Conway, Collatz, Chaos

19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1

Ivars Peterson discusses a recent "provocative" article from the always-interesting John Conway on the provability of various mathematical claims, with a focus on the Collatz conjecture (one of those famous easy-to-state, difficult-perhaps-impossible-to-prove conjectures):

http://mathtourist.blogspot.com/2013/03/wild-beasts-around-corner.html

It starts off thusly:

"Some mathematical problems are easy to describe but turn out to be notoriously difficult to solve. In some instances, these difficulties may stem from fundamental issues of provability, especially for mathematical problems apparently poised between order and chaos."

Even xkcd has taken notice of the Collatz conjecture.