He gave his name to the extension of Cauchy's equations in complex analysis and a curvature tensor which contracts to the Ricci tensor.  
He extended the differential geometry of 2D surfaces, developed by his teacher Gauss, generalizing the concept of metrics and geodesics.  Thus, in 1854, he almost stumbled on general relativity.  He gave his name to the extension of Cauchy's equations in complex analysis and a curvature tensor which contracts to the Ricci tensor.  For ten points, what German discovered the zeta function.
He extended the differential geometry of 2D surfaces, developed by his teacher Gauss, generalizing the concept of metrics and geodesics.  
Bernhard Riemann