Riemann hypothesis
We do not know the answer to the question yet. But we do know some good facts. These facts might help us. There is a way we can find facts about the real parts of the non-trivial roots. This is with Riemann's special equation (Riemann's functional equation). Riemann's functional equation tells us about the size of the real parts. It says that all the non-trivial zeros have a real part close to 1/2. It says how small the real parts can be, and how big they can be. But it doesn't say exactly what they are. Specifically, it says the real parts have to be bigger than 0. But they have to be less than 1. But we still don't know if there might be a non-trivial root with a real part very close to 1/2. Maybe there is, but we just have not found it yet. The group of complex numbers that have a real part bigger than 0 but smaller than 1 is called the "critical strip".