Is it possible to give a math lesson in 30 seconds? If you were to ask Doug Arnold, director of the Institute for Mathematics and Its Applications, he's now likely to tell you that it is.

In January, Arnold was given the opportunity to collaborate with an advertising agency to create a series of 30-second television commercials for ExxonMobil. The ads, which were broadcast during the Masters golf tournament in April, had a simple message: "Math and science are everywhere."

"My connection with the campaign began with an inquiry at the end of January from the advertising conglomerate Euro RSCG Worldwide, which was developing the ads," Arnold said. "The agency had at that time the basic story line for the two ads, to be called 'Swing' and 'Eraser.'" Referred to Euro RSCG by MAA President Joe Gallian, Arnold decided to take on an advisory role. As he became involved with the project, he was surprised to discover that a 30-second advertisement has a plot, much like a sitcom or a movie.

Both spots involved real-world footage combined with computer-generated graphs and equations, meant to show the viewer that mathematics is involved in almost all of our daily activities. Arnold's task was a tricky one: to come up with real equations and graphs that fit the plots.

The first ad, "Swing," slows down a tee shot by top golfer Phil Mickelson, while showing various graphs and equations related to the math and physics underlying Mickelson's swing. "One challenge was to come up with an equation that not only related to golf, but would somehow convey the relationship [between math and golf] to the audience," Arnold said.

The second ad, "Eraser," begins with a young girl erasing a chalkboard, then banging the dust out of the erasers. As the dust escapes, it turns into equations and diagrams. Blowing across the globe, the equations themselves change to match the settings in which they find themselves. For example, the formula *e* = *mc*^{2} shows up in a shot of Shanghai harbor (below) because nuclear power is a source of electricity there.

The different groups working on the ad campaign all stressed the importance of using both highly relevant and correct equations and graphs. "I worked with several artists from the production company, Motion Theory, who were simultaneously filming and interacting with me on the equations," Arnold noted. "I was very impressed by the importance they placed on getting the math right. The equations had to be correct and had to be relevant, even though they would swirl by so quickly almost no one would know."

Arnold fully understood the importance of using accurate mathematics, so he took the time to research which equations would work best in the context of the commercials. For ‘Swing,' for example, he consulted research articles on the flight and vibrational modes of a golf ball.

As an additional piece of the campaign, Euro RSCG wanted to develop a website that expands upon the ideas in the "Swing" advertisement. So Arnold was again asked to contribute his expertise to help explain the math that goes into a golfer's swing.

"The final part of this work was to provide the mathematical support to the Web team at Euro RSCG in the design of an educational website called 'The Science of a Drive,'" Arnold said. "The website builds on the message of 'Swing' with explanations of some of the math and physics behind a golf drive: the double pendulum, energy transfer, drag and lift, and similar concepts."

The website provides a fun, interactive way to learn a little bit about both mathematics and the game of golf. According to Arnold, it has garnered a surprisingly wide audience. "The site is aimed at a grade school audience but has proved interesting even to mathematicians," he said.

In the end, Arnold left very satisfied with his experience. "This mathematician," he concluded, "encountered Madison Avenue and Hollywood, and came away very impressed. And convinced: You can deliver a lesson about math in 30 seconds flat—that it is important, connected, exciting, and just plain fun."—*R. Miller*

Doug Arnold's own account of his experience can be found at http://www.ima.umn.edu/newsltrs/updates/spring07/index.shtml.