It often seems that mathematicians regularly provide answers well before the rest of the world finds reasons to ask the questions. The operation of the networks of relays used in the first computers is exactly described by Boolean functions. George Boole thereby made his contribution to computer science in the mid-1800s, and Boolean algebra is used today to represent modern TTL (transistor-transistor logic) circuits. In the 1930s, Alan Turing formalized the concept of an algorithm with his presentation of an abstract computing device and characterized the limitations of such