the past week has made me reflect further on my reasons for doing a math phd. here are some of my thoughts and what keeps me grounded.

• if i didn't have to worry about money, what i would do? i'd spend time with friends, travel, learn math and languages, write sapphic stories, run a math camp, and do all of my other hobbies. but actually, that's my life right now as a phd student. my friend also doing a phd brought up this question and had the same answer.
• what makes me fulfilled in life is my relationships with other people. while this applies much more generally in my life, grad school is also a community for doing math and learning together. my professor once told me that the most valuable part of grad school for him was learning from the older grad students in the lounge.
• i have a great academic sister who encouraged me to go to conferences even if i don't understand anything yet, but to meet people and get the vibes. and once i hear about things enough times i'll eventually internalize it.
• i'm coming into grad school knowing very little about my field, as in i'm taking algebraic topology right now which i also took two years ago but forgot most of it (at least this time i'm getting a lot more out of it). in undergrad, i took math classes in a lot of areas and didn't decide on algebraic topology until the very end, but a friend also told me it's good to start out broad. i also didn't do much math senior year, which i'll blame on grad apps and senioritis/wanting to hang out more with people.
• i've questioned if i'm passionate enough about my math phd compared to some e.g. environmental science phds i've met who are much more outwardly passionate about it and know the relevance of their research. but a friend pointed out that i might have less of this outward passion because i've liked math and done it from a young age. i just know that i like learning math enough, and i am enjoying my life right now.
• i'm thankful that my parents are supportive of me doing a phd. they want me to be happy and have never pushed me to choose a path that makes more money.
• i also really prioritize is my health (e.g. getting 8.5 hours of sleep each night, having meals at regular times, being active, hobbies, other self care) which ties into having free time. i feel like as a phd student, i have the energy, flexibility, and money to do everything i want in nyc.

now there's the question of what happens when the current system of math research is disrupted? also i think pure math is foundational, but has a long payoff time (say 100+ years). so in our rapidly changing world is it worth it?

• i might be okay if i didn't solve an original research question and my work was more teaching and expository. i don't have research experience yet in my field of algebraic topology, and there's first so much literature to learn about. it seems like one of the most rewarding parts about research for me would come from the social part of working or discussing with other people.
• becoming a professor used to be my ultimate goal. while i currently still would like to, i have also been thinking about what i would do if i didn't or couldn't. some things i have brainstorming about are environmental science, contest math or math education, running a math camp, writing, translation, international organizations, and diplomacy.
• my impact is not confined to my work, and i can have a more direct positive impact on the people and communities around me. academically, this can be through teaching and mentorship.
• i've had a lot of good conversations about this recently, and some things people have said that stuck with me: it's important to have interests outside of math. nonlinear paths are okay and usually very cool. you learn independence from doing a phd. academia is sort of an anomaly in this capitalistic world (making money while having so much freedom), so maybe it won't last.

if you want to chat about any of this, please comment or reach out!