Randym writes: Recently, Peter Schorer published the latest version of his potential solution to the Collatz Conjecture: a famous unsolved halting problem in mathematics. (Short version: X starts as any integer > or == 1; if X is odd, newX = 3*X+1; if X is even, newX = X/2. Does newX *always* eventually arrive at the number 1?) To quote from the abstract: "Our proofs are based on a structure called “tuple-sets” that represents the 3x + 1 function in the “forward” (as opposed to the inverse) direction. In our proofs, we show, by a simple inductive argument, that the contents of the set of at least one tuple-set are the same, regardless if counterexamples exist or not, and from this we are able to conclude that counterexamples do not exist." Read his short, simple paper and decide for yourself.
Randym writes: NASA scientists have some exciting new results from one of the rover's instruments. On the one hand, they'd like to tell everybody what they found, but on the other, they have to wait because they want to make sure their results are not just some fluke or error in their instrument.
The exciting results are coming from an instrument in the rover called SAM. "We're getting data from SAM as we sit here and speak, and the data looks really interesting," says John Grotzinger. He's the principal investigator for the rover mission. SAM (Sample Analysis at Mars) is a suite of instruments onboard NASA's Mars Science Laboratory rover, Curiosity.
Grotzinger says they recently put a soil sample in SAM, and the analysis shows something Earth-shaking. "This data is gonna be one for the history books. It's looking really good," he says.