I started to learn analysis when I was an undergraduate student in China. During my four-year undergraduate study, I found the beauty of analysis: it was simple and precise. Every definition and theorem are well posed in simplest forms (no more words need to be added and no more words can be taken away) and in precise words. All the symbols were well organized to make things easier.
When I was in my junior, I met one of my favorite teachers who always encouraged me to turn formulas into pictures. By doing that, I was able to understand and explain math much better. And once I had a picture in my mind, it never disappeared.
After I graduated, I worked as a middle school teacher for one year. But then I realized that I still wanted to continue my study in analysis. One day, I found Dr. Vixie’s blog and read one of his articles — An invitation to Geometric Measure Theory: Part I. In his blog, he started with the standard definition of derivative and went all the way to tangent cones using densities. All the pictures included were pretty helpful and very enlightening. I felt like I had more things to explore after I read that, especially the geometric intuitions. And that’s why I contacted Kevin afterwards and ended up being his student.
Right now, I am interested in geometric measure theory, especially in studying the regularity of the boundaries of shapes. It’s also quite interesting if you want to compare two shapes and measure the difference. Meanwhile, I also think visualization of big data is a lot of fun because turning numbers into graphs can really change the way how you think. Besides, before we analyze data, we always have some prior expectation. We are inclined to choose the models that match our expectations well. However, how to find an unbiased way to deal with big data and reveal its nature is more important. And I believe the approach to this will also be related to the geometric measure theory!