Hello! I’m Chris, a nonbinary math PhD student at UC Riverside. I got my undergraduate degree (in Discrete Math & Logic) from Carnegie Mellon, where I also studied music and computer science. My mathematical interests lie in the intersection of algebra, geometry, and logic – an intersection which is often made clearer with the language of category theory. Following in the great mathematical tradition, I will write my email as: cgros007 AT ucr DOT edu.
It’s not healthy to spend all of your time on math, and I keep myself busy with other passions as well. I’ve been playing flute for almost 20 years now, and have been composing for almost 10. I am a huge proponent of the Dalcroze School of music pedagogy, and I like to bring Dalcrozian ideas into my mathematics teaching. I also watch too much youtube.
I think examples are extremely important when learning anything, and computation is an invaluable resource when doing research. Unfortunately, I am often unable to find explicit examples of objects and theorems in higher mathematics. Moreover, there aren’t many resources for seeing how mathematicians “in the wild” use computers to help understand the problems they’re solving. I started a blog to try and combat both of these issues. Whenever I struggle to find (useful) concrete examples of a theorem I’m learning, I’ll make a post so that future students will have an easier time finding some. I’ll also post about my research, often with examples of sage code that I’ve used to play with the problem at hand.
I have had some mathematicians tell me that I need to “get over” a “reliance” on concrete examples. Out of spite, or perhaps to clarify my views on the topic, here is a quote that I deeply identify with:
“If you are, like me, someone who prefers large vistas and powerful theories (I was influenced but not converted by Grothendieck), then it is essential to be able to test general results by applying them to simple examples…. These are examples where one can do concrete calculations, sometimes with elaborate formulas, that help to make the general theory understandable. They keep your feet on the ground…. [M]ost of all a good example is a thing of beauty. It shines and convinces. It gives insight and understanding. It provides the bedrock of belief.” – Sir Michael Atiyah.
Perhaps less spitefully, here are some other quotes that I find impactful:

“Discipline is the difference between what you want now and what you want more” – Darryl Bott

“You should feel free to skip lightly over, or ‘read for culture’, explanatory material which seems difficult, or which uses idea of which you have not yet heard… You should think of them as something to return to when more of the pieces in the vast puzzle of mathematics have fallen into place for you.” – David Eisenbud.

Pablo Casals, at the age of 95, was asked why he still practiced six hours every day. He answered “Because I think I’m making progress.”

“The most useful piece of advice I would give to a mathematics student is always to suspect an impressive sounding Theorem if it does not have a special case which is both simple and nontrivial.” – Sir Michael Atiyah

“Never be happy with where you are, but always be happy with where you came from” – Dan D’Addio

I see mathematics, the part of human knowledge that I call mathematics, as one thing—one great, glorious thing. Whether it is differential topology, or functional analysis, or homological algebra, it is all one thing. … They are intimately interconnected, they are all facets of the same thing. That interconnection, that architecture, is secure truth and is beauty. That’s what mathematics is to me.” – Paul Halmos

“just a quick reminder that a society exists to serve the people within it. there’s no such thing as a person being “useless” to a society, only a society that is useless to a person” – Twitter User @HTHRFLWRS

“Nobody tells this to people who are beginners, I wish someone told me. All of us who do creative work, we get into it because we have good taste. But there is this gap. For the first couple years you make stuff, it’s just not that good. It’s trying to be good, it has potential, but it’s not. But your taste, the thing that got you into the game, is still killer. And your taste is why your work disappoints you. A lot of people never get past this phase, they quit. Most people I know who do interesting, creative work went through years of this. We know our work doesn’t have this special thing that we want it to have. We all go through this. And if you are just starting out or you are still in this phase, you gotta know its normal and the most important thing you can do is do a lot of work. Put yourself on a deadline so that every week you will finish one story. It is only by going through a volume of work that you will close that gap, and your work will be as good as your ambitions. And I took longer to figure out how to do this than anyone I’ve ever met. It’s gonna take awhile. It’s normal to take awhile. You’ve just gotta fight your way through.” – Ira Glass

“Learning mathematics is like climbing a cliff that’s sheer vertical in front of you and horizontal behind you.” – David Epstin, via Twitter user @nij4

“Works of art make rules; rules do not make works of art.” – Claude Debussy

“Science is what we understand well enough to explain to a computer. Art is everything else we do.” – Donald Knuth