The 3x+1 Problem: Status and Recent Work

The 3x+1 Problem is a long-standing conjecture. Let T be 
a map from the positive integers into itself, where T(x)=x/2 if x is even 
and T(x) = (3x+1)/2 if x is odd. The conjecture asks whether, under 
iteration of the map T, any positive integer eventually reaches the value 
one. This talk gives a survey of the various approaches and results, 
intersecting areas such as number theory, dynamical systems, and 
functional equations. The speaker's approach involving generating
functions is also presented.