# My Love For Modern Mathematics

I love the unarguable nature of mathematics, and how that, once proven, a mathematical truth is true forever. It fascinates me how most of the maths I am studying is hundreds or even thousands of years old, and still just as relevant and challenging. This led me to wonder as to what modern mathematicians study; what exciting new fields are being researched and just starting to be understood? Reading Ian Stewart's "From Here to Infinity" has given me a glimpse of these fields, reinforcing my desire to understand more deeply the reasoning behind the theories presented in the book, especially those regarding primes and cryptography. I relish the challenge presented by longer maths problems, and enjoy the satisfaction of a problem clicking into place and flowing to a neat solution.

When my school could not timetable me to take Further Maths A level, I asked for the resources and taught myself A1 Further Maths, in addition to my three A levels. This really developed my ability to study maths independently. In year 13, my timetable allows me to have 2 hours Further Maths teaching per week, teaching myself half of the course. I opted to take an additional level 2 certificate in Further Maths, in which I scored A* with distinction. Pure maths is my favourite because every theorem can be proven using a logical progression from a few simple rules. This is exemplified in Euclid's geometry, which I have watched several lectures on, and I am particularly interested in how the issues of postulate 5 led to the discovery of a whole new area of geometry, explored by Cliff Stoll in an intriguing talk discussing the possibility of 3 or 5 sided squares. I particularly enjoyed studying polar co-ordinates in Further Maths, with their affinity to non-Euclidean space, and their use in Euler's identity, which was manipulated to derive an interestingly real value for i to the power of i by Matt Parker in an engaging talk. This lecture demonstrated how sometimes logical steps from previously proven theorems can reveal unexpected answers, similarly to how Ramanujan proved the sum of all natural numbers equalled -1/12. For an independent research project, I looked at spherical co-ordinates and their uses in GPS, particularly by finding intersection points of spheres. I found this interesting because it gave an application for elliptic geometry which everyone uses every day. This shows just how relevant maths is in today's technological world. I studied History in year 12 and enjoyed the analytical side of the subject, applying the same critical thinking skills when solving maths problems. I decided not to continue with English Lit at A level, but find that poetry can share the same elegance and structure as maths. Economics is naturally a mathematical subject, but also keeps a capacity for writing and formulating arguments, which I like. I completed Access to Bristol for Economics, attending seminars which included an array of applied maths, particularly enjoying the lecture about using compound growth and decay to calculate returns and risks.

This year, I will participate in the London Institute of Finance Student Investor Challenge. For over a year I have tutored Maths to a variety of pupils, from year 4 up to GCSE. This has greatly improved my ability to communicate maths, as well as helping me further understand the concepts I teach. It has been very rewarding, with my GCSE pupil comfortably passing, achieving 3 grades above expected. In school, I volunteered to mentor a younger student to help grow his confidence and ability. In Y12 I volunteered in a Cancer Research shop, and for 3 years visited an elderly family friend once a week to keep him company. I worked in retail for 7 months, and this summer achieved distinction in grade 8 Jazz saxophone. I am also a keen club cricketer, mainly as an off spinner, and this season helped revive and play for my school XI.

29 April 2020

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