Is God a Mathematician_ - Mario Livio [84]
These humble words describe the initiation of what was to become a seminal effort in symbolic logic.
Laws of Thought
George Boole (figure 47) was born on November 2, 1815, in the industrial town of Lincoln, England. His father, John Boole, a shoemaker in Lincoln, showed great interest in mathematics and was skilled in the construction of a variety of optical instruments. Boole’s mother, Mary Ann Joyce, was a lady’s maid. With the father’s heart not quite in his formal business, the family was not well off. George attended a commercial school until age seven, and then a primary school, where his teacher was one John Walter Reeves. As a boy, Boole was mainly interested in Latin, in which he received instruction from a bookseller, and in Greek, which he learned by himself. At age fourteen he managed to translate a poem by the first century BC Greek poet Meleager. George’s proud father published the translation in the Lincoln Herald—an act that provoked an article expressing disbelief from a local schoolmaster. The poverty at home forced George Boole to start working as an assistant teacher at age sixteen. During the following years, he devoted his free time to the study of French, Italian, and German. The knowledge of these modern languages proved useful, since it allowed him to turn his attention to the great works of mathematicians such as Sylvestre Lacroix, Laplace, Lagrange, Jacobi, and others. Even then, however, he was still unable to take regular courses in mathematics, and he continued to study on his own, while at the same time helping to support his parents and siblings through his teaching job. Nevertheless, the mathematical talents of this auto-didact started to show, and he began publishing articles in the Cambridge Mathematical Journal.
Figure 47
In 1842, Boole started to correspond regularly with De Morgan, to whom he was sending his mathematical papers for comments. Because of his growing reputation as an original mathematician, and backed by a strong recommendation from De Morgan, Boole was offered the position of professor of mathematics at Queen’s College, in Cork, Ireland, in 1849. He continued to teach there for the rest of his life. In 1855 Boole married Mary Everest (after whose uncle, the surveyor George Everest, the mountain was named), who was seventeen years his junior, and the couple had five daughters. Boole died prematurely at age forty-nine. On a cold winter day in 1864, he got drenched on his way to the college, but he insisted on giving his lectures even though his clothes were soaking wet. At home, his wife may have worsened his condition by pouring buckets of water onto the bed, following a superstition that the cure should somehow replicate the cause of the illness. Boole developed pneumonia and died on December 8, 1864. Bertrand Russell did not hide his admiration for this self-taught individual: “Pure mathematics was discovered by Boole, in a work which he called The Laws of Thought (1854)…His book was in fact concerned with formal logic, and this is the same thing as mathematics.” Remarkably for that time, both Mary Boole (1832–1916) and each of the five Boole daughters achieved considerable fame in fields ranging from education to chemistry.
Boole published The Mathematical Analysis of Logic in 1847 and The Laws of Thought in 1854 (the full title of the latter read: An Investigation of the Laws of Thought, on Which Are Founded the Mathematical Theories of Logic and Probabilities). These were genuine masterworks—the first to take the parallelism between logical and arithmetic operations a giant step forward. Boole literally transformed logic into a type of algebra (which came to be called Boolean algebra) and extended the analysis of logic even to probabilistic reasoning. In Boole’s words:
The design of the following treatise [The Laws of Thought] is to investigate the fundamental laws of those operations of the mind by which reasoning is performed; to give expression to them in the symbolical language of a Calculus, and upon this