Background

I'm a current Year 12 student at a Grammar School in the UK, studying Mathematics, Further Mathematics, Computer Science and Physics.
I'm applying for the Joint Honours Mathematics and Computer Science course at Oxford in 2026.
My UCAS predicted grades are 4 A*s.
I have sat only one MAT practice paper (2007) in exam conditions so far, getting 80/100. Keep in mind earlier papers are generally considered to be slightly easier.

Market only resolves yes if I get in next year, not if I reapply for the following year.
Ask any questions and I will answer.

I will not bet on this market

This is the first draft of my personal statement, which is subject to change - any yes betters feel free to give advice.

Question 1: Why do you want to study this course or subject?

I've always used mathematics and computer science to explore my interdisciplinary interests and enjoy them as a tool for furthering my understanding of a wide variety of topics.

Recently, an exploration into quantum computing bridged my interests in maths, computer science and physics. A video on Grover’s algorithm sparked a deeper dive into the quantum circuit model and how it's used in quantum teleportation, and search algorithms. I learned Qiskit (a Python quantum computing library) to implement these, translating theory into code.

This deepened my understanding of matrix unitarity, inner products, and abstract vector spaces as well as showing me how useful mathematics can be as a tool in other disciplines. I learnt many ideas central to quantum mechanics such as state spaces, tensor products and measurement operators.

A visit to the Diamond Light Source Synchrotron introduced me to the use of AI to determine protein structure, convincing me of the power of interdisciplinary approaches in research. Curious about the function of this algorithm, I watched 3Blue1Brown's Deep Learning series to get theoretical understanding, and read an article on building a neural network from scratch for more detail. I derived and implemented backpropagation from first principles, learning the chain and product rules as well as partial differentiation and then used these to code this algorithm in Python.

I also gave a 5-minute talk on the risks of AI for Oxford's Big Think competition. Exploring reward hacking, instrumental convergence and corrigibility developed my scientific communication skills and understanding of AI safety.

Question 2: How have your qualifications and studies helped you to prepare for this course or subject?

Looking further into topics covered in class has given me a deeper understanding of the syllabus. For example, unsatisfied with the lack of mathematical detail when introduced to encryption, I looked deeper - I learnt the underlying mechanism of key production, investigated modular arithmetic, and programmed the RSA algorithm in python. Consolidating my quantum computing knowledge, I researched Shor's algorithm to see how it could one day break encryption and implemented the Quantum Fourier Transform used in it, improving my fluency with Qiskit.

Similarly, 3Blue1Brown's linear algebra series gave me an intuitive understanding of things I'd come to regard as simple fact such as the geometric interpretation of the dot product. I used this deeper geometric understanding to code a shader with GLSL, rendering multiple reflective spheres. I used raymarching and calculated reflections in 3D, putting to use what I'd learnt within a low-level language. A series on complex analysis inspired me to revisit GLSL and render the Mandelbrot set, consolidating my Further Maths knowledge of complex numbers.

For my computing NEA, I developed an automated stock-trading bot. I analysed large datasets using pandas, designed a GUI, and integrated an API, which developed my ability to build and design large projects.

Question 3: What else have you done to prepare outside of education, and why are these experiences useful?

I hone my problem-solving through competitive programming, achieving a distinction in the 2023 Perse Coding Challenge Round 1 (top 5% and best in my school) with a Merit in the final, and top 25% on the 2023 British Informatics Olympiad. I use these programming skills to explore my hobbies - for example, coding a pitch recognition training program to sharpen my music skills, or an automatic solver for a Rubik's Pyramid I received on Christmas, which required implementing a brute force search.

A conversation with a friend introduced me to the Busy Beaver problem (finding the longest halting Turing Machine for n-states), and how BB(5) was solved by amateur mathematicians using the Rocq interactive theorem prover. Fascinated by the power of proof assistants, I completed Kevin Buzzard's Natural Numbers Game to learn Lean. I used Peano's axioms to prove statements rigorously, learning about formal proofs and how type-theory based theorem provers differ from typical programming languages.