### John Napier Background

John Napier was born in Edinburgh, Scotland, into the Scottish nobility. Since his father was Sir Archibald Napier of Merchiston Castle, and his mother, Janet Bothwell, was the daughter of a member of Parliament, John Napier became the laird (property owner) of Merchiston. Napier's father was only 16 when his son, John, was born. As was the practice for members of nobility, Napier did not enter school until he was 13. He did not stay in school very long, however. It is believed that he dropped out and traveled in Europe to continue his studies. Little is known about these years, where or when he may have studied.

In 1571, Napier turned 21 and returned to Scotland. The following year he married Elizabeth Stirling, daughter of Scottish mathematician James Stirling (1692-1770), and bat a castle at Gartnes in 1574. The couple had two children before Elizabeth died in 1579. Napier later married Agnes Chisholm, with whom he had ten children. On the death of his father in 1608, Napier and his family moved into Merchiston Castle, where he lived the rest of his life.

Napier's father had been deeply interested and involved in religious matters, and Napier himself was no different. Because of his inherited wealth, he needed no professional position. He kept himself very busy by being involved with the political and religious controversies of his time. For the most part, religion and politics in Scotland at this time pitted Catholics against Protestants. Napier was anti-Catholic, as evidenced by his 1593 book against Catholicism and the papacy (office of the pope) entitled *A Plaine Discovery of the Whole Revelation of St. John*.

This attack was so popular that it was translated into several languages and saw many editions. Napier always felt that if he attained any fame at all in his life, it would be because of that book.

### Inventor

As a person of high energy and curiosity, Napier paid much attention to his landholdings and tried to improve the workings of his estate. Around the Edinburgh area, he became widely known as "Marvellous Merchiston" for the many ingenious mechanisms he built to improve his crops and cattle. He experimented with fertilizers to enrich his land, invented an apparatus to remove water from flooded coal pits, and bat devices to better survey and measure land. He also wrote about plans to bad elaborate devices that would deflect any Spanish invasion of the British Isles. In addition, he described military devices that were similar to today's submarine, machine gun, and army tank. He never attempted to build any of the military instruments, however.

Napier had a great interest in astronomy. which led to his contribution to mathematics. John was not just a stargazer; he was involved in research that required lengthy and time-consuming calculations of very large numbers. Once the idea came to him that there might be a better and simpler way to perform large number calculations, Napier focused on the issue and spent twenty years perfecting his idea.

The result of this work is what we now call logarithms.

Napier realized that all numbers can be expressed in what is now called exponential form, meaning 8 can be written as 23, 16 as 24 and so on. What make logarithms so useful is the fact that the operations of multiplication and division are reduced to simple addition and subtraction. When very large numbers are expressed as a logarithm, multiplication becomes the addition of exponents.

Example: 102 times 105 can be calculated as 10 2+5 or 107. This is easier than 100 times 100,000.

Napier first made this discovery known in 1614 in his book called 'A Description of the Wonderful Canon of Logarithms.' The author briefly described and explained his inventions, but more importantly, he included his first set of logarithmic tables. These tables were a stroke of genius and a big hit with astronomers and scientists. It is said that English mathematician Henry Briggs was so influenced by the tables that he traveled to Scotland just to meet the inventor . This lead to a cooperative improvement including the development of Base 10.

Napier was also responsible for advancing the notion of the decimal fraction by introducing the use of the decimal point. His suggestion that a simple point could be used to separate whole number and fractional parts of a number soon became accepted practice throughout Great Britain.

### Contributions to Math

Written Works:

- A Plaine Discovery of the Whole Revelation of St. John. (1593)
- A Description of the Wonderful Canon of Logarithms. (1614)
- Construction of Logarithms ( 1619)

### Famous Quote:

"Seeing there is nothing that is so troublesome to mathematical practice.... than the multiplications, divisions, square and cubical extractions of great numbers, which besides the tedious expense of time are... subject to many slippery errors, I began therefore to consider [how] I might remove those hindrances."

---Excerpt from A Description of the Wonderful Canon of Logarithms.

Edited by Anne Marie Helmenstine, Ph.D.