Scientists from North America, Europe, Australia, and South America haveresolveda complexmath problem, proposed a millennium ago, and have foundbillions of solutions. The milestone was made possible by atechnique that allows multiplying numberssolongthat if all the digits were written by hand on a sheet of paper it would occupy twice the distance that separates us from the Moon.
According to Brian Conrey, director of the American Institute of Mathematics, “Old problems like this may seem” dark, “butgenerate a great deal of useful and interesting researchas researchers develop new ways of dealing with them. “
The problem solved consisted in determiningwhat whole numbers can be the area of a right triangle whose sides are whole numbers or fractions. The area of this triangle is called “congruent number“For example, the right triangle whose sides measure 3, 4, and 5, very typical in geometry, has an area of 1/2 x 3 x 4 = 6, making 6 a congruent number. The calculation found 3,148. 379,694 new congruent numbers.
The researchers took special care to verify their results, performing the calculation twice on different computers, using different algorithms, and forming two independent groups to write them. The team of Bill Hart (University of Warwick, in the United Kingdom) and Gonzalo Tornaría (University of the Republic, in Uruguay) used the “Selmer” computer at the University of Warwick, with funding from the Engineering and Physical Sciences Research Council from United Kingdom. Most of the code was written in a workshop held at the University of Washington in June 2008.
The team of Mark Watkins (University of Sydney, in Australia), David Harvey (Courant Institute, NYU, in New York) and Robert Bradshaw (University of Washington, in Seattle) used the “Sage” computer from the University of Washington. Sage is funded by theNational Science Foundationfrom the USA, and the equipment code was developed during a workshop held at the Benasque Pedro Pascual Science Center – CSIC in Benasque (Huesca) in July 2009.
