John Napier | Biography

The history of mathematics might be a very different story were it not for the accomplishments of Scottish mathematician John Napier. Born near Edinburgh in 1550, Napier held the title of Laird of Merchiston. Educated in France, Napier spent much of his free time studying mathematics. Very involved in Protestantism, Napier published a book in 1594 entitled Plaine Discovery of the Whole Revelation of St. John, an anti-Catholic commentary and the first Scottish work on biblical interpretation. Preparing for the possibility of war against Spain, Napier spent considerable time thinking of devices to combat a Spanish invasion, including plans for burning mirrors, armored war chariots and submarines. When news of Napier's ideas leaked out, he gained a reputation for dealing in black magic, or at the very least, of being a bit unbalanced. Fortunately for the rest of the world, the need for Napier's war devices never came about, and he instead turned his talents toward simplifying mathematical calculations. One story of his eccentricity involves Napier's method of identifying a servant who was stealing from him. He told his servants that his black rooster would identify the thief. Each servant was sent alone into a darkened room to pet the rooster on the back. Napier had coated the back of the rooster with soot, and the guilty servant came out of the room with clean hands, being unwilling to touch the rooster.

Wishing to remove the drudgery from mathematical calculations, yet improve their accuracy, Napier experimented with different methods of expressing numbers. In 1594 he discovered a new method of calculating using exponential, or compressed numbers. When using exponents, 4 can be written as 2₂ (meaning 2 multiplied by itself), 8 as 2₃ (meaning to multiply by 2 three times), and so forth. Once written in such a format, multiplication and division could be carried out by adding or subtracting the exponents. Napier spent the next twenty years working on tables of logarithms, which allowed numbers to be written as exponents, and published the completed tables in 1614. The tables had a tremendous impact on astronomers, navigators and others who benefited greatly from the simplified process of mathematical calculation. In the next several years, Napier took his concept one step further and invented several automatic calculating devices. One such device, a small box containing plates to perform multiplication was known as the promptuary of multiplication. In 1617 Napier placed his logarithmic tables on a device containing cylinders made of wood, ivory or bone, which became known as Napier's bones, (although Napier preferred to call the device "rabdologia"). Napier's bones became an important basis for future calculators and helped streamline mathematical calculations even further. During the twenty years that Napier spent computing and drawing up the logarithmic tables, he produced another important concept--the use of the decimal point, or decimal notation in arithmetic. Napier's logarithmic tables remained unchanged for nearly a century, enjoying widespread use and popularity. Their only modification being the change to base ten, suggested to Napier by Henry Briggs in 1616. Napier died in 1617 at his home in Merchiston Castle. Although Napier regarded his most important achievement to be in the area of religious reformation, his discovery of logarithms played a much larger role in history.