Today, I came across some of the handwritten notes from my last semester in college. The photos below are only a tiny fraction of the total amount. I must have written hundreds of pages of math notes throughout my 3-year undergraduate degree.

There were some long nights when I was deep in exam revision, writing page after page of stochastic calculus and advanced statistics, wondering if all this effort would be for nothing, when all I wanted to do at the time was coding.

It wasn’t until I started doing AI research, started reading papers and reimplementing them, that I realized how all the former years of intensive math training had given me a good foundation to pursue these endeavours.

Today, even without the exam obligations, sometimes I still like to learn things from first principles and taking hand-written notes. For example, these are my notes from when I first started exploring diffusion models:

I think this is actually the bigger value we get from studying math, or anything hard for that matter. The understanding that learning hard but important things will and should take time. The desire to understand things deeply and not feeling complacent with being a mere tool-user without knowing how the tools actually work to some degree. In the age of AI abundance, it’s easy to feel like you’re falling behind if you spend too much time learning foundational things slowly. These days, you will undoubtedly feel frustrated with your learning progress because the field is evolving so quickly. The gap between your knowledge and the state-of-the-art is only getting wider and wider every day. But I believe we can actually do both - be agile and adaptable with the latest technologies & be biased towards action, without sacrificing honest understanding for the sake of speed.

I’m actually a huge advocate of agentic engineering and personally use AI a lot at work, who doesn’t nowadays? But for my own learning endeavours, doing things from scratch just makes more sense :) Although I have to say, typing out math notations is still just as painful now as it was during my university days.

Coincidentally, a few weeks after I wrote the first draft for this post, I came across this quote reposted by Andrej Karpathy on X, which echoes my sentiments perfectly:

I hope it somewhat makes you happy with your decision to pursue knowledge honestly.