supercomputer tagged posts

Credit: Victorgrigas/Wikideia/ CC BY-SA 3.0

A trio of researchers has solved a single math problem by using a supercomputer to grind through over a trillion color combination possibilities, and in the process has generated the largest math proof ever—the text of it is 200 terabytes in size.

The math problem has been named the boolean Pythagorean Triples problem and was first proposed back in the 1980’s by mathematician Ronald Graham. In looking at the Pythagorean formula: a2 + b2 = c2, he asked, was it possible to label each a non-negative integer, either blue or red, such that no set of integers a, b and c were all the same color. He offered a reward of $100 to anyone who could solve the problem.

To solve this problem the researchers applied the Cube-and-Conquer paradigm, which is a hyb...

Schematic illustration of the experiment. An initial density modualtion is imprinted onto the ultracold atoms held in the optical lattice potential (1). Without any disorder, the density modulation is washed out completely in the ensuing dynamics, indicating relaxation towards a thermal equilibrium state (2). In the presence of sufficiently strong disorder, the researchers find that even for long evolution times the system retains memory of the initial state, indicating a non-thermal state in which the system remains stuck (3). Credit: M. Schreiber, LMU

Using ultracold atoms trapped in light crystals, scientists have observed a novel state of matter that never thermalizes...