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Biographies of Mathematicians - John Napier

Napier is best known for his invention of logarithms and for formulas used in solving spherical triangles.

Napier was born in the Tower of Merchiston, now at the center of Napier University’s Merchiston campus, in 1550. At the age of 13 he went to St. Andrews studying at St. Salvator’s College for two years. It is thought he travelled in Europe between 1566-1571 perhaps studying in Paris or Holland but there is no corroborative evidence of this.

He had a son called Archibald to his first wife Elizabeth, who became the first Lord Napier. He also had a daughter called Janet, about whom nothing is known beyond that. In 1572 he married his second wife Agnes Chisholm and they settled on his family estate at Gartness in Stirlingshire, bringing up five more sons and five daughters. Napier died in April 1617 and was buried at St. Cuthbert’s Church in Edinburgh.

In his lifetime he was known as the Marvellous Merchiston, a well-deserved title, for his genius and imaginative vision encompassed a number of fields.

Napier was educated at St Andrews University although he seems to have left without obtaining a degree. He then studied in Europe.

In 1571, Napier returned to Scotland and devoted himself to running his estate and taking part in the religious controversies of the time. He was a fervent Protestant and published, what he considered his most important work, the Plaine Discovery of the Whole Revelation of St. John (1593).
John Napier lived during one of the most interesting periods of Scottish history with Mary Queen of Scots dethroned and the Reformation still bristling at the challenge posed by Roman Catholicism. Science was not separated from religion and philosophy at this stage and scholars were well-versed in all three.

Napier's study of mathematics was only a hobby.

He is best known, however, for his invention of logarithms but other mathematical contributions include a mnemonic for formulas used in solving spherical triangles, two formulas known as Napier's analogies used in solving spherical triangles and an invention called Napier's bones used for mechanically multiplying dividing and taking square roots. Napier also found exponential expressions for trigonometric functions, and introduced the decimal notation for fractions.

Napier's discussion of logarithms appears in Mirifici logarithmorum canonis descriptio in 1614. Unlike the logarithms used today Napier's logarithms are to base 1/e and involve a constant 10[^7]. Napier hoped that his logarithms would save astronomers much time and free them from the "slippery errors" of calculations. Laplace, 200 year later, agreed, saying that logarithms by shortening the labours, doubled the life of the astronomer .

Napier presented a mechanical means of simplifying calculations in his Rabdologiae in 1617.

He described a method of multiplication using rods with numbers marked off on them.

Napier's rods were made of ivory, so that they looked like bones which explains why they are now known as Napier's bones. To multiply numbers the bones were placed side by side and the appropriate products read off.

Other achievements include his revolutionary methods for tilling and fertilizing soil. To defend the country against Philip of Spain he came up with a number of "Secret Inventions" including the round chariot with firepower but offering protection (the tank); an underwater ship (the submarine); an artillery piece which would mow down a field of soldiers (the machine gun).

References:

Rice University, USA
Clarke University, USA
http://www.maxmon.com/1600ad.htm
http://www.astro.virginia.edu/~eww6n/bios/Napier.html
http://www.ualr.edu/~klheller/napier.html

This project was prepared and presented by students Grant Smith and Abbey Smith in 1998.