My Math Journey

December 18, 2024 in life4 minutes

In this blog post, I will write about my past life as a math student, and how my perspective changed about pure math throughout these years.

Disclaimer

I am by no means a math researcher now, or never one (although probably close to being one), so there might be biases in how my words represents the math world, so please take everything in this article with a grain of salt.

However, I hope that through my struggles and some of the general lessons I learned, this article could serve as a source of inspiration or ideas for people that are walking along a similar career path as me.

Work In Progress

1. The Start of a Mathematical Dream

I was fortunate enough to encounter many good teachers when growing up, that enabled me to discover to joy of math. In my younger days - probably before high school, I enjoyed math, for the satisfication and self-confidence gained from problem solving. Starting from high school, through self-studying, I found the beauty of abstract mathematical theories.

It is hard to concisely describe the beauty of math in a few words, but roughly speaking, it is a mixture of:

  1. The intellectual joy of exploring something that is both science and philosophy - understanding the inner workings of the world through the elegance of logic and the rigor of proofs.
  2. The inherent beauty of its abstract nature - its self-contained world of concepts that can exist independently of physical reality yet still profoundly shape our understanding of the world.
  3. The thrill of discovery - the unexpected surprises and patterns that emerge from frameworks built upon abstract symbols, blending both intuitive and novel ideas, as well as moments where we see seemingly unrelated theories intersect with each other.
  4. Its profound usefulness - as the universal language of science and technology, it provides tools to model and solve real-world problems.
  5. The learning experience - I have found that many texts are written so well and beautifully that left me in awe1, and continued to experience the joy of problem-solving through working out exercises, that are both challenging and rewarding.

From this list, I hope that you have been convinced that I am fervent lover of math. I wanted to do math as a living before entering college, but I had concerns -

  1. I always felt like in order to be a good mathematician, both effort and talent are the most crucial factors - I do not think I have what it takes to become one, as I am not a math olympiad person, nor someone that had obtained success in individual research in my highschool days.
  2. I was ignorant about the job market for math graduates and was way too narrow-minded - I though it was either staying in the academia, or unhappily waiting my life to end in a place that doesn’t require any expertise in “true” abstract math (such as being a high school or cram school math teacher). I also had the impression that becoming a professor at National Taiwan University (my alma mater) is going to be extremely difficult, as a lot of the professors at that time did their PhDs in highly extinguished universities in the states (Harvard (six of them!), Stanford, U.C.Berkeley, UIUC, …).
  3. I thought being an engineering student with abstract math skills can be a plus.
  4. I recognized that I still know nearly nothing about what a math researcher’s life was.

I ended up making the best use of my college entrance exams scores, and enrolled in NTU as a student majoring in mechanical engineering. Eventually, I became unhappy - I can’t stand the lack of rigor of many academic subjects, I suck at making things in workshop and was often scolded for not remembering many safety instructions. In one semester, I went to take classes in the math department, and I successfully transfered at the start of my sophomore year.

It was one of my happiest moments in my life, as the transfer process wasn’t easy. I made up my mind to completely isolate myself in the world of math, disengaging in any meaningless social interactions, and dedicate every time and energy to learning math, to get exceptional in at least one field.

It was like living in a dream, where I constructed a character named “self”, with clear definitions of who this “self” is, what this “self” likes, and what kind of person this “self” eventually wanted to become.

2. The Dream Became a Nightmare


  1. To name a few of my lifetime favorite classic textbook authors: John Milnor, Jean-Pierre Serre, Walter Rudin, Tom M. Apostol, Hideyuki Matsumura, Michael Atiyah, William Fulton, Peter May, Robin Hartshorne, Tom Leinster, James Humphreys. ↩︎