Fall 2007

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From the Director

Is the Public Hungry for Math?

Douglas N. Arnold
Doug Arnold,
IMA Director

Anna Nicole Smith's drug overdose, Britney Spears's child-custody battle, Paris Hilton's jail term, Barry Bond's steroid use, Larry Craig's hand gestures, and Michael Vick's dogfighting all figure on CNN's list of the top stories of 2007. This hardly suggests that the American public is hungry for the sort of intellectual stimulation that comes from exploring mathematics. Yet I am more optimistic. While the director's office in a mathematics research institute is admittedly not the best place to gauge the interests of John Q. Public, I have garnered a little evidence with the IMA's public lecture series Math Matters. The series regularly bring in crowds of several hundred to spend an hour in the evening hearing about current research in mathematics and its applications. Recently my optimism received remarkable support from an unlikely source: YouTube. YouTube—for any readers of this column who really are completely removed from popular culture—is the Google-owned web site at which over 60 million user-contributed videos can be viewed. In June, a colleague, Jonathan Rogness, and I completed a short mathematical video entitled Möbius Transformations Revealed and posted it to YouTube. As I write this column, the video has been viewed by one and a quarter million people, and declared a "favorite" by over 10,000 of these, putting it into into YouTube's "Top Favorites of All Time" category. By contrast, the most popular video about Anna Nicole Smith, a brief segment from Fox News entitled Anna Nicole Wacked Out Of Her Mind In Clown Makeup!, was posted five months earlier but has 10% fewer viewers and does not come close in the favorites category. So maybe optimism is justified.

Celebrities Mobius transformation
Could it be that the public wants to hear less about
naughty celebrities and more about math?

The story of how this two-and-a-half minute video came into being starts in 1997, when I made a brief animation for a graduate course on complex variables, depicting the image of a colored, gridded square in the complex plane, deformed by a continuously varying Möbius transformation. (A Möbius transformation is a linear fractional transformations of the complex plane, i.e., a map of the form f(z) = (az + b)/(cz + d)). Ten years later, in January 2007, there was a confluence of three events. First, I was contacted by a Canadian filmmaker, Jean Bergeron, who had found the old animation on the web, and asked if I could produce it in higher resolution for inclusion in a documentary he was making about for Canadian television about the mathematics in the work of Dutch artist M.C. Escher. Second, I attended a talk by Jon Rogness on his use of high end graphics in teaching and began a discussion with him in which he suggested we collaborate on a joint project. Third, the National Science Foundation announced an International Science and Engineering Visualization challenge.

Jon and I decided to submit a video entry to the NSF contest. Möbius transformations were on my mind thanks to Bergeron's request, and I had recently learned a different characterization of them, namely that they were the transformations obtained through stereographic projection from the plane to a sphere, followed by a rigid motion of the sphere in three dimensions, followed by stereographic projection back to the plane. (If that sounds confusing, just watch the video!) This result appealed to me, since it revealed an inherently two dimensional phenomenon as simpler when viewed in three dimensions. Most important, it is a very visual result. We made it the basis of Möbius Transformations Revealed.

Four months later we sent the completed video to the NSF challenge, where it won an honorable mention. At the same time, we posted it to YouTube, as a simple way to share the video with a few friends and colleagues. While I hoped that some others would stumble upon it and find it interesting, even at my most optimistic I would never have anticipated the response it would generate. In the first two months, about 15,000 people viewed the video. Some viewers reported on it in blogs, driving more traffic, and by mid-November the view count was up to 75,000. Then the editors of YouTube chose it to feature on the site's home page, and the view rate went way up, peaking at about 3 views per second for several days. As of the year's end, the video has been watched over 1,250,000 times on YouTube.

One of the first people we shared the video with was Jean Bergeron, the filmmaker who had contacted me five months earlier for his documentary on Escher. Jean was interested in incorporating part of the new video in his film, but this was difficult, because the film was just about finalized. He asked if we could rerender a portion of the video in high definition on a very tight schedule. I agreed, but with a price: the U.S. premier of his film should take place at the IMA. Jean assented and we had a deal.

On November 1, 2007, Bergeron's brilliant documentary film Achieving the Unachievable was screened in Minneapolis, the second showing ever, following by a week its world premier in Montreal. The film was not only beautiful, but also intellectually challenging, as it explored many aspects of the mathematics in Escher's work. Hearing the thunderous applause from the audience of about 700, ranging from high school students to art collectors, it certainly seemed clear to me: the public is hungry for math.

Best wishes to all for a happy, healthy, mathematically rich new year!