John Napier: Biography, Contributions And Works

John Napier (1550 – 1617) was a Scottish mathematician and theological writer known for having originated the concept of logarithms as a mathematical device to aid in calculations.

He also invented the so-called “Napier bones”, used to multiply mechanically by dividing and taking square and cube roots. In addition, the use of the decimal point was frequent in arithmetic and mathematics.

Other mathematical contributions were the mnemonics for the formulas used in solving spherical triangles, as well as finding exponential expressions for trigonometric functions.

On the other hand, he had deep interests in astronomy and religion; in fact, he was a staunch Protestant. Through his work entitled Revelation of Saint John, he was able to be frank and uncompromising with the Catholic Church and influenced the contemporary political actions of the Church.

Napier managed to intervene in the change of the Scottish religious situation due to the concern that Felipe II of Spain could invade Scotland. Through his work, Napier managed to gain a reputation not only in Scotland, but also in the rest of Western Europe.


Early years

John Napier, also called Napier Neper, was born in 1550 at Merchiston Castle, near Edinburgh, Scotland. However, there are no records of the exact date of his birth.

He was the son of Scottish landowner Sir Archibald Napier and his mother Janet Bothwell, daughter of politician and judge Francis Bothwell and sister of Adam Bothwell who later became Bishop of Orknet. His father was only 16 when John Napier was born.

As a member of the nobility at the time, he received private tutoring and formal education classes at age 13 until he was sent to St. Salvator’s College in St. Andrews.

However, it is believed that he dropped out of university in Scotland to travel to continental Europe to continue his studies. Much of its activity in those years is unknown.

It is believed that his uncle Adam Bothwell wrote a letter to his father suggesting that he send him to France or Flanders to continue his studies, which is perhaps why Napier made the decision to do so.

Although there is no knowledge of how he acquired his training in mathematics, it is believed that on his trip to continental Europe he obtained his preparation in this area. You have probably studied at the University of Paris and also spent time in Italy and the Netherlands.


In 1571, Napier returned to Scotland and three years later bought a castle in Gartness at just 21 years old. Most of the properties of his father’s family were transferred to him in 1572.

Napier was the one who began to make the arrangements for his marriage, so that same year he managed to marry Elizabeth, 16, daughter of James Sterling of the Sterling clan.

Napier had his first two children with Elizabeth. Then in 1574, while at Gartness he dedicated himself to managing the properties. In addition, he approached agriculture in a scientific way and experimented with the improvement of compost.

He engaged in mathematical research during his spare time as well as actively participating as an ardent Protestant. The religious controversies of the time often hampered his scientific activities.

After the death of his wife Elizabeth, Napier married Agnes Chisholm, with whom he had ten more children.

Church and theology

Under the influence of the sermons of the English clergyman, Christopher Goodman, he developed a strong reading against the Pope. In addition, he used the Book of Revelation, by means of which he tried to predict the Apocalypse.

In 1593 he published the work entitled The Discovery of all the Revelation of Saint John ; a religious work written with the intention of influencing contemporary political events. The text has been considered one of the most relevant works in Scottish ecclesiastical history.

On the other hand, James VI of Scotland hoped to succeed Elizabeth I to the English throne and it was suspected that he had sought the help of the Catholic Philip II of Spain to achieve this end.

Napier was a member of the general assembly of the Scottish Church, so on several occasions he was appointed to address the Scottish king regarding the welfare of the church.

In January 1594, Napier wrote to the king a letter that forms the dedication of his Revelation of Saint John . In this sense, he advised the king to reform the universal enormities of his country, to start with his own house, family and court, through the phrase: “that justice be done against the enemies of the church of God.”

Mathematical works

Napier devoted most of his free time to the study of mathematics and in particular to methods to facilitate computing. The greatest of these logarithms is associated with its name.

In 1594, he began to work on logarithms, gradually developing his computational system. Using this, roots, products, and coefficients could be quickly determined from tables showing powers of a fixed number used as a base.

Much of Napier’s work on logarithms appears to have been done while he lived at Gartness; in fact, there are references that state that when he started to carry out his calculations, the noise of the mill that was near his house disturbed his thoughts and did not allow him to concentrate.

Finally, in 1614 he discussed logarithms in the text entitled A Description of the Wonderful Table of Logarithms, which he published first in Latin and later in English.

The prominent English mathematician Henry Briggs visited Napier in 1615 to work together on a revised table, which made calculations by hand much faster and easier. In this way logarithms found application in various fields, including astronomy and other areas of physics.

Last years

After his father’s death, Napier moved to Merchistin Castle in Edinburgh with his family. There he resided until the last day of his life.

In 1617, he published his last work, entitled Rabdología. In it he discovered an innovative method of multiplication and division with small rods in a device that became popular, known as “Napier’s bones.”

After publishing his work, he died on April 4, 1617 at the age of 67. He died under the effects of gout; a type of arthritis due to excess uric acid in the body.

In addition to his mathematical and religious interests, it is believed that Napier was often perceived as a kind of magician and that he dabbled in the world of alchemy and necromancy; Furthermore, it is believed that he was involved in a treasure hunt.



The contributions to this powerful mathematical invention were contained in two treatises: Description of the wonderful canon of logarithms published in 1614 and Construction of the wonderful canon of logarithms, published two years after his death.

Napier was the first who coined the term from the two ancient Greeks “logos”, which means proportion and “arithmos” which means number, which together form the word “logarithm”.

For the Scotsman, logarithms were designed to simplify calculations, especially multiplication, such as those needed in astronomy, dynamics, and other areas of physics.

Logarithms transform multiplication into addition and division into subtraction, so that mathematical calculations are simpler.

Napier is the founder of what is now known as the “natural logarithm”; the term is often used to mean the “natural logarithm”.

Napier Bones

Many of the mathematicians of the day were aware of computational problems and were dedicated to relieving practitioners of the computational burden; in this sense, Napier helped with computing.

The Scotsman succeeded in inventing a manually operated mathematical artifact (the numbering bars), better known as “Napier’s bones” or “Neperian abacus”, which offered mechanical means to facilitate mathematical calculation.

The artifact contains multiplication tables embedded in the bars, so that the multiplication can be reduced to addition and division to subtraction, so that the work is easier. The most advanced use of rods can even be to extract square roots.

The Napier artifact generally includes a base plate with a rim on which the person places the Napier rods within the rim to perform multiplication or division. The left edge of the board is divided into 9 squares (with numbers from 1 to 9).

Napier rods consist of strips of wood, metal, or heavy cardboard; on the other hand, Napier’s bones are three-dimensional, square in cross-section with four different rods engraved on each. The set of such bones could be included in a case.

Spherical trigonometry

John Napier also discussed theorems on spherical trigonometry, which later became known as Napier’s Rules of Circular Pieces .

Napier was able to reduce the number of equations used to express trigonometric relationships from 10 to 2 general statements. Certain trigonometric relationships, Napier’s analogies, are also attributed to him, although the English mathematician Henry Briggs apparently participated in them.

Although the origins come from Greek and Islamist mathematics, Napier and other authors later gave an essentially complete form to the concept. Spherical trigonometry is important for calculations in astronomy, geodesy, and navigation.

Trigonometry deals with the relationships between the trigonometric functions of the sides and the angles of spherical polygons (more specifically spherical triangles) defined as a series of large intersecting circles on the sphere.


Discovery of the entire Revelation of Saint John

The work entitled Discovery of the entire Revelation of Saint John was written by John Napier in the year 1593, dedicated directly to King James VI of Scotland. Through this work, Napier became more involved in the political and religious life of the time.

This was Napier’s first job leading to a reputation in Scotland and on the continent. It was reissued more than thirty times and translated into several languages.

This work was, in part, a response to the threats of King Felipe II of Spain with the intervention in the British Isles. For this reason, Napier thought that the best way to avoid this event would be through a change in the religious conditions of Scotland, so that his interest had been the king of the country himself.


In 1617 a treatise in Latin entitled Rabdology by John Napier was published in Edinburgh . The book makes a detailed description of the devices to help and facilitate the work of arithmetic calculations.

Napier explains in his work that the devices themselves do not use logarithms, but are tools to reduce multiplication and division in natural numbers to simple addition and subtraction operations.

The second device explained in the work was a message system or “store of meanings” for its translation into Latin and consisted of a set of strips that could multiply multi-digit numbers more easily than bones.

To explain the third device he used a chessboard as a grid and counters that move on the board in order to perform binary arithmetic.

Napier’s intention to publish this treatise was the motivation for the manufacture of his invention, since the bones were easy to manufacture and to use. However, the time indicator was never used because it was believed to be too complex to manufacture.

The computing devices in Rabdology were overshadowed by his work on logarithms; they turned out to be more useful and widely applicable. Despite this, these devices are examples of Napier’s ingenious creations.


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  3. John Napier, Portal University of St Andrews, Scotland, (nd). Taken from
  4. John Napier, Famous Scientists Portal, (nd). Taken from
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