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.

Temple University

Related Mathematics Articles from Brightsurf:

A new method for boosting the learning of mathematics
How can mathematics learning in primary school be facilitated? UNIGE has developed an intervention to promote the learning of math in school.

Could mathematics help to better treat cancer?
Impaired information processing may prevent cells from perceiving their environment correctly; they then start acting in an uncontrolled way and this can lead to the development of cancer.

People can see beauty in complex mathematics, study shows
Ordinary people see beauty in complex mathematical arguments in the same way they can appreciate a beautiful landscape painting or a piano sonata.

Improving geothermal HVAC systems with mathematics
Sustainable heating, ventilation, and air conditioning systems, such as those that harness low-enthalpy geothermal energy, are needed to reduce collective energy use and mitigate the continued effects of a warming climate.

How the power of mathematics can help assess lung function
Researchers at the University of Southampton have developed a new computational way of analyzing X-ray images of lungs, which could herald a breakthrough in the diagnosis and assessment of chronic obstructive pulmonary disease (COPD) and other lung diseases.

Mathematics pushes innovation in 4-D printing
New mathematical results will provide a potential breakthrough in the design and the fabrication of the next generation of morphable materials.

More democracy through mathematics
For democratic elections to be fair, voting districts must have similar sizes.

How to color a lizard: From biology to mathematics
Skin color patterns in animals arise from microscopic interactions among colored cells that obey equations discovered by Alan Turing.

US educators awarded for exemplary teaching in mathematics
Janet Heine Barnett, Caren Diefenderfer, and Tevian Dray were named the 2017 Deborah and Franklin Tepper Haimo Award winners by the Mathematical Association of America (MAA) for their teaching effectiveness and influence beyond their institutions.

Authors of year's best books in mathematics honored
Prizes for the year's best books in mathematics were awarded to Ian Stewart and Tim Chartier by the Mathematical Association of America (MAA) on Jan.

Read More: Mathematics News and Mathematics Current Events is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to