John Napier: Champion of the Decimal Point and an Early Calculator

Read about the fascinating world of 16th-century Scottish mathematician, John Napier, and his critical discoveries.

By Lillie Therieau

John Napier was a 16th-century Scottish mathematician who made several important discoveries that facilitated easier and faster computations. He discovered logarithms, popularized the use of the decimal point, and invented his own mechanical system of calculation, called Napier’s bones.

However, John was far ahead of his time. His Scottish neighbors did not appreciate his cool head and rational approach to science and math. They believed that he was a magician in league with the Devil!

Learn more about John Napier’s unique approach to life in late-medieval Scotland, as well as the influential discoveries that rose out of his “hobby” of recreational mathematics.

John Napier was born in 1550, in Edinburgh, Scotland. His father was a noble and lord of Merchiston Castle, while his mother was the daughter of a renowned Scottish politician and judge. John was born into nobility, as he would one day inherit Merchiston Castle from his father. As a young boy, he was privately tutored at home. At the age of 13, he was enrolled at a local university. However, the quality of the education was poor, as Scotland was mired in conflict between the Reformation Protestants and traditionalists. John decided he had to leave Scotland to complete his education in mainland Europe.

Little record exists about where John may have traveled for school, but it is known that he returned to Scotland in 1571 after finishing his education. He purchased a castle of his own in the hamlet of Gartness, where he lived with his wife Elizabeth. There he focused on agriculture, tending to his grounds, and new inventions that might make the former tasks easier. He experimented with different fertilizers and manures to boost his crop yields.

However, his scientific discoveries and experimentation did not endear him to locals, who believed he was a magician and in league with the Devil. They were convinced that all of the time he spent reading in his study was actually time he spent communing with Satan and were terrified of his penchant for nightly walks around his grounds in a nightgown. When John removed the pigeons from his estate to prevent them from eating his grain, there was an uproar. He laid out alcohol-laced grain for them to eat, catching them when they had become too drunk to fly. To outsiders, the plan must have seemed like witchcraft!

John and his wife Elizabeth had two children before Elizabeth died tragically in 1579. John quickly remarried Agnes Chisholm, and the two had ten more children. In 1608, John’s father died, and he and his family moved into Merchiston Castle. He would live there primarily for the rest of his life, though he occasionally traveled back to Gartness or another piece of property he owned in the city of Edinburgh.

John was involved in mathematics and theology throughout his life. He also contributed a notable paper detailing new inventions in maritime defense for Scotland in 1596. Personally, John was a passionate Protestant, committed to the study of theology. As a member of court and a religious academic, he was also involved in heated negotiations with the new King James IV of Scotland to steer him and the country away from the Catholic Church. John Napier died from gout in 1617 and was buried in Edinburgh.

John Napier’s Critical Mathematical Discoveries

John was primarily a theologian, and his mathematical work was a hobby that he enjoyed. However, his simple hobby is responsible for several critical discoveries that shaped the future of mathematics. He is credited with discovering natural logarithms and beginning the common usage of the decimal point in arithmetic. He also invented an early calculation aid, called Napier’s bones, which assisted in complex calculations.

A logarithm is the inverse function of exponentiation (I.e. b^n or b to the nth degree). A logarithm of the variable x is the exponent (n) to which the base (b) must be raised to get to x. Therefore, x = b^n. For instance, 9 = 3^n when n = 2. Logarithms are an important way to simplify calculations and were immediately put to use by mathematicians, navigators, engineers, and surveyors to do complex calculations that demanded highly accurate results with more ease and speed.

John was also responsible for the widespread use of the decimal in mathematics and arithmetic. Though it had been invented by Simon Stevin in 1585, John was the first to embrace the system and show how it would make arithmetic easier. Finally, John also invented Napier’s bones, a system to make division and multiplication easier. Napier’s bones were based on Fibonacci’s lattice multiplication system, which he transformed into a physical tool.

Napier’s Bones calculating table from around 1680, via Wikimedia

The device includes a baseboard with a rim marked with the numbers 1-9 on the left edge. The user places rods made of bone, metal, or wood on the board. Each rod has two or four faces, and each face is divided into 9 squares. The squares hold a simple multiplication table, from 1-9 for each single-digit number. Different amounts of rods are needed depending on the size of the numbers being multiplied or divided. For example, 10 four-sided rods are needed to multiply 4-digit numbers, while 20 four-sided rods are needed for 8-digit numbers, and so on. This system alleviated the time-consuming burden of doing massive calculations by hand, allowing the user to simplify the process mechanically. It’s a precursor of later calculation methods and machines.

John Napier’s Influence and Legacy

Logarithms immediately became important in math and science, empowering generations of thinkers to come. Many subsequent mathematicians across Europe continued John’s work and used his discoveries to launch their own.

In French and Portuguese, logarithms are still named after John Napier. There is an alternative unit to the decibel used in electrical engineering called the neper, and a crater on the Moon called the Neper crater. Finally, John’s hometown of Edinburgh is home to Edinburgh Napier University. The University’s campus includes John’s home estate of Merchiston Castle.

The Brilliant Lives of Famous Mathematicians

This article is the fourteenth in our series exploring the lives and achievements of famous mathematicians throughout history. (Our last article was about the Swiss mathematicians who came out of the Bernoulli family!)

Through the lives of these brilliant folks, we hope you’ll find connections, inspiration, and empowerment.

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