I would say that though obtaining results is crucial, introducing new concepts, new connections, or even new perspectives looking at classical mathematics sometimes are more important.
Gauss, for example, introduced the concept of congruence in number theory and, arguably, number theory has then been developed systematically. The introduction of irrational numbers also solves old problems such as squaring a circle.
Einstein, for instance, found the connection between gravitation and curvature, so that differential geometry has been involved with physics. Kolmogorov, for another example, noted the connection between probability and measure theory, so that we have the modern theory of probability.
Klein, for example, proposed to view the geometries from the group-theoretic point of view and contributed a lot to modern geometries. Hilbert, for another instance, looked through the nature of mathematics and rigorously treated mathematics axiomatically.
Personally, I believe that these contributions to mathematics are of higher form of contributions.