1854 – England
‘Logical operations can be expressed in mathematical symbols rather than words and can be solved in a manner similar to ordinary algebra’
Boole’s reasoning founded a new branch of mathematics. Boolean logic allows two or more results to be combined into a single outcome. This lies at the centre of microelectronics.
Boolean algebra has three main logical operations: NOT, AND, OR.
In NOT, for example, output is always the reverse of input. Thus NOT changes 1 to 0 and 0 to 1.
Boole’s first book ‘Mathematical Analysis of Logic’ was published in 1847 and presented the idea that logic was better handled by mathematics than metaphysics. His masterpiece ‘An Investigation into the Laws of Thought’ which laid the foundations of Boolean algebra was published in 1854.
Unhindered by previously determined systems of logic, Boole argued there was a close analogy between algebraic symbols and symbols that represent logical interactions. He also showed that you could separate symbols of quality from those of operation.
His system of analysis allowed processes to be broken up into a series of individual small steps, each involving some proposition that is either true or false.
At its simplest, take two proposals at a time and link them with an operator. By adding many steps, Boolean algebra can form complex decision trees that produce logical outcomes from a series of previously unrelated inputs.