Computer science began by discovering both the universal computer and the things computers cannot do.

A Turing machine is a stripped-down mathematical model of computation: an imaginary device with an endless tape, a read-write head, and a finite set of rules. At each step, it reads one symbol, writes another, moves left or right, and changes state. From these tiny actions, surprisingly elaborate computations can emerge. The machine is not meant to be practical hardware; its power lies in showing what an algorithm can, in principle, accomplish. It also reveals the boundary between problems that can be computed and those that cannot. It is used primarily in computability theory, complexity theory, and computer science education.