Writing a short biography on him as a project for an abstract algebra course and I was wondering what people more familiar with the field would consider his greatest contributions to be. I'm currently looking into Riemann surfaces, but I'm not 100% sure that's a true "abstract algebra" application.
EDIT: I've been combing through a few history texts that my professor recommended but most of them focus on his contributions to geometry. I haven't been able to find anything other than the surfaces which seem to be related to abstract algebra. Part of the issue is I'm not sure what constitutes an abstract algebra application.
EDIT 2: I'll keep this question open just to see what people think, but for the time being I chose to give an overview of Riemann's major accomplishments (I chose his contributions to differential geometry, Riemann sums, and Riemann surfaces) and then decided to give extra focus to the Riemann hypothesis. I decided to make this edit just in case anyone was curious. I'll continue to read answers and will accept an answer as well.
There exists an equivalence of categories between compact Riemannian surfaces $\mathcal{C}$ and algebraic function fields $\mathcal{F}$ in one variable over $\Bbb C$, given by $\mathcal{C}\mapsto \mathcal{M(C)}$, the field of meromorphic functions. In this sense, I suppose, we could also mention the "algebra" context for Riemannian surfaces. However, it is also clear that they belong mainly to geometry and not to abstract algebra.