George Boole laid the mathematical foundations of the information age. His ground-breaking advances — Boolean algebra and symbolic logic — provided the cornerstones for modern mathematics, microelectronic engineering and computer science.
Boole had an intense personal mission, in which intellectual endeavour was sustained by deep religious belief. Boole regarded the human brain as God’s finest creation, and became convinced that the workings of the human mind could be explained through rational analysis.
That conviction can be traced back to the age of 17, when he was beginning his study of advanced mathematics. Walking across a field near Lincoln, Boole experienced a near-mystic revelation, in which he felt God calling him to explain the workings of the mind to humanity.
Boole came to recognise that the human brain has limits in terms of the quantity of information it can handle. He saw that if ideas were represented using the symbolic forms of algebra, the capacity to manipulate ideas could be vastly increased using mathematics.
Boole’s first book was The Mathematical Analysis of Logic, 1847, which he proposed as “a first step towards understanding the thought processes of the human mind as expressed in speech, that classes of objects and logical operations could be represented by mathematical symbols, and that algebraic operations could be used to process those classes."
Boole was conscious that his first book was written rapidly and had shortcomings. His Cork professorship provided him with the time and space needed to sharpen and expand his ideas.
Boole’s masterwork appeared in 1854, An Investigation of the Laws of Thought. The book’s purpose was ‘. . . to investigate the fundamental laws of those operations of the mind by which reasoning is performed . . .’ and it extended Boole’s methods and theories to logic and probability. Published in London, this book gained him an international reputation.
For centuries, philosophers and logicians from Aristotle to Leibniz, Pascal and Babbage had been seeking a way for mathematics to handle thought. Boole had now shown the way, with an inspired choice of algebraic notation. His friend, the mathematician Augustus de Morgan, commented; ‘. . . he has I think, got hold of the true connection of algebra and logic . . .’
After Boole’s premature death in 1864, the full potential of his ideas lay unrealised for 70 years. But in the mid-twentieth century an American engineer, Claude Shannon, recognised the relevance for engineering of Boole’s symbolic logic. Consequently, Boole’s thinking came to empower a new generation of electrical and electronic engineers and inventors.
Claude Shannon graduated in 1936 from the University of Michigan with two bachelor’s degrees, one in electrical engineering and the other in mathematics. He transferred to the Massachusetts Institute of Technology (MIT) for his Master’s. Here he was recruited by Vannevar Bush, Dean of the School of Engineering, to work on maintenance of the Differential Analyzer, an early analog computer which Bush had developed from 1927 onwards.
The Differential Analyzer was a large mechanical computer with electrically-powered shafts, developed to solve scientific and engineering problems expressed through differential equations. Shannon was given the tedious task of manually configuring its gears to process each problem, and began to explore ways of replacing mechanical parts with electric circuits.
At Michigan, while studying electrical engineering, Shannon had attended a philosophy class which introduced him to Boolean algebra. He commented some time later; ‘it just happened that no one else was familiar with both fields at the same time’. Shannon saw that the binary character ‘yes/no’ or ‘one/zero’ of Boolean logic could be applied to laying out electrical switching circuits, and this became the subject of his 1937 master’s thesis.
In 1938 he published a seminal paper, A Symbolic Analysis of Relay and Switching Circuits, drawing on Boole’s Mathematical Analysis of Logic to demonstrate how to build decision circuits from electromechanical relay switches. This paper established the logical basis on which modern digital computer circuits are based.
Shannon’s ideas were recognised as ground-breaking and were applied rapidly to the design of automatic telephone switching systems. In 1940, MIT awarded him both a master’s degree in electrical engineering and a PhD in mathematics. In 1941, Shannon joined the Mathematics Department at Bell Laboratories, to which he remained affiliated until 1972.
In the late 1940s, Shannon published two further papers of fundamental importance for the information age; in 1948 A Mathematical Theory of Communication, in which he explained the transmission of information in digital terms, and in 1949 Communication Theory of Secrecy Systems, which is credited with establishing cryptography as a science.
Boole via Shannon inspired an industry which has transformed the world in which we live. The relay switches used by Shannon were soon followed by much faster vacuum tubes, then much smaller transistors, and finally microchips which reach ever-greater levels of miniaturisation.
Computers, information storage and retrieval, electronic circuits, controls and sensors, and much of the world of technology that supports life, learning and communications in the twenty-first century depend on the inventive, versatile mathematics devised by George Boole.