Page "Unifying theories in mathematics" Paragraph 13

On a less grandiose scale, there are frequent instances in which it appears that sets of results in two different branches of mathematics are similar, and one might ask whether there is a unifying framework which clarifies the connections.

We have already noted the example of analytic geometry, and more generally the field of algebraic geometry thoroughly develops the connections between geometric objects ( algebraic varieties, or more generally schemes ) and algebraic ones ( ideals ); the touchstone result here is Hilbert's Nullstellensatz which roughly speaking shows that there is a natural one-to-one correspondence between the two types of objects.