Coming from a poor working-class family, George Buhl was born at the wrong time, in the wrong place, and definitely in the wrong social class. He had no chance of growing up to be a math genius, but he became one against all odds.
George Buhl: biography
Born on November 2, 1815 in the English industrial city of Lincoln, Boole was lucky enough to have a father who himself was fond of mathematics and gave lessons to his son. In addition, he taught him how to make optical instruments. Young George took up his studies with zeal, and at the age of eight he surpassed his self-taught father.
A family friend helped teach the boy basic Latin and exhausted himself in a few years. By the age of 12, Buhl was already translating ancient Roman poetry. By the age of 14, George was fluent in German, Italian and French. At the age of 16 he became a teacher's assistant and taught at the West Riding country schools in Yorkshire. At twenty, he opened his own educational institution in his hometown.
During the next few years George Boole spent short periods of free time reading mathematical journals borrowed from the local Mechanics Institute. There he read Isaac Newton's "Principia" andthe works of the French scientists Laplace and Lagrange of the 18th and 19th centuries "Treatise on Celestial Mechanics" and "Analytical Mechanics". Soon he mastered the most difficult mathematical principles at that time and began to solve difficult algebraic problems.
It's time to move on.
Star Rising
At the age of 24, George Boole published in the Cambridge University Mathematical Journal his first paper "Investigations in the Theory of Analytic Transformations" on algebraic problems of linear transformations and differential equations, focusing on the concept of invariance. Over the next ten years, his star rose with a steady stream of original papers pushing the limits of mathematics.
By 1844, he concentrated on using combinatorics and calculus to operate on infinitesimal and infinitely large numbers. In the same year, for his work published in the Philosophical Transactions of the Royal Society, for his contribution to mathematical analysis and discussion of methods for combining algebra with differential and integral calculus, he was awarded a gold medal.
Soon George Boole began to explore the possibilities of using algebra to solve logical problems. In his 1847 work The Mathematical Analysis of Logic, he not only extended Gottfried Leibniz's earlier suggestions about the correlation between logic and mathematics, but also proved that the former was primarily a mathematical discipline, not a philosophical one.
This work aroused not only the admiration of the outstanding logicianAugustus de Morgan (Ada Byron's mentor) but secured him a position as professor of mathematics at Queen's College in Ireland, even without a university degree.
George Buhl: Boolean Algebra
Freed from school duties, the mathematician began to delve deeper into his own work, focusing on improving the "Mathematical Analysis", and decided to find a way to write logical arguments in a special language, with which they could be manipulated and solved mathematically.
He came to linguistic algebra, the three basic operations of which were (and still are) "AND", "OR" and "NOT". It was these three functions that formed the basis of his premise and were the only operators necessary to perform comparison operations and basic mathematical functions.
Boole's system, described in detail in his work "Investigation of the laws of thought, which are the basis of all mathematical theories of logic and probability" in 1854, was based on a binary approach and operated only with two objects - "yes" and "no", "true" and "false", "on" and "off", "0" and "1".
Private life
The following year he married Mary Everest, niece of Sir George Everest, after whom the highest mountain in the world is named. The couple had 5 daughters. One of them, the oldest, became a teacher of chemistry. The other was in geometry. George Boole's youngest daughter, Ethel LillianVoynich became a famous writer who wrote several works, the most popular of which is the novel The Gadfly.
Followers
Surprisingly, given the authority of the mathematician in academic circles, Boole's idea was criticized or completely ignored by most of his contemporaries. Fortunately, the American logician Charles Sanders Pierce was more open.
Twelve years after the publication of The Study, Peirce gave a brief speech describing Boole's idea to the American Academy of Arts and Sciences, and then spent more than 20 years modifying and expanding it to realize the potential of theory in practice. This eventually led to the design of the basic electrical logic circuit.
Pierce never actually built his theoretical logic circuit, as he was more of a scientist than an electrician, but introduced Boolean algebra into university courses in logical philosophy.
Eventually, one gifted student, Claude Shannon, took this idea and developed it.
Recent works
In 1957, George Boole was elected a Fellow of the Royal Society.
After the "Investigation" he published a number of works, of which the two most influential are "Treatise on Differential Equations" (1859) and "Treatise on the Calculus of Finite Differences" (1860). Books have been used as textbooks for many years. He also tried to create a general method of probability theory, which would allow from the given probabilities of any system of events to determine the subsequentthe probability of any event associated with given logically.
Last proof
Unfortunately, Boole's work was interrupted when he died of a "feverish cold" at the age of 49 after walking 3 km in the rain while lecturing in wet clothes. By this, he once again proved that geniuses and common sense sometimes have little in common.
Legacy
George Boole's "Mathematical Analysis" and "Research" laid the foundation for Boolean algebra, sometimes called Boolean logic.
His system of two values, dividing arguments into distinct classes that can then be operated on according to whether or not they have certain properties, allowed inferences to be drawn regardless of the number of distinct elements.
Buhl's work has led to applications he could never have imagined. For example, computers use binary numbers and logical elements, the design and operation of which is based on Boolean logic. The science, whose founder is George Boole, computer science, explores the theoretical foundations of information and calculations, as well as practical methods for their implementation.
