Выходец из бедной рабочей семьи Джордж Буль born at the wrong time, in the wrong place, and, of course, in the wrong social class. He had no chance to grow a mathematical genius, but he became it, against all odds.
Born November 2, 1815 in Englishindustrial city of Lincoln Boole was lucky to have a father who himself was fond of mathematics and gave lessons to his son. In addition, he taught him to make optical instruments. Young George zealously set to study, and at the age of eight surpassed his self-taught father.
A family friend helped teach a boy basic Latinand for several years it has been exhausted. By age 12, Buhl had already translated Roman poetry. By age 14, George was fluent in German, Italian and French. At 16, he became a teacher's assistant and taught at West Ryding Village Schools in Yorkshire. At twenty, he opened his own educational institution in his hometown.
Over the next few years shortGeorge Bul spent his free time periods reading mathematical journals borrowed from the local Institute of Mechanics. He also read the work of Isaac Newton "Principia" and the works of French scientists Laplace and Lagrange of the XVIII and XIX centuries "Treatise on celestial mechanics" and "Analytical mechanics". Soon he mastered the most complex at that time mathematical principles and began to solve difficult algebraic problems.
It's time to move on.
At the age of 24, George Boole published inMathematical journal of the University of Cambridge, his first article "Studies of the theory of analytical transformations" on the topic of algebraic problems of linear transformations and differential equations with an emphasis on the concept of invariance. Over the next ten years, his star ascended with a constant stream of original articles that extended the limits of mathematics.
By 1844, he concentrated on usingcombinatorics and mathematical analysis for operations with infinitely small and infinitely large numbers. In the same year, he was awarded a gold medal for his work in mathematical analysis and discussion of the methods of combining algebra with differential and integral calculus, published in the journal of the Royal Society Philosophical Works.
Soon George Boole began to explore the possibilitiesapplications of algebra to solve logical problems. In 1847, Mathematical Analysis of Logic, he not only expanded Gottfried Leibniz’s earlier assumptions about the correlation between logic and mathematics, but also proved that the former was mainly a mathematical discipline, not a philosophical one.
This work has caused not only the admiration of outstandingThe logic of Augustus de Morgan (mentor of Ada Byron), but also provided him with a position as a professor of mathematics at Queens College in Ireland, even without a university education.
Freed from school duties, geniusmathematicians began to delve deeper into his own work, focusing on improving the "Mathematical Analysis", and decided to find a way to record logical arguments in a special language with which they could be manipulated and solved mathematically.
Он пришел к лингвистическое алгебре, тремя The main operations of which were (and still remain) "AND", "OR" and "NOT". It was these three functions that formed the basis of its premise and were the only operators necessary for performing comparison operations and basic mathematical functions.
Система Буля, подробно описанная в его труде "The study of the laws of thinking, which are the basis of all mathematical theories of logic and probabilities" in 1854, was based on a binary approach and operated with only two objects - yes and no, true and false, on and off "," 0 "and" 1 ".
В следующем году он женился на Мэри Эверест, Sir George Everest's niece, whose name is the highest mountain in the world. The couple had 5 daughters. One of them, the oldest, became a teacher of chemistry. Another was engaged in geometry. George Boule's youngest daughter, Ethel Lilian Voinich, became a famous writer who wrote several works, the most popular of which is The Gadfly.
Удивительно, но учитывая авторитет математика в academic circles, the idea of Buhl was criticized or completely ignored by most of his contemporaries. Fortunately, the American logician Charles Sanders Pierce was more open.
Twelve years after publication"Research" Pierce gave a brief speech describing the idea of Buhl of the American Academy of Arts and Sciences, and then spent more than 20 years changing and expanding it to realize the potential of the theory in practice. This ultimately led to the design of a basic electrical logic circuit.
Pierce never really built his theoretical logic circuit, because he was more a scientist than an electrician, but he introduced Boolean algebra into university courses in logical philosophy.
In the end, one gifted student, Claude Shannon, took this idea and developed it.
In 1957, George Boule was elected a member of the Royal Society.
After the "Research", he published a series of works fromwhich the two most influential are the Treatise on Differential Equations (1859) and the Treatise on the Calculation of Finite Differences (1860). Books have been used as textbooks for many years. He also tried to create a general probability theory method, which would allow to determine the subsequent probability of any event related to given logical values from the given probabilities of any event system.
Unfortunately, Buhl's work was interrupted when heHe died of a “feverish cold” at the age of 49 after walking 3 km in the rain, lecturing in wet clothes. By this he once again proved that geniuses and common sense sometimes have little in common.
"Mathematical analysis" and "Research" by George Boole marked the beginning of Boolean algebra, which is sometimes called Boolean logic.
His system of two meanings, separationarguments to various classes, with which it is possible to conduct operations in accordance with the presence or absence of certain properties, allowed to draw logical conclusions regardless of the number of individual elements.
Buhl's work led to the creation of applications thathe could never even imagine. For example, computers use binary numbers and logic elements whose design and operation is based on Boolean logic. Science, the founder of which is considered George Boole, computer science, explores the theoretical foundations of information and computing, as well as practical methods for their implementation.
