Program Proves Mathematical Statements

February 18, 1998

Temple University mathematics professor Doron Zeilberger and University of Pennsylvania mathematics professor Herbert Wilf have received the 1998 Leroy P. Steele Prize for Seminal Contribution to Research. Conferred by the American Mathematical Society, it is one of the most prestigious awards given for mathematical achievement.

Zeilberger and Wilf have freed their colleagues from a whole class of laborious calculations by discovering a method for proving a particular type of mathematical equation: "the combinatorial identity." Fellow mathematicians are impressed, and grateful for the time (and pencils) they will save. A previous winner of the Steele prize, Donald Knuth, said "I fell in love with these procedures as soon as I learned them, because they worked for me immediately. . . . The success rate was astonishing."

The prize citation anticipates a time when their method will be incorporated into a wide variety of computer systems and "many people will be using it without being aware it is what makes their calculations possible."

Now Professor Zeilberger has taken the breakthrough a step further, creating a computer program called EKHAD which, he explains, "proves mathematical statements--not just performing empirical or numerical calculations, but actually producing a complete mathematical proof." Such a program is a new and exciting development in the field of mathematics, which has long relied on the calculating power of computers, but never before used them to provide proofs for mathematical statements. Zeilberger's computer, which he has named "Shalosh B. Ekhad," has even been published under its own name.

Acknowledging the award, Zeilberger said, "Computers, by themselves, are not yet capable of creating the most beautiful math. Conversely, humans do much better math in collaboration with computers. . . . Combining different and sometimes opposite approaches and viewpoints will lead to revolutions."

He also called for greater use of internet technology within the field of mathematics, stating that "it is very important to make information, in particular mathematical information, freely accessible." Zeilberger has enabled free downloading of EKHAD from the Temple mathematics department website.

The Steele prize was awarded on Jan. 8 at the American Mathematical Society's Joint Mathematics Meeting in Baltimore.
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Temple University

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