13.8 billion years on a 10.1'' screen

Some moments in one’s life can be awe-inspiring. You know, those moments when you feel deeply connected to something; when things make sense. Some people would label this feeling as spiritual; not being a very spiritual person myself (at least according to the common definition), I don’t really know how appropriate this attribution is, but I ca... Read more 04 Aug 2023 - 9 minute read

Lie derivatives and cluttered notation

I’ve always had a love-hate relationship with notation in mathematics. On the one hand, I am an intuitive person who needs to understand the big picture of something before jumping into the details. In this sense, I prefer my math to be uncluttered and focusing on the key steps of a derivation. On the other hand, I also need my understanding ... Read more 25 Jun 2023 - 11 minute read

How Cartesian can we make coordinates on Earth?

Earth is locally flat. This is true not only for the (surface of) the Earth, but for any so-called Riemannian manifold, a generalization of surfaces to any number of dimensions. Even though there is curvature, if one zooms enough into a point, curvature disappears and their neighborhood will look flat. This is why some individuals in our planet... Read more 11 May 2023 - 27 minute read

My favorite math problem

Back in the second year of high school, a friend shared with me a problem that his geometry teacher had shown him. I was going through a small crisis regarding my future career. I couldn’t decide whether I wanted to pursue a major in the Humanities (Arts or Design were on the top of the list) or in STEM. Before eventually settling down on Physi... Read more 16 Apr 2023 - 4 minute read

AUC as Loss: directly fitting to optimize ROC AUC

A common application of binary classification models is ranking, more than classification itself. The difference between the two is subtle: In classification, you want to say how likely a point is to belong to class 1 or class 0; In ranking, you care whether point A, who is in class 1, is more likely than another point B, in class 0, to be... Read more 27 Jan 2023 - 13 minute read