A Mathematical Journey, Part 1

Hi everyone! This post marks the first in the series of blogs where I document my mathematical journey in 2025.

After I graduated from Oxford last year, I applied to a number of PhD places specialising in geometry. I am currently waiting for results back; some of them have already sent back the rejection. Reading mathematics is still a daily activity that I keep up with. However, I can’t help but feel that my sentiment towards doing maths is markedly different compared to when I was in uni. Since there is no classes or examinations, there is not really the end goal or the finish line of reading to be seen. It is all “up in the air” and leads nowhere. This, in some regard, makes the whole thing rather difficult to maintain motivation.

So I decided to change things up a bit.

Maybe a blog would help? Maybe, maybe not. But at least I love to get the opportunity to write something.

The purposes of this blog are manifolds (pun intended). Firstly I intend to write about what I have learnt each week; perhaps a proof of a theorem that I would like to share, or a connection between two objects which is interesting/important. If I could maintain this blog for a considerable while, it should be amazing to look back and take stock of my mathematical progress throughout the year.

I sometimes feel that my mathematical knowledge didn’t expand as much as I hoped during my studies. A part of me says this is not the case. While I sometimes doubt myself, I know these feelings are common among mathematicians. But I noticeably had this eerie impression persistently after finishing my master’s, and seeing the vast gaps between me and my peers there. I hope that this blog could serve as a reminder of how far I have come.

As for the second purpose, this blog might motivate me to finish a topic quicker than the usual, leisurely reading schemes which I was used to. Of course, I am not in a rush to learn a wide range of mathematics, but having to write something each week might function as a good measure of progress.

Finally, it should help with my English writing skills. I regularly think in English, at least the study of mathematics in my mind is predominantly in English. In my mind it flows continuously, but it is a real struggle to put into words what I wanted to say. This is what I like to call the local problem of writing. On a bigger scale, there is the global problem of turning a piece of writing into a coherent whole. This is certainly a good way to practice my writing.

So that is how this blog is born.