liked how simple symbols can represent abstract ideas as propositions. While researching valid argument forms to familiarise myself with its syntax, I was intrigued by the principle of explosion due to its strange interpretation: any derived theory where a contradiction exists is useless, as any proposition that follows will be a theorem. This helped me justify coherentism and proof by contradiction. Realising the many assumptions and instinctive concepts I have never questioned, it became a personal challenge to identify the axioms and premises that the concepts in A-level Maths stem from. I am eager to become part of a like-minded community at university with others who share my fascination with the intellectual challenges of the philosophical side of mathematics.
Learning about Bell’s Inequality and thus the impossibility of local realism, I was baffled by the idea of true randomness, as I believe that apparent randomness is the consequence of lack of information. My views also oppose the idea of freedom from causal determinism, and since nothing is truly random, everything is predetermined. Hence, I agree with Hume’s argument that free will should be understood in terms of the ability to act according to one’s desires and motives, rather than the ability to act outside of causal determinism.
Outside of academics, I honed my time management and communication skills by tutoring my peers in maths and physics. My creative thinking and discipline are also developed in competitive climbing. During my employment at a programming education centre, I built a robotic arm and developed software to move it using inverse kinematics, applying my knowledge of geometry and programming. I also wrote guides for future educators and students, explaining the code and maths behind it. This enhanced my ability to communicate complex ideas clearly in both writing and speaking.
Maths and philosophy have a beautiful intersection, and can produce logical answers to many metaphysical and philosophical questions, ultimately helping us understand the world. I hope to explore these more during a career in academia.
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