The Collatz Conjecture is a deceptively simple math problem. It has only two rules. First, pick any number. If it's even, divide it by two. If it's odd, multiply it by three and add one. This will ...

Summer Haag, Clyde Kertzer, James Rickards and Katherine E. Stange disprove the Local-Global Conjecture for Apollonian circle packings in a summer research project.

The deceptively simple Kakeya conjecture has bedeviled mathematicians for 50 years. A new proof of the conjecture in three dimensions illuminates a whole crop of related problems.