My beginnings in math can probably be traced back to the “Murderous Maths” series of popular math books, which attracted me with their humorous yet clear presentation of mathematical concepts. My mom is a math teacher, and my earliest memory of mathematical beauty was when she taught me basic calculus. I learnt how bringing two points on a curve together allows the line joining them to approximate a tangent, and how that led to the limit of the difference quotient.
I began doing math research in 2008 on origami math, specifically the origami design of certain polyhedra. I generalized the polyhedra that could be folded in the following years in more projects, culminating in a project that won awards at the Intel ISEF 2011. I’d describe that research as applied math though, since I was constantly formulating algorithms and calculations for the sake of the research target of polyhedral origami design.
Since then, my “research style” has been to construct my own algebras, often involving matrices, and mine their interesting properties. Logic is my canvas and mathematical objects are my paints. I formulated another analogy of math as a complex, intertwining cave system, and it’s really fun to run around the tunnels and check out all the beautiful scenery (full analogy in the “Math and Caves” essay).
As an amateur math explorer, my efficiency and potential in research could be raised by learning about the modern status and techniques of math. For now, I’ll still keep exploring and having fun.
I can't help chirping about my favourite pieces of mathematics to anyone who will listen, so I gave many presentations about math and other topics. I also write about math, including an essay about mathematical thought that may grow into a book if I have time.
I think research projects are some of the most important things a math student should undertake. Many know about olympiads, but those are about solving problems set by others using a largely fixed set of tools. But research is about asking your own interesting questions and answering them with little or no guidance at the forefront of knowledge. It's a test, and training, of perseverance, ingenuity and mathematical taste.