From the Director
Is the Public Hungry for Math?
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.
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
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
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!