Sheon Han in Quanta:
Some scientific discoveries matter because they reveal something new — the double helical structure of DNA, for example, or the existence of black holes. However, some revelations are profound because they show that two old concepts, once thought distinct, are in fact the same. Take James Clerk Maxwell’s equations showing that electricity and magnetism are two aspects of a single phenomenon, or general relativity’s linking of gravity with a curved space-time.
The Curry-Howard correspondence does the same but on a larger scale, linking not just separate concepts within one field, but entire disciplines: computer science and mathematical logic. Also known as the Curry-Howard isomorphism (a term meaning there exists some kind of one-to-one correspondence between two things), it establishes a link between mathematical proofs and computer programs.
More here.