Wired, This Day in Tech Blog: 2-Nov-1815, Boole Born, Boolean Logic, .... Binary and Boolean can solve any mathematical problem. Boolean logic is used to build systems that not only solve mathematical problems.
My master thesis was about "Free Algebraic Structures (Universal Algebras)" (a look into the "language" aspects of algebraic structures - simplified: extensions over an "alphabet" isomorphic to any algebraic structure of that type with those "variables").
If I remember right (mid 1970s!) I looked into free cylindric algebras (A. Tarski) that arise in the algebraization of first order logic with equality. Cylindric algebras are Boolean algebras with operations that model quantification and equality. Not a bad foundation to study formal languages ...
However, at that time a felt a bit like an "abstract astronaut" who did not know, where to fly .....