Applied in: Winter 2013
University Offers: Cambridge, Imperial College, UCL
Maths can leave me feeling stupid, frustrated and pleased with myself at the same time. Frustrated from extended periods of getting nowhere, pleased when the crux move reveals itself, and stupid when it seems so obvious in retrospect. But regardless of the variance in the problem solving process, Maths never fails to amaze.
So why do I enjoy maths? Firstly is the room for creativity. Experimenting with geometries on dotted paper and being exposed to Conway's surreal numbers alerted me both to the difficulties and possibilities in defining new objects. In addition to the creation of entities, I am often struck by ingenuity in theorems, proofs, and problems. I love it when you're working on, say, an algebraic inequality and find a nice geometric solution to it. The different ways of visualising problems or theories, especially through using tools from other branches, adds a new dimension to problem solving.
Secondly is the challenge it brings. I have spent many hours puzzling over problems that seem completely inaccessible at first, but gradually open up under examination. An example is proving that, for every point P in an equilateral triangle ABC, one can construct a triangle with sides PA, PB and PC. Many failed attempts at coordinate bashing helped me discover the rotation of 60 degrees about A that transformed the mess into a rather elegant reflective solution. Adding new tricks to my arsenal by building on previously developed techniques is particularly satisfying. It always surprises me how solutions seem so simple in retrospect, and how they often come when I'm in the shower or in bed. As a result of these efforts, I was fortunate to have received Outstanding Gold awards in international competitions, and the Sixth Form Maths Prize.
Another way of tackling challenges is through teamwork. I was a member of our school maths team, which became the UKMT Senior Team Maths Challenge national champions and went on to represent the UK in the Gare a Squadre in Italy. It was exciting working collaboratively, and observing how others approached problems. Maths stands out for me also because of its rigour. Stanford University's Education Program for Gifted Youth first introduced me to analysis through the study of limits, Riemann integrals and the Taylor series. This culminated in my obtaining a 5 in AP Calculus BC (UCAS equivalent of an A at A Level) in Year 10 in Hong Kong. I also had the opportunity to write proofs as I took part in the BMO and tackled Zeitz's The Art and Craft of Problem Solving, which exposed me to a wide variety of techniques and problems, and helped further my problem-solving skills as well as my perseverance.
Applied Mathematics also interests me. I am particularly interested in game theory in behavioural economics, and so wrote an essay on 'The Evolution of Discriminatory Social Norms', which looks at these norms through the lens of evolutionary game theory. I came up with my own model based on Axelrod's model for symmetric games, and based my conclusions on data from running computer simulations, and analysing existing data and arguments (main sources include Hargreaves Heap & Varoufakis and others).
My involvement in extra-curriculars allowed me to improve relevant skills. In debating, I had to come up with creative ways to construct and deconstruct arguments, as well as present them in a clear and concise way. I was a finalist in LSE, Durham, and Dulwich Schools, was invited to trial for Team England, and organised a tournament to promote debating as Vice President of the HKIDO. I have learned to listen to and respect others, set clear goals and manage time efficiently. I hope these skills will contribute to my current role as school monitor. But much of Maths is still inaccessible. I look forward to meeting some of those sects as I further my education, and work towards my ambition of wielding Maths in all its elegance to make an impact.