Saturday, to me, was about the magic and beauty of mathematics: how it connects to art, how do we learn it, how do we make fun of it, and the big questions ahead.
It was a great pleasure to wake up and go see internet celebrity Vi Hart talk about her approach to hyperbolic space through art. Hart said she didn’t just want to know what it was abstractly, she said that to really understand it, she needed to “feel hyperbolic space”. And so she set out to find a good way of representing it, starting with the usual Poincare disk representation. She tried knitting (a very popular hobby among mathematicians these days), strings and beads, twisting balloons, and even giant models using water bottles as really big beads. It was fun to hear her relate her train of thought from one representation to another. This is where you see mathematicians and artists really think the same way, and in Hart’s case, she is constantly thinking about both mathematics and art simultaneously, in a way that most of us can’t replicate. If you haven’t seen her videos or website, do yourself a favor and click here http://vihart.com/. (A bit of trivia: her dad, George Hart, has recently become Chief of Content at the Museum of Mathematics, which I will talk a bit more about below.)
Kannan Soundararajan and Brian Conrey
Later in the day I got to see a different kind of genius, Kannan Soundararajan talking about The Riemann zeta-function and related L-functions: A progress report. What I loved about this talk (besides the eloquent delivery by this great speaker) was that it really was a progress report on the zeta-function: from the moment it was conceived by Riemann (1859) to present day. The historical details and even images of the original documents really gave a whole new dimension to a problem that most of us are familiar with, the Generalized Riemann Hypothesis. He also mentioned the applications of proving GRH, from the most immediate, in a way that would tells us more about primes (like finding a polynomial time algorithm to determine primality), to the more “exotic”, like Arithmetic Quantum Unique Ergodicity. He then presented partial progress towards proving GRH and connections with L-functions (which are a generalization of zeta-functions and thus exhibit a lot of the same properties). It was also a real treat to see how Sound’s (as he is called by his friends) work fit into this big picture. There is something really beautiful (there’s that word again) about seeing mathematics in a historical context, and to see a true leader in the field give credit to all the mathematicians that have worked or are still working on a problem.
The French Quarter
On the way to lunch I was inspired by the light and this strange cloud-line in the sky (are the clouds organizing themselves in an homage to mathematics?), so I took this (overexposed) photo.
After lunch I walked around the exhibits, sacrificing the Current Events Bulletin series of talks. I was surprised to find that Vi Hart was doing a demonstration/group project to build a representation of the hyperbolic plane using balloons, as described in her morning talk. Hart, her father (George Hart) and Glen Whitney (President of the Museum of Mathematics, or the MOMATH, http://momath.org/), encouraged people to blow up their balloons and explained how they should be twisted. Then Hart helped the participants put the pieces together. I’m not sure everyone was understanding what they were making (this is the picture we were trying to replicate http://vihart.com/balloons/hyperbolic/hyperbolictilingsnub2_medium.png), but I’m sure the non-mathematicians went home to google more about the subject, and the rest of us tried to think of how we could do something like this in our classes. All in all, it was really fun to participate in this group effors (my piece of the puzzle wasn’t very symmetric, but I think I got some cool photos, which I have posted on here).
Had to get that shot
It's all about the teamwork
After the hands-on fun, I went to a panel on hands-on teaching (and learning) titled Inquiry-proof intrusctional techniques, featuring Dev Sinha, Glenn Stevens, Michael Starbird, David Pengelley, and Margaret Robinson. The five panelists brought different experiences and shed light on different aspects of inquiry-based classrooms. The moral of the story was that every person has their own way of approaching active learning, but there are some key principles that seem to be common to all these styles. Stevens, from Boston University, has worked with the Ross and PROMYS programs, which are geared towards pre-service teachers and talented high school students, and is a problem-based approach to dicovery learning. Stevens said that in these programs the emphasis is on experiencing mathematics, and on using mathematical language as a tool for understanding the experience. Starbird, from the University of Texas at Austin, talked about his experiences using modified Moore method and listed the main principles (which all the other panelists seemed to echo in their own words). The goals for the students, according to Starbird, are: to understand simple things deeply, to ask questions, to learn to learn from failure (not a typo). Robinson, from Mount Holyoke, talked about her writing intensive lab courses. Basically, students learn to understan mathematics through a series of modules and the approach is more geared towards their being able to read and write mathematics, as a bridge from the entry-level courses like Calculus to the upper-level courses like Real Analysis and Abstract Algebra. Pengelley, from New Mexico State University, talked about using historical sources instead of textbooks. Pengelley claims the value of this is it gives students an approach to mathematics that is similar to the approach of the mathematicians who discovered it, more so than the digested and packaged content from a textbook. Sinha, from the University of Oregon, talked about pre-lecture owrk, as a way to get students to think about the material before it is covered in class. This panel was definitely a great source of ideas for people who want to teach classes in this way, and the panelists were very diplomatic in the sense that they did not claim this is the best way to teach period, but rather it’s the way that’s worked best for them.
Yours truly posing with the debaters and moderator (from left to right, Derivative, Integral, and moderator)
After this I gave my 10-minute talk, which turned out better than I thought it would. Again, I think it’s impossible to give any information in a talk of this lenght other than “I did this.”
In the evening (after waiting for the silly Sheraton elevators for about 15 minutes… I think they should hire one of the many mathematicians in the Sheraton to come up with a better elevator algorithm) I went to the dramatic presentation Derivative vs. Integral: The Final Showdown, by Williams College professors Tom Garrity and Colin Adams (“Integral” and “Derivative”, respectively, and pictured on the left). I will not do this debate justice by relating it to you, but mostly, Derivative’s platform was “derivatives are useful for applications and are easy to compute” and Integral claimed to be more “beautiful and poetic”, on top of going further than the derivative. Our moderator asked for a vote, and Integral won by a small margin. I hope that doesn’t mean I have to teach my Calculus course without using derivatives, because I have no idea how I would go about doing that (which is why I, personally, voted for derivative).
Then I closed the day by eating some more beignets at Cafe du Monde.