 Until late in the 20th century, the inconsistency in Frege’s Grundgesetze overshadowed a deep theoretical accomplishment that can be extracted from his work. The Grundgesetze contains all the essential steps of a valid proof (in second-order logic) of the fundamental propositions of arithmetic from a single consistent principle. This consistent principle, known in the literature as “Hume’s Principle”, asserts that for any concepts \(F\) and \(G\), the number of \(F\)-things is equal to the number \(G\)-things if and only if there is a one-to-one correspondence between the \(F\)-things and the \(G\)-things. Though Frege derived Hume’s Principle from Basic Law V in the Grundgesetze, the subsequent derivations of the fundamental propositions of arithmetic from Hume’s Principle do not essentially require Basic Law V. So by setting aside the problematic Basic Law V and the derivation of Hume’s Principle, one can focus on Frege’s derivations of the basic propositions of arithmetic using Hume’s Principle as an axiom. His theoretical accomplishment then becomes clear: his work shows us how to prove, as theorems, the Dedekind/Peano axioms for number theory from Hume’s Principle in second-order logic. This achievement, which involves some remarkably subtle chains of definitions and logical reasoning, has become known as Frege’s Theorem.