My Mathematical Journey

Around early 2016, I decided to learn math. The trigger was a comment I came across about someone who had struggled with math but was able to rebuild their understanding through proofs. That idea stayed with me. I had always been comfortable with biology, and it became clear that a deeper command of mathematics would open up entirely new ways of thinking about it.

I started with enthusiasm but very little structure. Like many beginners, I jumped too far ahead and picked up a book on stochastic methods. That attempt did not go far. At the time, I was finishing graduate school, and the effort faded.

The real shift began during my first postdoc, where I worked with both a physicist and a biologist. My physicist advisor suggested I learn linear algebra and pointed me to Strang’s lectures. I supplemented this with visual material like 3Blue1Brown. That phase gave me an initial intuition for the subject, but it was still shallow. I was beginning to see patterns, but without enough precision to reliably work with them.

For a while, my approach remained inconsistent. I revisited calculus, explored different areas, and often tried to move ahead faster than my foundations allowed. In hindsight, the pattern was clear. I was prioritizing exposure over consolidation.

Around 2023, two things changed. I began a second postdoc at TIFR in Mumbai, and I started learning regularly with a close friend who had trained in physics. This introduced something I had been missing steady pacing and feedback at the right level. Instead of jumping topics, I focused on building depth.

I returned to linear algebra with more discipline, working through Strang’s lectures again and using problem sets to reinforce the material. This time, the concepts became operational rather than just familiar. I also began studying probability and statistics in a more structured way, following recommendations from faculty at TIFR. With consistent practice, I developed a working understanding of both.

Later, I explored number theory using Silverman’s A Friendly Introduction to Number Theory, on the recommendation of a professor. This was challenging in a different way. It required a level of abstraction and precision that exposed remaining gaps in my thinking. Working through it has been slow, but it has also been one of the most valuable parts of the process.

Looking back, the main change has been in how I learn. Early on, I chased exposure and intuition without enough grounding. Now I focus on building foundations, testing understanding through problems, and progressing layer by layer.

Today, I have a solid base in linear algebra, probability, and statistics, along with exposure to other areas. More importantly, I have a process that works. The trajectory is steady, and each layer builds on the last.

I continue from there.