Courant Part of Team to Resolve Ancient Mathematics Problem

Mathematicians from North America, Europe, Australia, and South America have resolved the first one trillion cases of an ancient mathematics problem on congruent numbers. The advance, which included work by David Harvey, an assistant professor at New York University’s Courant Institute of Mathematical Sciences, was achieved through a complex technique for multiplying large numbers.
The problem, first posed more than 1000 years ago, concerns the areas of right-angled triangles. A congruent number is a whole number equal to the area of a right triangle. The surprisingly difficult problem is to determine which whole numbers can be the area of a right-angled triangle whose sides are either whole numbers or fractions. For example, the 3-4-5 right triangle has area 1/2 × 3 × 4 = 6, so 6 is a congruent number. The smallest congruent number is 5, which is the area of the right triangle with sides 3/2, 20/3, and 41/6.
The first few congruent numbers are 5, 6, 7, 13, 14, 15, 20, and 21. Many congruent numbers were known prior to this new calculation. For example, every number in the sequence 5, 13, 21, 29, 37, …, is a congruent number. But other similar looking sequences, like 3, 11, 19, 27, 35, …, are more mysterious and each number has to be checked individually. The new calculation found 3,148,379,694 new congruent numbers up to a trillion. The quantity of numbers involved in this calculation is significant-if their digits were written out by hand, they would stretch to the moon and back....

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