first major contribution to Gauss’ theory in 200 years

[rdelmonico]

Deleted post.

[Richard Amiel McGough]

http://www.simonsfoundation.org/quanta/20140812-the-musical-magical-number-theorist/

Although Bhargava uses his office primarily for meetings, the mathematical toys decorating its surfaces are more than just a colorful backdrop. When he was a graduate student at Princeton, they helped him solve a 200-year-old problem in number theory.

If two numbers that are each the sum of two perfect squares are multiplied together, the resulting number will also be the sum of two perfect squares (Try it!). As a child, Bhargava read in one of his grandfather’s Sanskrit manuscripts about a generalization of this fact, developed in the year 628 by the great Indian mathematician Brahmagupta: If two numbers that are each the sum of a perfect square and a given whole number times a perfect square are multiplied together, the product will again be the sum of a perfect square and that whole number times another perfect square. “When I saw this math in my grandfather’s manuscript, I got very excited,” Bhargava said.


Fascinating stuff. Here's a rather advanced mathematical paper (http://www2.warwick.ac.uk/fac/sci/maths/people/staff/bouyer/gauss_composition.pdf) that reviews his work.