What did Turing establish about the limits of computers and the nature of mathematics
Jack Copeland · 2013
In the 1930s, a group of iconoclastic mathematicians and logicians launched the field we now call theoretical computer science. These pioneers embarked on an investigation to spell out the meaning and limits of computation. Pre-eminent among them were Alan Turing, Kurt Godel, and Alonzo Church. These three men are pivotal figures in the story of modern science, and it's probably true to say that, even today, their role in the history of science is underappreciated. The theoretical work they carried out in the '30s laid the foundations for the computer revolution, and the computer revolution in turn fuelled the rocketing expansion of scientific knowledge that characterizes modern times. Previously undreamed of number-crunching power was soon boosting all fields of scientific enquiry, thanks in large part to these seminal investigations. Yet at the time Turing, Godel, and Church would have thought of themselves as working in a most abstract field, far flung from practical computing. Their concern was with the very foundations of mathematics...