**200 years ago, was born on 2 November 1815 the father of algebra of logic,**

** ****which is one of the foundations of modern information technology and computer science,**

**outstanding English mathematician George Boole**

In 1854, Boole published a exposition entitled An Investigation of the Laws of Thought, on Which are Founded the Mathematical Theories of Logic and Probabilities. This work contains the full expression of the first practical system of logic in algebraic formOffsite Link.

This year marks the 150th anniversary of the publication of the book that set the scene for the introduction of the computer a century later: George Boole's The Laws of Thought, first published in 1854. The dramatic breakthrough that the book represented is reflected today in our use of the terms "boolean logic" or "boolean algebra" to mean the combination of ideas using the operations AND, OR, and NOT, and our use of the term "boolean search" to mean a database or Web search involving combinations of key words using AND, OR, and NOT. (The fact that we generally do not capitalize "boole" in those contexts indicates just how pervasive Boole's influence has been.)

Boole's book begins with these words: The design of the following treatise is to investigate the fundamental laws of those operations of the mind by which reasoning is performed; to give expression to them in the symbolic language of a Calculus, and upon this foundation to establish the science of Logic and construct its method.

By the phrase "the symbolic language of a Calculus" Boole meant algebra. Not just the use of algebraic symbols like x, y, z, p, q, r to denote unknown words, phrases, or propositions. That much had been done by the logicians of ancient Greece. What Boole was talking about was using the entire apparatus of the high school algebra class, with operations such as addition and multiplication and the employment of methods to solve equations. Boole's algebra required the formulation of a symbolic language of thought. Solving an equation in that language would not lead to a numerical answer; it would give the conclusion of a logical argument. His algebra was to be an algebra of thought.

Boole's idea was to try to reduce logical thought to the solution of equations -- a logical holy grail ever since the German mathematician Gottfried Leibniz had tried to do it in the 17th century. Leibniz attempted to develop an "algebra of concepts", in which algebraic symbols had denoted concepts, such as big, red, man, woman, unicorn, but he had met with only limited success.

Boole wanted his algebra to encompass all of Aristotle's insights into human reasoning (the famous Greek "All men are mortal" syllogisms) as well as the Stoics' logic of propositions (what we now refer to as propositional calculus). He took his symbols x, y, z, etc. to denote arbitrary collections of objects. For example, the collection of all men, the collection of all mortals, the collection of all bankers, or the collection of all natural numbers. He then showed how to do algebra with symbols that denote collections -- to write down and solve equations -- in a way that corresponds to performing logical deductions.

In order to be able to write down and solve algebraic equations involving collections, Boole had to define what it meant to add and to multiply two collections. Since his algebra was intended to capture some of the patterns of logical thought, his definitions of addition and multiplication had to correspond to some basic thought processes. Moreover, it would be easier to do algebra if he could define addition and multiplication in such a way that they had many of the familiar properties of addition and multiplication of numbers, making his new algebra of thought similar to the algebra everyone was used to.

In honor of the 200th anniversary of the birth of George Boole students of National University of Ireland, where he taught, created a special website.

Interesting coincidence - the daughter of George Boole Ethel Lilian wrote the novel "The Gadfly." She worked under the pseudonym Voynich. Roman rocked the world and has become a classic.