Unification of Different Fields of Mathematics

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During WWII, André Weil proposed an idea for linking three fields of mathematics: number theory, geometry, and finite fields.

For the full story, please see the following link it Quanta Magazine's  article describing the unification of three major branches of mathematics: A Rosetta Stone of Mathematics. 

Also related, is the work begun by Robert Langlands, known as the Langlands program.