About the Authors

In the following excerpt, taken from the introduction to The First Five Years, the compilation of Team Tests from 1990 to 1995, Sam Vandervelde recalls how the Mandelbrot Competition was first created and what has transpired since then.

It was eight summers ago during the summer of 1990 that I received a phone call from Richard Rusczyk inviting me to take part in an exciting venture for only a modest outlay in venture capital. He wanted to create a mathematics competition for high school students and wondered if I would like to join Sandor Lehoczky and himself in a partnership to produce this contest. Their progress to date on this grand scheme consisted of naming the partnership: Greater Testing Concepts.

I thought it was a crazy idea.

Within a week I called Richard back. “I've been playing around with this neat iterative process lately which produces the most fantastic picture,” I related enthusiastically. “It's called the Mandelbrot set, named after Benoit Mandelbrot who discovered it. Maybe we could call the contest the Mandelbrot Competition and use the set as the logo!” So I was hooked after all.

In a flurry of phone calls the basic structure of the competition rapidly took shape. Richard wrote Benoit Mandelbrot and obtained permission to use his name for our contest. Dr. Mandelbrot must have been flattered, because he agreed; we still have his response stored with other Mandelbrot memorabilia. Richard and Sandor had in mind a challenging short answer type of contest, while I suggested a test in which students would write out proofs rather than fill in blanks. Both ideas were greeted enthusiastically by the newly elected Greater Testing Concepts board of managers (us), particularly since mathematical writing was a component we felt was sorely lacking in contests we took while in high school. Thus the Individual and Team Test components of the contest were born.

In three short months we somehow accomplished the impossible: a full set of five Individual and Team Tests and solutions were written, invitations were mailed to almost 3000 high schools, and the rules and policies for this fledgling competition were decided upon. To this day it is a mystery to me how Richard found addresses to that many high schools, much less how he had the time and patience to stuff and seal that many envelopes.

Of course, we made our fair share of mistakes. One of the most comical occurred when I altered the contest layout to the design which has remained essentially unchanged to this day. Richard did not get word of my revisions in time to prevent him from making a rather large number of copies of the sample Team Test on gold paper. I insisted that we use the new layout, which we did, so Richard was left with several reams of the brightly colored sample tests. Ever resourceful, Richard used the blank side of these sheets for college homework assignments. He tells me that the supply lasted him for the greater part of his Princeton career. Furthermore, no teacher ever mistakenly handed his paper back to the wrong student, or even had to look at the name atop his homework after the first week or two.

Miraculously, the Mandelbrot Competition was a mathematical and organizational success the first year, and did not even plunge us too heavily into debt. In fact, we ended with a modest profit which was enough to get us started on the next year's preparations. The project proved to be immensely stimulating and rewarding, which has caused it to thrive and develop over the ensuing years.

While the scope of the contest has increased only gradually, its presentation has undergone some significant changes. Between the second and third years Sandor made the brilliant observation that our contest could benefit from two levels of differing difficulty, which has led to the regional and national tests in place today. A year or so later he again hit the jackpot when he suggested using LaTeX to typeset the tests and solutions, which is why the mathematical formulas and expressions on the tests come out looking so sharp. Finally, some years ago Sandor and Richard had the vision to make the Mandelbrot Competition available via the World Wide Web, a daring move for three young men who couldn't have explained the difference between URL and NFL. (We learned.) With all of these innovations running smoothly we trust that this will be the best year of Mandelbrot yet. We hope that you will agree.

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