John Napier was born into a wealthy family, as his father was Master of the Mint in Scotland. Napier entered St. Andrews University at the age of 13, though he left to study in Europe before completing a degree. It is likely that he studied at the University of Paris, and perhaps Italy and the Netherlands as well. Napier took part in the religious controversies of the time. He had been a fanatical Protestant from his days as an undergraduate at St Andrews.

He married, built himself a castle, and took over the job of running his estate. This task he took very seriously and, being a great genius as an inventor, he applied his skills to these tasks. He approached agriculture in a scientific way and he experimented with improving the manuring of his fields. Napier's study of mathematics was only a hobby, and in his mathematical works he writes that he often found it hard to find the time for the necessary calculations between working on theology.

He is best known for his invention of logarithms. Napier's discussion of logarithms appears in a text in 1614. Two years later an English translation of Napier's original Latin text was published. Unlike the logarithms used today, Napier's logarithms are not really to any base although in our present terminology it is not unreasonable to say that they are to base 1/e. His notation was Nap.log x. Briggs had suggested to Napier that logs should be to base 10, and Napier suggested in return that Nap.log 1 should be zero. Briggs later made tables of these. Napier also presented a mechanical means of simplifying calculations in 1617. He described a method of multiplication using "numbering rods" with numbers marked off on them. To multiply numbers the bones were placed side by side and the appropriate products read off. They were made of ivory, and because they looked like bones, they are now known as Napier's bones.

Napier's 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, exponential expressions for trigonometric functions, and the decimal notation for fractions.

It would be surprising if a man of such great an intellect as Napier did not appear rather strange to his contemporaries and, given the superstitious age in which he lived, strange stories began to circulate. Many traditions suggest that Napier was in league with the powers of darkness.

Napier, however, will be remembered for making one of the most important contributions to the advance of knowledge. It was through the use of logarithms that Kepler was able to reduce his observations and make his breakthrough which then in turn underpinned Newton's theory of gravitation. Laplace, 200 year later, said that logarithms, by shortening the labors, doubled the life of the astronomer.