John Napier Biography

John Napier is best remembered as the inventor of the first system of logarithms. A logarithm is the power to which a number, called the base, must be raised to produce a given number. Napier's work with logarithms was described in two Latin treatises, Mirifici logarithmorum canonis descriptio (1614; "A Description of the Wonderful Canon of Logarithms") and Mirifici logarithmorum canonis constructio (1619; "The Construction of the Wonderful Canon of Logarithms"). This work was immediately recognized by other mathematicians as a great advance. Three hundred years later, in an essay marking the publication anniversary of the Descriptio, P. Hume Brown wrote that Napier's most notable achievement "has given him a high and permanent position in the history of European culture."

Napier, the eighth laird of Merchiston, was born in 1550 at Merchiston Castle near Edinburgh, Scotland. He came from a line of influential noblemen and statesmen. His father, Sir Archibald Napier, was a prominent public figure who was allied with the Protestant cause. Among other roles, Sir Archibald served for more than 30 years as Master of the Mint. Sir Archibald's first wife and Napier's mother, Janet Bothwell, was the daughter of an Edinburgh burgess.

Napier entered the University of St. Andrews at age 13, which was typical of wellborn boys of the time. However, he was a dropout, staying at the university for only a short while. It is likely that Napier then traveled to the European continent to continue his studies, although little is known of this period. By 1571, however, he had returned to Scotland and was living at Gartnes, where he built a castle. In 1572 Napier married Elizabeth Stirling. The couple had two children, Archibald and Joanne, before Elizabeth's death in 1579. Napier later married Agnes Chisholm, with whom he had ten children. These included a son named Robert, who eventually served as his father's literary executor. The family stayed in Gartnes until 1608, when Napier inherited Merchiston Castle upon Sir Archibald's death.

Napier lived an active life as a Scottish landowner. He was an amateur scientist who never held a professional post. Nevertheless, his varied accomplishments earned him the nickname of "Marvelous Merchiston." He experimented with fertilizers to improve his land, and he invented a hydraulic screw and revolving axle that could be used to remove water from flooded coal pits. Not surprisingly, Napier was also intrigued by the religious and political controversies of his day. A staunch Protestant, he published A Plaine Discovery of the Whole Revelation of St. John in 1593. This book, a virulent attack on Catholicism that concluded the Pope was the Antichrist, was read widely and translated into several languages.

Napier's preoccupation with defending his faith and country prompted him to design various weapons. These included burning mirrors for setting enemy ships on fire, an underwater craft, and a tank-like vehicle. He invested much time and money in these projects, even building prototypes in some cases. In one instance, Napier was said to have built and tested an experimental rapid-fire gun that he claimed would have killed 30,000 Turks without the loss of a single Christian.

Astronomy was another of Napier's passions, and it was this pursuit that led to his greatest discovery. Napier's astronomy research required him to do a number of tedious calculations involving trigonometric functions. Over the course of more than two decades, he gradually developed and refined new ideas for speeding such calculations through the use of logarithms. The Descriptio briefly explained his invention and presented the first logarithmic tables. The Constructio, published after his death, described how the tables had been computed.

The Descriptio attracted the attention of English mathematician Henry Briggs, who traveled to Edinburgh to discuss the new tables. Napier and Briggs worked on such improvements as using the base 10. The result was Briggs's development of a standard form of logarithmic table that remained in common use until the advent of calculators and computers. Thanks to his efforts, logarithms were quickly adopted by mathematicians throughout Europe.

Napier made other advances in spherical trigonometry. The so-called "Napier's analogies" were formulas for solving spherical triangles. "Napier's rules of circular parts" were ingenious rules for stating the interrelationships of the parts of a right spherical triangle. In addition, Napier pioneered the use of the decimal point to separate the whole number part of a number from its fractional part. As one of the first to use decimal fractions, he helped to popularize them.

Napier's contributions to mathematics did not end there, however. His concern with simplifying calculations led him to invent mechanical aids for doing arithmetic, described in Rabdologia (1617). Among these aids were rods with numbers marked off on them, often known as "Napier's bones" because they were usually made of bone or ivory. Using the rods, multiplication became a process of reading the appropriate figures and making minor adjustments. In addition, Napier invented other types of rods for extracting square roots and cube roots.

It is not clear when Napier first began to dabble in mathematics. However, some early writings, dealing mainly with arithmetic and algebra, seem to date from the period just after his first marriage. These writings were collected and transcribed after Napier's death by his son Robert. They were first published in 1839 by descendant Mark Napier under the title De arte logistica, revealing the keenness of Napier's mathematical ruminations. Among other subjects, it appears that he investigated imaginary roots of equations.

During his lifetime, Napier was reputed to be not only a mathematician, but a magician as well. It was rumored that he possessed supernatural powers, and that he owned a black rooster as a spiritual familiar. Given his wide-ranging interests, Napier was almost never idle. A combination of overwork and gout finally led to his death at Merchiston on April 4, 1617. His burial place is uncertain, but it is probably at the old church of St. Cuthbert's parish in Edinburgh.

In 1914, the 300th anniversary of the publication of the Descriptio was commemorated by the Royal Society of Edinburgh. In his inaugural address, Lord Moulton lauded Napier as one who "stands prominent among that small band of thinkers who by their discoveries have substantially increased the powers of the human mind as a practical agent." In 1964 Napier University, named for the mathematician, was founded in Edinburgh. Among its campuses is one at Merchiston, which houses courses in science, technology, and design.