A native of a poor working family, George Bull was born at the wrong time, in the wrong place, and, of course, in the wrong social class. He had no chance to grow up as a mathematical genius, but he became one, contrary to everything.
George Bull: biography
Born November 2, 1815 in the English industrial city of Lincoln, Bul was lucky to have a father who was fond of mathematics and gave lessons to his son. In addition, he taught him how to make optical instruments. Young George zealously embarked on his studies, and at the age of eight he surpassed his self-taught father.
A family friend helped teach the boy basic Latin and for several years was exhausted. By the age of 12, Boule was already translating ancient Roman poetry. By the age of 14, George was fluent in German, Italian, and French. At 16, he became an assistant teacher and taught at West Riding Village Schools in Yorkshire. At twenty, he opened his own educational institution in his hometown.
Over the next few years, George Boole spent short free time reading math journals borrowed from the local Institute of Mechanics. In the same place, he read Isaac Newton's work Principia and the works of French scientists Laplace and Lagrange of the 18th and 19th centuries, A Treatise on Celestial Mechanics and Analytical Mechanics. Soon he mastered the most complicated mathematical principles at that time and began to solve difficult algebraic problems.
It's time to move on.
Star rise
At the age of 24, George Bull published his first article in the mathematical journal of the University of Cambridge, “Investigations of the theory of analytic transformations,” on the subject 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 steady stream of original articles that expanded the scope of mathematics.
By 1844, he concentrated on using combinatorics and mathematical analysis for operations with infinitesimal and infinitely large numbers. In the same year, he was awarded a gold medal for his work published in the journal of the Royal Society “Philosophical Works”, for his contribution to mathematical analysis and discussion of methods for combining algebra with differential and integral calculus.
Soon, George Boole began to explore the possibilities of using algebra to solve logical problems. In his 1847 paper, “Mathematical Analysis of Logic,” he not only extended 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 was not only admired by the outstanding logician Augustus de Morgan (Ada Byron's mentor), but also provided him with a position as a professor of mathematics at Queens College in Ireland, even without a university education.
George Boole: Boolean Algebra
Relieved of his responsibilities at school, the genius of mathematics 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 main operations of which were (and still remain) “AND”, “OR” and “NOT”. It was these three functions that formed the basis of his premise and were the only operators necessary for performing comparison operations and basic mathematical functions.
Buhl’s system, described in detail in his work “The Study of the Laws of Thinking, which are the Basis of All Mathematical Theories of Logic and Probabilities” of 1854, was based on a binary approach and operated on only two objects: “yes” and “no”, “truth” and “ false ”,“ on ”and“ off ”,“ 0 ”and“ 1 ”.
Personal life
The following year, he married Mary Everest, the niece of Sir George Everest, who named the highest mountain in the world. The spouses had 5 daughters. One of them, the oldest, became a chemistry teacher. Another dealt with geometry. George Boule's youngest daughter, Ethel Lilian Voynich, became a well-known writer who wrote several works, the most popular of which is the novel “Gadfly”.
Followers
Surprisingly, given the authority of mathematics in the academic community, Buhl'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 Research, Pierce gave a short speech describing Buhl’s idea at 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 ultimately led to the design of a basic electrical logic circuit.
In fact, Pierce never built his theoretical logical scheme, since he was more a scientist than an electrician, but introduced Boolean algebra to university courses in logical philosophy.
In the end, one gifted student, Claude Shannon, took this idea and developed it.
Last works
In 1957, George Bull was elected a member of the Royal Society.
After the “Research”, he published a number of works, of which the two most influential are “A Treatise on Differential Equations” (1859) and “A 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 one to determine from the given probabilities of any system of events the subsequent probability of any event associated with the given ones logically.
Last evidence
Unfortunately, Buhl’s work was interrupted when he died of a “febrile cold” at the age of 49, after walking 3 km in the rain and giving lectures in wet clothes. By this, he proved once again that geniuses and common sense sometimes have little in common.
Heritage
George Bull's "Mathematical Analysis" and "Research" laid the foundation for Boolean algebra, which is sometimes called Boolean logic.
His system of two values, the division of arguments into different classes, with which you can then 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 that he could never have imagined. For example, computers use binary numbers and logic elements whose device and operation are based on Boolean logic. Science, the founder of which is considered to be George Bull, computer science, explores the theoretical foundations of information and computing, as well as practical methods for their implementation.