TITLE: Can someone please explain the Riemann Hypothesis to me... in English?
QUESTION [68 upvotes]: I've read so much about it but none of it makes a lot of sense. Also, what's so unsolvable about it?

REPLY [2 votes]: It is straight forward. We have a Zeta function, 'analytically continued' that says
$\zeta(s)[1-2/2^s] = 1 - 1/2^s + 1/3^s - 1/4^s + ......$ Here s is a complex variable. Thus $s=\Re(\sigma) + \Im(\omega).$ (Where $\Re$ indicates the real part and $\Im$ indicates the imaginary part). The above series converges in the region of our interest which  is  $0 < \sigma < 1.$
To find the zeroes of $\zeta(s)$ we need to first substitute $\zeta(s) = 0$ and solve for $s$ and the sigmas and omegas.
That is 
Solve $0= 1 - 1/2^s + 1/3^s -1/4^s + ...$, for sigmas and omegas. Riemann hypothesized that the zeros will have their sigmas equal to 1/2 while the omegas are distinct. To this date, after 150 years, no one has any clue why sigma takes a single value of 1/2 in the critical strip $0 < \sigma < 1.$ Apart from the consequences I hope I explained it well. Wikipedia on Riemann Hypothesis is a good source for reading up.