Why is there a deep mysterious relation between string theory and number theory, elliptic curves, $E_8$ and the Monster group? Why is there a deep mysterious relation between string theory and number theory (Langlands program), elliptic curves, modular functions, the exceptional group $E_8$, and the Monster group as in Monstrous Moonshine?
Surely it's not just a coincidence in the Platonic world of mathematics.
Granted this may not be fully answerable given the current state of knowledge, but are there any hints/plausibility arguments that might illuminate the connections?
 A: I'll answer the relation between string theory and $E(8)$ -- a common appearance of $E(8)$ in string theory is in the gauge group of Type HE string theory $E(8)\times E(8)$ (see here for an explanation why). But it's interesting physically because it embeds the standard model subgroup.
$$SU(3)\times SU(2)\times U(1)\subset SU(5)\subset SO(10)\subset E(6)\subset E(7)\subset E(8)$$    
Indeed, the ones in between are GUT subgroups, and $E(8)$ happens to be the "largest" of the exceptional lie groups.
Wikipedia has some things to say about the connections to monstrous moonshine, I'm not familiar with it. See [1], [2] re: the connections to number theory. Another example is how "1+2+3+4=10" demonstrates a 10-dimensional theory's ability to explain the four fundamental fources -- EM is the curvature of the $U(1)$ bundle, the weak force is the curvature of the $SU(2)$ bundle, the strong is the curvature of the $SU(3)$ bundle and gravity is the curvature of spacetime.
[Archiving Ron Maimon's comment here in case it gets deleted --]

There is another point, that E(8) is has embedded  E6xSU(3), and on a Calabi Yau, the SU(3) is the holonomy, so you can easily and naturally break the E8 to E6. This idea appears in Candelas Horowitz Strominger Witten in 1985, right after Heterotic strings and it is still the easiest way to get the MSSM. The biggest obstacle is to get rid of the MS part--- you need a SUSY breaking at high energy that won't wreck the CC or produce a runaway Higgs mass, since it seems right now there is no low-energy SUSY.  

