## Hong Kong Students Rise To Wide-Open Math Challenge

March 13, 2007

I am writing about a high school mathematics competition in Hong Kong. The personalities and the place made it a unique event. But my purpose in describing it here is to encourage others, in very different places, to see the possibility that was realized in Hong Kong. The experience of those hundreds of students and teachers could then be widely shared, as it deserves.*

The plan of the Hang Lung competition is simple. Every two years, teams of students from any high school in Hong Kong look for original mathematics problems. Their teachers can suggest directions, but this seldom happens. With help from books, and more often from Wikipedia, the students work together and report what they have discovered.

Hong Kong mathematicians led by Thomas Au had chosen this year's 15 finalists. In their presentations to the judges in December, all but one used PowerPoint. (We identified him as the mathematician. . . .) Among the nine judges were visiting mathematicians Tony Chan (the Chief Justice), John Coates, Jean-Pierre Kahane, and Yang Lo. Tony, a graduate of what he recalls as the "very structured and curriculum-focused" Hong Kong high school system, was impressed by the students' creativity. The awarding of prizes was a Hong Kong pageant, but readers of SIAM News will want to know about the projects.

Fibonacci and Sudoku had their attractions. I don't think they could lead to the gold medal. The Prime Number Theorem was the choice of the silver medalist (the mathematician, who presented neat conjectures but no proofs). The winner of the gold medal (also a one-student team) simply put a cylinder partly filled with liquid on its side, and wondered whether the wet area of the cylinder would decrease. Sometimes it does, depending on the height and radius and fluid volume. The winner's decisive step was to tilt the cylinder and minimize the wet area again---he solved an isoperimetric problem for the best orientation with fixed shape.

You or your students might like to consider a related problem: What shapes hold volume V with minimum wet surface area A? But the true question is whether a competition like this could succeed in the schools near you. You won't have Ronnie Chan, the CEO of Hang Lung Properties, to provide generous support and such an astonishing spark. (He emphasizes that the idea for the competition came from his friendship and conversations with S.T. Yau.) But you do have students and teachers, perhaps ready to test themselves on a wide-open challenge. The students do the work, write up their best efforts, and deal with tough questions from the judges---and grow visibly from the experience.---Gilbert Strang, Department of Mathematics, MIT.

*Early this month, teams of high school students in the metropolitan New York City area participated in a mathematics competition structured in a completely different way. The Moody's Foundation funds and SIAM organizes the annual competition---the Moody's Mega Math Challenge---in which the teams are given 14 hours to solve a realistic modeling problem. Details can be found at M3Challenge.siam.org.

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