Summer for me means: road trips, freckles, mosquito bites, the sound of crickets, the smell of grass, cutoff jean shorts, family, friends, and music.
I’m working at Vanderbilt again this summer, but only for 2 weeks (for the math and music class.) I drove down to Nashville on Saturday and hit the ground running – four days down already. We have learned about some mathematical elements of music (complex meter, metric modulation, cross rhythms… to name a few), explored interval pitch classes and best normal order, discussed frequency of pitches and equal temperament, delved into a bit of mathematical set theory, put John Cage on trial for “crimes against music,” and had some fun with postmodern music. It’s a blast to work with Dawson and I tend to spend the entire day with my brain in high gear – whirring through new ideas with barely enough time to process them all; finding myself longing for the time I never seem to have to deepen my understanding of the fields that I love.
To that end, I decided a few months ago that for the rest of the summer following my time at VSA, I would allow myself that time to be selfish – time to explore, time to learn. Time to let my mind wander and see what interesting mathematical discoveries I end up making. I have a bit of a game plan for things I want to delve into, read, and study, but it’s still a work in progress. (And the list gets longer every day – even yesterday an old problem in class sparked an entirely new idea that led to an awesome, and interesting connection that I’m still exploring.)
Here are a few things on my list:
- to-solve: a few problems each week from Professor Stewart’s Cabinet of Mathematical Curiosities by Ian Stewart
- to-read: The Man Who Loved only Numbers by Paul Hoffman
- to-understand: the connection between binomial coefficients and polynomials that I happened upon yesterday
- to-solve: the ant on a rubber rope problem
- to-create: mathematical art (in the vein of geometry daily)
- to-create: figure out what I can make with Skallops (my school ordered me a few kits)
- to-understand: roots of unity in the complex plane
- to-understand: revisit Hilbert’s Hotel and cardinality, understand cardinality more formally
- to-read: The Calculus of Friendship by Steven Strogatz
- to-read (again): Flatland by Edwin Abbott
- to-watch: Flatland: The Movie (2007)
- to-understand: Einstein’s theory of relativity as it relates to the fourth dimension
Paul Erdos says:
“Mathematics is the only infinite human activity.”
“It will be millions of years before we’ll have any understanding and even then it won’t be a complete understanding, because we’re up against the infinite.”
There is so much that I don’t know that I am hungry to learn.