He also invented the so-called "Napier's bones" and made common the use of the decimal point in arithmetic and mathematics.

Near the time of his matriculation the quality of the education provided by the university was poor, owing in part to the Reformation's causing strife between those of the old faith and the growing numbers of Protestants.

[4] It is believed he left Scotland to further his education in mainland Europe, following the advice given by his uncle Adam Bothwell in a letter written to John Napier's father on 5 December 1560, saying, "I pray you, sir, to send John to the schools either to France or Flanders, for he can learn no good at home".

On the death of his father in 1608, Napier and his family moved into Merchiston Castle in Edinburgh, where he resided the remainder of his life.

[7] On 7 June 1596 Napier wrote a paper Secret inventions, profitable and necessary in these days for defence of this island.

[2] Many mathematicians at the time were acutely aware of the issues of computation and were dedicated to relieving practitioners of the calculation burden.

He invented a well-known mathematical artefact, the ingenious numbering rods more quaintly known as "Napier's bones",[9] that offered mechanical means for facilitating computation.

In addition, Napier recognized the potential of the recent developments in mathematics, particularly those of prosthaphaeresis, decimal fractions, and symbolic index arithmetic, to tackle the issue of reducing computation.

III  The book also has a discussion of theorems in spherical trigonometry, usually known as Napier's Rules of Circular Parts.

[11] His invention of logarithms was quickly taken up at Gresham College, and prominent English mathematician Henry Briggs visited Napier in 1615.

Among the matters they discussed were a re-scaling of Napier's logarithms, in which the presence of the mathematical constant now known as e (more accurately, e times a large power of 10 rounded to an integer) was a practical difficulty.

The computational advance available via logarithms, the inverse of powered numbers or exponential notation, was such that it made calculations by hand much quicker.

Napier may have worked largely in isolation, but he had contact with Tycho Brahe who corresponded with his friend John Craig.

Craig had notes on a method of Paul Wittich that used trigonometric identities to reduce a multiplication formula for the sine function to additions.

The remaining parts can then be drawn as five ordered, equal slices of a pentagram, or circle, as shown in the above figure (right).

Under the influence of the sermons of Christopher Goodman, he developed a strongly anti-papal reading, going as far as to say that the Pope was the Antichrist in some of his writings.

It was written in English, unlike his other publications, in order to reach the widest audience and so that, according to Napier, "the simple of this island may be instructed".

[17] A Plaine Discovery used mathematical analysis of the Book of Revelation to attempt to predict the date of the Apocalypse.

[17] In his dedication of the Plaine Discovery to James VI, dated 29 Jan 1594,[18] Napier urged the king to see "that justice be done against the enemies of God's church," and counselled the King "to reform the universal enormities of his country, and first to begin at his own house, family, and court."

In 1602 the work appeared at La Rochelle in a French version, by Georges Thomson, revised by Napier, and that also went through several editions (1603, 1605, and 1607).

A new edition of the English original was called for in 1611, when it was revised and corrected by the author, and enlarged by the addition of With a resolution of certain doubts, moved by some well affected brethren.

A German translation, by Leo de Dromna, of the first part of Napier's work appeared at Gera in 1611, and of the whole by Wolfgang Meyer at Frankfurt-am-Main, in 1615.

[20] In addition to his mathematical and religious interests, Napier was often perceived as a magician, and is thought to have dabbled in alchemy and necromancy.

[21][22][23] Some of Napier's neighbours accused him of being a sorcerer and in league with the devil, believing that all of the time he spent in his study was being used to learn the black art.

Napier told his servants to go into a darkened room and pet the cockerel, claiming the bird would crow if they were the one who stole his property.

"[12][26] This contract was never fulfilled by Napier, and no gold was found when the Edinburgh Archaeological Field society excavated the castle between 1971 and 1986.

[27][28][29] The development of logarithms is given credit as the largest single factor in the general adoption of decimal arithmetic.

In Finnish and Italian, the mathematical constant e is named after him (Neperin luku and Numero di Nepero).

Napier's father-in-law, Sir James Chisholm of Cromlix, was one of many excommunicated by the General Assembly of the Presbyterian party following the Spanish blanks plot.

Napier sat on the General Assembly that excommunicated the plotters, and petitioned the King James VI and I to enforce the punishment on the plotters, but was ultimately ignored since the King believed the ministers were acting cruelly, and was in favor of pursuing policies of more appeasement.