The picture in the top-right corner of this page shows the Riemann zeta function. The non-trivial roots are shown with the white dots. They look like they're all in a line down the very middle of the picture. They're not too far to the left and not too far to the right. The real part is how far left-to-right you are. Being in the middle of the picture means they have a real part of 1/2. So all the non-trivial roots in the picture have a real part of 1/2. But our picture doesn't show everything because the Riemann zeta function is too big to show. So what about the non-trivial roots above and below the picture? Would they be in the middle too? What if they break the pattern of being in the middle? They could be slightly to the left or right. The Riemann hypothesis asks if "every" non-trivial root (white dot) would be on the line down the middle. If the answer is no, we say the "hypothesis is false". This would mean that there are white dots which are not on the line given. 