Answer
Mirsky's theorem (1971) in order theory has been discovered late.
Background
In 1950, Robert Dilworth published what is today known as Dilworth's theorem:
In any finite poset $(X,\leq)$, the size of the largest antichain equals the minimum number of blocks of a partition of $X$ into chains.
By now, several proofs are known, but for the "hard" implication "$\Rightarrow$", all of them are somewhat involved inductive proofs.
There is a pretty obvious "dual" of the statement, today known as Mirsky's theorem:
In any finite poset $(X,\leq)$, the size of the largest chain equals the minimum number of blocks of a partition of $X$ into antichains.
Surprisingly, noone seemed to have thought about for two decades, until it was published in 1971 by Leon Mirsky. All the more as the proof turned out to be much simpler than everything known for Dilworth's theorem. For the hard implication "$\Rightarrow$", there is a direct construction of the partition as the preimages of the map$$X \mapsto \mathbb{N},\quad x\mapsto \text{size of the largest chain with maximal element }x.$$Nothing comparable is known for Dilworth's theorem.
