Mathematical Logic

George Boole (1815-1864), a self-taught English mathematician, philosopher and logician, showed that logic could be studied with the precision of algebra -- his work on Boolean algebra and binary numbers underlies digital computing today. The Greek philosopher Aristotle (384-322 BCE) wrote the first book on logic; the German philosopher-mathematician Gottfried Leibniz (17th century) first proposed using symbols for logic; George Boole and Augustus de Morgan realised this idea in the 19th century, linking logic, symbols and algebra together. Mathematical logic matured in the late 19th and early 20th centuries.

In 1930, researchers (echoing von Neumann's remark that "$0$ and $1$ are going to rule the world") recognised that the binary digits $0$ and $1$ could describe electrical circuits, laying the groundwork for electronic computers -- today's digital computers and circuits are built to implement exactly this binary arithmetic. …