http://en.wikipedia.org/wiki/Goldbach%27s_weak_conjecturehttp://en.wikipedia.org/wiki/Goldbach's_conjecture
My math knowledge is pretty weak, but I don't think the joke is more complicated than it seems. The two base cases are actual conjectures made by Goldbach and the subsequent "very" and "extremely" are riffs on the originals which clearly aren't true.
The alt text I'm less sure about, I think the second half is a reference it the nature of the weak conjecture (holds true only if the strong conjecture is true, and doesn't have much weight of its own), but that's mostly conjecture on my part ;)