English mathematician George Buhl: biography, works

A native of a poor working-class family George Buhl was born at the wrong time, in the wrong place, and certainly not in that social class. He did not have a chance to grow up a mathematical genius, but he became it, in spite of everything.

George Boule: Biography

Born on November 2, 1815 in the English industrial city of Lincoln, Buly was fortunate 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 began to study, and at the age of eight years he surpassed his father-self-taught.

A friend of the family helped to teach the boy a basic Latin and for a few years was exhausted. By the age of 12, Buhl had already translated ancient Roman poetry. By the age of 14, George spoke fluent German, Italian and French. At the age of 16 he became assistant teacher and taught at the village schools of West Riding in Yorkshire. At twenty he opened his own educational institution in his hometown.

During the next few years, short periods of free time, George Buhl spent reading mathematical journals borrowed from the local Institute of Mechanics. There he read the work of Isaac Newton "Principia" and the work of the French scientists Laplace and Lagrange XVIII and XIX centuries "Treatise on celestial mechanics" and "Analytical Mechanics." Soon he mastered the most difficult at that time mathematical principles and began to solve difficult algebraic problems.

It's time to move on.

Sunrise of the star

At the age of 24, George Buhl published his first article in the mathematical journal of the University of Cambridge, "Studies in 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 constant stream of original articles expanding the limits of mathematics.

By 1844, he concentrated on using combinatorics and mathematical analysis for operations with infinitesimal and infinitely large numbers. In the same year, for the works published in the journal of the Royal Society "Philosophical Works," he was awarded a gold medal for his contribution to the mathematical analysis and discussion of methods of combining algebra with differential and integral calculus.

Soon, George Buhl 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 primarily a mathematical discipline, not a philosophical one.

This work not only aroused admiration for the outstanding logic of Augustus de Morgan (Ada Byron's mentor), but also provided him with a position as a mathematics professor at Queens College in Ireland, even without a university education.

George Boule: Boolean algebra

Freed from his school duties, 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 its premise and were the only operators necessary to perform comparison operations and basic mathematical functions.

The Boolean system, described in detail in his work "The study of the laws of thought that are the basis of all mathematical theories of logic and probabilities" of 1854, was based on a binary approach and operated only on 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, whose name is the highest mountain in the world. The couple had 5 daughters. One of them, the oldest one, became a chemistry teacher. The other was engaged in geometry. The youngest daughter of George Buhl, Ethel Lillian Voynich, became a famous writer who wrote several works, the most popular of which is the novel "Gadfly".

Followers

Surprisingly, given the authority of mathematics in academic circles, the idea of Boole 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, Pierce gave a short speech describing the idea of the Bull of the American Academy of Arts and Sciences, and then spent more than 20 years changing and expanding it to realize the theory's potential in practice. This, ultimately, led to the design of the basic electrical logic circuit.

Pierce did not really build his theoretical logic scheme in reality, as he was more a scientist than an electrician, but he introduced Boolean algebra into university courses of logical philosophy.

In the end, one gifted student, Claude Shannon, took this idea and developed it.

Last works

In 1957, George Buhl was elected a member of the Royal Society.

After the "Study" he published a number of works, of which the two most influential are the Treatise on Differential Equations (1859) and The 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 that would allow from the probabilities of any system of events to determine the subsequent probability of any event associated with the given logically.

The last proof

Unfortunately, Boole's work was interrupted when he died of a "febrile cold" at the age of 49 after walking 3 km in the rain and lecturing in wet clothes. This he once again proved that geniuses and common sense sometimes have little in common.

Heritage

"Mathematical Analysis" and "Studies" by George Buhl initiated the Boolean algebra, which is sometimes called Boolean logic.

Its system of two values, the separation of arguments into different classes, with which it is then possible to carry out operations in accordance with the presence or absence of certain properties, made it possible to draw logical conclusions regardless of the number of individual elements.

The works of Boole led to the creation of applications, which he could never have imagined. For example, computers use binary numbers and logical elements, the device and operation of which is based on Boolean logic. Science, founded by George Buhl, informatics, explores the theoretical foundations of information and computing, as well as practical methods for their implementation.