Besides introducing Turing machines, Turing (1936) proved several seminal mathematical results involving them. In particular, he proved the existence of a universal Turing machine (UTM). Roughly speaking, a UTM is a Turing machine that can mimic any other Turing machine. One provides the UTM with a symbolic input that codes the machine table for Turing machine M. The UTM replicates M’s behavior, executing instructions enshrined by M’s machine table. In that sense, the UTM is a programmable general purpose computer. To a first approximation, all personal computers are also general purpose: they can mimic any Turing machine, when suitably programmed. The main caveat is that physical computers have finite memory, whereas a Turing machine has unlimited memory. More accurately, then, a personal computer can mimic any Turing machine until it exhausts its limited memory supply.