Five years ago today, I embarked on a crazy experiment. It was the summer after I finished my undergraduate degree, and I was filled with lots of exciting things I learned from my mentor Shiv Chandrasekaran and my own self-study. I kept asking, “Why did no one teach me that subject in this way? If Shiv hadn’t taught me this trick, how would I have ever have learned this? How does everyone not know this cool theorem?” I was young and naïve. But I also was brimming with passion for my subject, and I had a lot I wanted to say.
Applied mathematics, and mathematics in general, is a rare subject in which its best researchers are also among its best communicators. Writers like Joel Tropp, Nick Trefethen, and Nick Higham were my heroes, and I desperately wanted to be like them. I figured that practice is the best way to learn any skill, and I decided that writing a blog was the best way to hone my skills as a mathematical communicator and to share this burning list of mathematical curiosities I had collected on my travels. I had my doubts—was this a waste of my time? would anyone actually want to read this? did I really have anything worth saying?—but I pushed them aside and published my first blog post on July 8, 2020.
To my great surprise, this experiment has been a bigger success than I ever could have imagined. An early success came just a month after starting the blog when my post on Galerkin approximation was posted to Hacker news and received 18,000 page views in a few-day span: what a rush! But perhaps a bigger surprise to me was how writing the blog has helped connect me to people in my field. I can’t count how many times the blog comes up within minutes of meeting a new researcher, and—to my great shock—the blog has now started to garner citations in academic papers. To everyone who’s read this blog and gotten something out of it, thank you.
It is hard to truly internalize how much things have changed for me over the past five years of blogging. I went from incoming PhD student to PhD student to person with a PhD. I met my heroes—not just Joel Tropp, Nick Trefethen, and Nick Higham—but also many more like John Urschel, Heather Wilber, Anne Greenbaum, Yuji Nakatsuksa, and Lin Lin, to name just a few. I am honored that many of them are now my collaborators. Truly, computational mathematics is a wonderful research community, and I am proud to be a member of such a warm and inviting group. I am excited to continue my research—and blogging—later this summer as a Miller postdoctoral fellow at UC Berkeley.
Let me end with a message to my former self or anyone else thinking about writing a blog, producing a YouTube video, or creating any other type of expository content: Just start! The world is hungry for clear explanations of difficult subjects, and your unique perspective on your subject is worth sharing. Your writing might not be very good at first (mine certainly wasn’t), but you’ll improve with practice. Just start. You may be surprised where you end up.