This chapter concerns computation during the modernist period. Reading this in the twenty-first century, you may conclude that this will be a chapter about computers: the devices we use daily to interact with the Internet, to stream film and music, to chat with distant relations or to do most of our shopping. It will partly be about that but, more broadly, this chapter considers computation, the general process digital computers (and their analogue and human precursors) were created to perform.

Despite using computers on a day-to-day basis – especially when we consider that most mobile phones, TVs and smart home devices are all digital computers – most people probably could not offer a definition of computation. Wikipedia offers an easily accessible definition: ‘any type of calculation that includes both arithmetical and non-arithmetical steps and follows a well-defined model’ (‘Computation’ 2019: n.p.). Mathematician Robert I. Soare offers a more technical definition, drawn from computability theory (the branch of mathematics that models the underlying logic of computation outside the instantiation in particular machines):

This merely formalises the earlier definition: a computation follows a series of repeatable steps to transform given inputs (which could be something you shout at Siri, as much as a differential equation you need solved) into desired output. This focus on step-by-step procedure is why computer science studies and creates algorithms.

The Oxford English Dictionary defines an algorithm as ‘a procedure or set of rules used in calculation and problem-solving’ (‘Algorithm’ n.d.: n.p.). So, while there are other models possible for describing it, computation, in its present digital incarnation, often involves a series of calculations performed in service of a series of steps designed to produce some more complex project. Computation becomes particularly important to mathematics after the invention of calculus, when mathematics begins to require increasingly complex calculations. To manage these labour-intensive tasks, mathematicians devised computers, which were rooms of people performing calculations by hand or machine, both analogue and digital, that could compute the results of a particular equation or problem.