A few things to be thankful for

That I wrote this post near Thanksgiving was coincidence. I wasn’t volun-told to do this. There’s no official holiday edition of the PLSE blog. I just happened to get this date. Unfortunately, this is my first Thanksgiving away from my family in 8 years. I skipped intentionally to run the Seattle marathon. I’ve been training since last May but, tragically, hurt my knee too late to change plans. I miss my family. Nevertheless, as an evergreen optimist, I maintain that when we are feeling down, life gives us a chance to pick ourselves back up again. This is that chance for me.

If my lab-mates and our blog readers (you) will indulge me, I’d like to make this my unofficial gratitude post. Although there are many things in my life I am grateful for, I want to call out two in particular: the math textbook Ideals, Varieties, and Algorithms and my support network.

Thankful for the people in my life

Grad-school is like a rollercoaster ride where you can’t know the next twist and turn.
The highs are utterly jubilant and the lows utterly devastating. Through all the turbulence, the steady current in my life, encouraging me ever forward, are my lab mates, my friends, and my family. The people in my life are partitioned into two groups: those in Seattle and those not. To all my friends and family far away, thank you for all the phone calls. At times, our conversations might seem mundane (“Ugh my sleep was terrible this week”) but that’s OK! I like hearing those details because a lot of life is kind of boring. I need to hear the everyday stuff to really be a part of your lives.

To the lab mates, without you I would be lost! Every whiteboard session, every paper discussion, every PLSE Lunch talk is infinitely better because of you. Your insightful questions and insatiable curiosity have made this group a place where I can grow as an intellectual and as a person. I would be remiss for not acknowledging all the fun and personality folks bring. The constant baked goods, snacks, hot sauces, Big Time gatherings and College Inn nights have added so much joy in my life. I am forever grateful.

Thankful for Ideals, Varieties, and Algorithms

I’ve had a mixed relationship with mathematics. From a young age I love the subject. I love deeply knowing math. I love seeing mathematical patterns emerge in all the hidden places of the world. I love the feeling of fluency that comes from commanding an abstract structure. I love the coherence when symbol manipulation and semantics intent are one. These feelings are so rare, often so clouded in misunderstanding. It takes constant work to maintain these feelings and expertise. It is worth it.

I have not always been so enamored. My burning curiosity was nearly extinguished in the Spring of 2019. Having never taken an upper-level, proof-based mathematics course before, I took Complex Analysis. Saying it went horribly would be an insult to horror. I passed only by the mercy of the professor. I spent countless hours studying, doing practice problems, in office hours, etc. etc. I ground myself into exhaustion with little improvement or retention to show for it. My love was crushed. I left that class with the taste of soap in my mouth. Even the thought of semi-rigorous mathematics would cause my stomach to churn. I avoided that feeling until avoidance became stubborn habit. Fortunately, I escaped undergrad without too many more encounters.

In time, I began to unlearn my disdain for rigor. My thirst for my first academic love was yet to be quenched. Eventually, I went to grad school and was engulfed in rigorous mathematics once again. I struggled through papers, homework, project meeting, etc. Without my lab mates (the wonderful people writing the other blog posts), I wouldn’t have made it (thus, the first part of this post).

Fortunately, my advisor helped me identify and root out my aversion. In my second year, we worked through chapters from Ideals, Varieties, and Algorithms. This textbook is an incredible example of rigorously constructing the theory of polynomial rings. The proofs are legible, the “flavor” text accompanying proofs is illuminating, The homework problems are thought provoking ¹. With each lemma proven, my mathematical maturity improved. Over months, we reshaped how I thought about and approached my own work on polynomial initial value problems (see my other posts). Digesting difficult proofs is still hard, but the task isn’t as anxiety inducing.

Thank you to my advisor and to Ideals, Varieties, and Algorithms for making mathematics a joy once more.

Conclusion

Time to get back to my Thanksgiving stuffed mushrooms and Coquito. Happy holidays!