From 6th Grade to Advanced Physics...

Just a couple of links that hint at the breadth of mathematics, to start the week with:

a)  Brian Hayes, who is not a 6th-grader ;-) is off-and-running with an analysis of an arithmetic problem Fawn Nguyen previously posed to her 6th graders (...both delightful and interesting):
http://bit-player.org/2015/mrs-nguyens-prestidigitation

b)  Despite David Hilbert famously chastising the detractors of Cantor's "infinity," that "no one shall drive us from the paradise which Cantor has created for us," physicist Max Tegmark argues for finding "the true laws of physics" by finally getting rid of infinity:
http://blogs.discovermagazine.com/crux/2015/02/20/infinity-ruining-physics/#.VOs2kcZDTLX