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Visualizing the Path from Fermat's Last Theorem to Calabi-Yau Spaces

Published on Dec 21, 2011

Andrew Hanson, Professor of Computer Science at Indiana University:

Three decades ago, Alan Barr at CalTech introduced the computer graphics community to an influential modeling technique that created smooth deformations by varying the power of the sphere's quadratic algebraic equation. These so-called "superquadrics" eventually found their way into the machine vision community, and were used extensively for modeling and recognition of generic shapes. In 1990, we presented a paper, at the IEEE's very first Visualization Conference, in which we fancifully toyed with the idea that Fermat's Last Theorem might have some connection to complexified superquadrics. To support this idea, we developed extensive interactive 4D computer graphics methods to display these bizarre shapes.

Our hopes were dashed when Fermat's theorem was actually proven by Andrew Wiles in 1995. However, the graphical images motivated by complexified superquadrics rose from the ashes of Fermat's theorem when they turned out to correspond exactly to the Calabi-Yau spaces embodying the "hidden dimensions" of string theory. These images were included in Brian Greene's 1999 best-seller "The Elegant Universe" and since then have appeared in literally hundreds of other venues, including Scientific American, a 2003 NOVA television special on string theory, the cover image of Shing-Tung Yau's 2010 book "The Shape of Inner Space," and even a recent London billboard advertisement.

In this talk, we will guide the audience through this improbable series of events with a wide variety of images and animations.
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