NEW YORK (Diya TV) — Manjul Bharagava, a mathematics professor at Princeton University and winner of the 2014 Fields Medal, has found the solution to a 200-year-old theory law with the help of a 6th Century mathematician and a Rubik’s Cube.
Bharagava said German mathematician Carl Friedrich Gauss showed that if two numbers — each sum of two perfect squares — are multiplied, the result will also be the sum of two perfect squares. The professor’s grandfather was a Sanskrit professor in Rajasthan, and said he’d once seen Sanskrit manuscripts written by Brahmagupta, an Indian mathematician from 628 CE, that carried a similar formula.
The similarity?
If two numbers 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 sum of a perfect square and that whole number times another perfect square.
When Bharagava came across the German’s 18th Century composition law on binary quadratic forms, he sought an easier way to simplify the process. The moment of truth came when Bharagava employed a Rubik’s and mini-cube, a more petite version with four squares on each side.
Bharagava discovered that if he placed numbers on each of the four corners of the mini-cube and cut it in half, the eight corner numbers could be combined to produce a binary quadratic form. Even more, the cube had the capability to generate three binary quadratic forms when using this method since there were three ways to cut the cube in half.
The cube-slicing gave a new reformulation to Guass’ law.
Additionally, Bharagava found that if he arranged numbers on a Rubik’s domino, he could produce a composition law for cubic forms, ones whose exponents are three.
Ultimately, Bharagava discovered 12 more compositions, all which became part of his PhD thesis. Later, Benedict Gross, a mathematician from Harvard University, said the thesis was “first major contribution to Gauss’ theory of composition of binary forms for 200 years.”
