UNT mathematics professors find solution to 50-year-old math problem

After four years of careful consideration, two UNT professors have solved a 50-year-old problem that has stumped mathematicians worldwide.

The problem was first posed in the 1950s by Polish mathematician Hugo Steinhaus. Dan Mauldin, Regents Professor of mathematics, and Stephen Jackson, professor of mathematics, used four different sets of theories and principles to find the answer.

Steinhaus' problem asks if there is exactly one point in a set of points in a plane that will always intersect with a lattice or grid when that lattice is rotated or moved horizontally or vertically.

Imagine the set of points is a constellation of stars and the lattice is a wire grid. Now, throw the grid against the sky. Exactly one star in the constellation is captured at one of the intersections in the grid.

Repeat the process by throwing the lattice up in another direction. Another star in the constellation is captured at another intersection of the lattice. No matter how many times this happens, exactly one star in the constellation always hits an intersection.

"The Steinhaus lattice problem pushes the boundaries of classical geometry," says Mauldin. "So, we had to solve the problem using number theory, set theory, real analysis and mechanical engineering principles."

Jackson agrees with Mauldin.

"We used these principles of solving other problems to solve the Steinhaus problem," he says. "Our solution is another building block in mathematical knowledge."

The mathematicians' findings were published in the October 2002 issue of the Journal of the American Mathematical Society and in the December 2002 issue of The Proceedings of the National Academy Sciences.

Read more about Mauldin and Jackson's solution online at www.math.unt.edu.

BY CATHY CASHIO ccashio@unt.edu

Other web resources

• UNT Math Department web site

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