Maths has always been my primary passion. My dad trained to be a Maths teacher when I was at the end of primary school. At that time, I was fascinated by the university-level maths he was doing, and he was always happy to patiently explain things to me.
After finishing my A-levels at Exeter Mathematics School, I left Devon to go to Cambridge to study Maths a Trinity College. There, I first encountered topology in a course in second year. It was clear to me then that this was a fascinating area that relies heavily on visual/spatial intuition as well as a deep understanding of algebra and the interactions between the two.
I am continuing to grapple with topology now in my PhD at Imperial College. My area of research concerns four-dimensional spaces, called manifolds. Specifically, I focus on using tools from theoretical physics, like gauge theory, to study problems involving the difference between the smooth and topological structures on four-manifolds.
In the last three years, I have worked with undergraduate students at Imperial College and Trinity College, Cambridge as a teaching assistant. Recently, I taught a four-week evening course on Ordinals and Cardinals for London Maths Outreach to children aged fourteen to eighteen. This summer, I also lead a workshop on knot theory for the London Maths Outreach Summer Day. It is such a privilege to work with talented young people, to see their minds working as they come to a big realisation for the first time.
The students at 1729 are a pleasure to teach. They all have an innate curiosity to them that is fundamental to the development of any mathematician. Sometimes they will breeze through problems at astonishing pace, other times, they will amaze me by how quickly they respond to feedback and questioning and on occasion, they will present me with an idea that I hadn't even considered and for a brief moment, the roles of student and teacher are reversed.
My main role at 1729 is to use my mathematical expertise to push the children beyond getting the answer to a question, to be able to convince other people (mathematicians, mostly) that their answer is correct. This idea of mathematical communication, using the language of proof, is seldom covered in schools until university. I am routinely blown away by how well the children here are taking to this mathematical framework, especially the year 7s. I was somewhat apprehensive to work with children so young at first: after all, what could an 11-year-old possibly be able to do in maths? This worry was swiftly and overwhelmingly assuaged in the first session I had with the year-7 class. They are bright and quick thinkers; they respond to new ideas very well, and are always eager to solve the hardest problems available to them.