School of Mathematics & Physics, University of Lincoln
The year of 2015 is the bicentennial anniversary of George Boole, a famous mathematician born and bread in Lincoln. He became one of the most influential minds of the 19th century whose ideas laid the foundations of modern algebra and mathematical logic, as well as paved the way to applications in computer science and technology.
George Boole’s early fascination with mathematics and academic subjects was induced by his father, who was an owner of a cobbler’s shop in Silver Street in Lincoln but maintained interest in mathematics and sciences. Although the family could not afford the best school education, George taught himself Latin, Greek, French and German, and later differential and integral calculus. Having to support his parents and siblings after his father’s business collapsed, George Boole in his twenties found himself teaching and running schools in Waddington and Lincoln. At the same time, he managed to pursue his mathematical studies, corresponding with his peers such as Duncan Gregory and Augustus de Morgan. Remarkable progress of Boole’s research was such that his paper of 1844 was awarded a Medal of the Royal Society. Boole was appointed to the chair of mathematics at Queens College, Cork, in 1849; he also later became a member of the Royal Society.
George Boole’s most influential works contributed to a revolution in our approach to logic, which can be seen as science of thinking itself. Logic used to be a part of philosophy, or even psychology. Works of Boole and de Morgan showed that logical manipulations can be expressed by algebraic symbolism governed by mathematical laws. This is why Boole is regarded as one of the fathers of mathematical logic. Boolean algebras became important throughout many other parts of mathematics, especially algebra. Later in the 20th century Boolean approach to logic became a theoretical foundation of modern computer science including the construction of logical circuits in technical realizations of computers.
The development of mathematical logic by means of algebra pioneered by Boole gave very fruitful feedback to mathematics and to algebra in particular. For example, methods of mathematical logic gave a solution of the continuum problem, gave rise to various decidability and complexity theories, and so on. In my work I often use the so-called local theorems, which were brought by Mal’cev from logic into algebra.