The Marvellous Merchiston and the Invention that Changed Mathematics
John Napier of Merchiston stands as one of Scotland's most brilliant mathematical minds, a man whose single invention - logarithms - revolutionised scientific calculation for over three centuries. Born into the Scottish nobility at a time of religious upheaval and intellectual awakening, Napier became known as "Marvellous Merchiston", a nickname that reflected both admiration for his mathematical genius and the popular belief that he possessed supernatural powers. While history remembers him primarily as the inventor of logarithms, Napier was also a passionate Protestant theologian, an ingenious inventor of calculating devices, and a man whose eccentricities and secluded lifestyle fuelled local legends of wizardry.
Early Life and Education
John Napier was born on 1 February 1550 at Merchiston Castle, near Edinburgh, the eldest son of Sir Archibald Napier, who would become the 8th Laird of Merchiston. His mother, Janet Bothwell, was the daughter of the prominent politician and judge Francis Bothwell, and the sister of Adam Bothwell, who would later become Bishop of Orkney. Napier was born into privilege and power - his family had owned the Merchiston estate since the 1430s, along with properties at Lennox, Menteith, and a residence at Gartness.
Archibald Napier married Janet Bothwell in 1549 when he was only 15 years old, and John was born the following year. Tragically, John's mother died when he was just 13 years old. Around this time, he was enrolled at St Salvator's College at the University of St Andrews, where the Principal, John Rutherford, took personal care of him. However, Napier's stay at St Andrews was brief, and he left without taking a degree. His uncle, Adam Bothwell, wrote to Napier's father in December 1560 advising that young John should be sent abroad to further his education, possibly to France or Flanders where he could study Greek, a language essential for his growing interest in theology and biblical texts.
Little is known definitively about Napier's time on the Continent, but when he returned to Scotland in 1571 at the age of 21, he had transformed himself into an outstanding mathematician, proficient in both Latin and Greek. The following year, in 1572, he married Elizabeth Stirling, the daughter of James Stirling, 4th Laird of Keir and Cadder, who was himself a noted mathematician. The young couple had two children together, but their happiness was short-lived - Elizabeth died in 1579. A few years later, Napier married Agnes Chisholm, with whom he would have ten more children, eventually raising a family of twelve.
Life at Gartness - The Hermit Mathematician
In 1574, Napier purchased Gartness Castle in Stirlingshire, and it was here that he would spend much of his adult life until 1608, living in relative seclusion and dedicating himself to his twin passions - theology and mathematics. His lifestyle at Gartness was so withdrawn that local people found it peculiar, believing him to be a wizard engaged in occult practices. These rumours were not entirely discouraged by Napier himself, who seemed to enjoy his mysterious reputation.
At Gartness, Napier developed his groundbreaking work on logarithms. According to historical accounts, he worked near the old mill at Gartness, and an interesting detail reveals much about his character and dedication. The constant noise of the waterfall never disturbed his concentration, but the intermittent clacking of the mill wheel would interrupt his train of thought. When deeply engaged in calculations, Napier would sometimes ask the miller to stop the mill entirely so his work would not be disrupted - a testament to the intense focus required for the mathematical innovations he was developing.
The Protestant Firebrand
Before Napier became famous for his mathematical work, he first gained public attention through his fierce Protestant theology. Scotland in the late 16th century was a nation torn by religious strife following the Reformation, and Napier was an ardent and uncompromising Protestant who viewed the Catholic Church with deep suspicion and hostility.
In 1593, Napier published "A Plaine Discovery of the Whole Revelation of St John", a work dedicated to King James VI of Scotland. The book was a comprehensive study of the Biblical Book of Revelation, in which Napier argued that the Pope was the Antichrist and urged the king to take decisive action against Catholics. He wrote urgently to James, declaring: "Let it be your Majesty's continuall study to reforme the universall enormities of your country, and first to begin at your Majesty's owne house, familie and court, and purge the same of all suspicion of Papists and Atheists and Newtrals."
The work proved enormously popular in Protestant Scotland and across Europe, going through multiple editions and being translated into Dutch, French, and German. Ironically, while Napier's theological work was what made him famous during his lifetime, it is rarely read today, whilst his mathematical innovations continue to shape modern science. Napier applied his mathematical skills to biblical prophecy, calculating that the end of the world would arrive in either 1688 or 1700 - predictions that were, thankfully, proven incorrect.
The Revolutionary Invention - Logarithms
Napier's true genius lay in mathematics, though he always considered it merely a leisure pursuit compared to his theological studies. His motivation for developing logarithms came from his interest in astronomy, where he found the calculations involved to be extraordinarily time-consuming and prone to error. Napier set himself the monumental task of simplifying these computations, and he succeeded beyond anyone's imagination.
Beginning around 1594, Napier worked for approximately twenty years developing what he called "artificial numbers" - what we now know as logarithms. The fundamental insight was brilliant in its elegance: by converting multiplication and division into simple addition and subtraction, logarithms made complex calculations dramatically easier. For astronomers, navigators, engineers, and scientists, this was nothing short of revolutionary.
In 1614, Napier published "Mirifici Logarithmorum Canonis Descriptio" (Description of the Marvellous Canon of Logarithms), containing 57 pages of explanatory text and 90 pages of logarithmic tables of trigonometric functions. The work created an immediate sensation in mathematical circles across Europe. The French mathematician Pierre-Simon Laplace would later write that logarithms, "by shortening the labours, doubled the life of the astronomer."
Napier's work caught the attention of Henry Briggs, professor of geometry at Gresham College in London, who was so excited by the invention that he wrote to a friend: "Neper, lord of Markinston, hath set my head and hands a work with his new and admirable logarithms. I hope to see him this summer, if it please God, for I never saw a book which pleased me better or made me wonder more."
True to his word, Briggs made the long and arduous four-day journey from London to Edinburgh in the summer of 1615 to meet Napier. During this visit, and another the following year in 1616, the two mathematicians discussed improvements to the logarithmic system. Briggs suggested modifications that would result in what we now call common logarithms (base 10), making them even more practical for everyday use. Napier agreed to these changes, but his declining health meant that he delegated the massive task of computing new tables to Briggs. Briggs had planned to visit Napier again in the summer of 1617, but Napier died that spring before they could meet again.
Napier's Bones and the Decimal Point
Beyond logarithms, Napier made other significant contributions to mathematics. He invented a calculating device known as "Napier's Bones" or "Napier's Rods" - a set of numbered rods that could be arranged to perform multiplication, division, and the extraction of square and cube roots mechanically. Made from bone, ivory, wood, or metal, these rods were precursors to the slide rule and represented an early step towards mechanical calculation.
Napier also played a crucial role in popularising the decimal point. While decimal fractions had been introduced earlier by the Flemish mathematician Simon Stevin in 1586, Stevin's notation was cumbersome and unwieldy. Napier's systematic use of a point to separate the whole number from the fractional part - appearing frequently in his posthumously published "Mirifici Logarithmorum Canonis Constructio" (1619) - helped establish the decimal notation we use today.
The Wizard of Merchiston
Napier's reclusive lifestyle and brilliant mind gave rise to numerous legends about his supposed magical powers. He was believed by many to be a wizard, and several colourful stories circulated about his abilities. One famous tale concerns a theft from his property. Napier announced he would use his black rooster to identify the thief. He told each of his servants to enter a dark room alone and stroke the bird, claiming it would crow when touched by the guilty party. In reality, Napier had coated the rooster with soot. The innocent servants stroked the bird and emerged with blackened hands, whilst the guilty party, too frightened to actually touch what they believed to be a supernatural creature, came out with clean hands and was thus exposed.
Another incident that enhanced his reputation for wizardry involved pigeons from a neighbour's property that were eating his crops. Napier warned that any pigeons found on his land would be confiscated. The next day, locals witnessed him casually walking about, collecting docile birds and placing them in a sack. The truth was prosaic but clever - he had scattered grain soaked in wine on his property, and the intoxicated birds were easily gathered.
In 1594, Napier was even employed to search for hidden treasure at Fast Castle, entering into a contract with Robert Logan of Restalrig. The contract specified that Napier should "do his utmost diligence to search and seek out, and by all craft and ingine to find out the same, or make it sure that no such thing has been there." The contract was never fulfilled, and modern archaeological excavations between 1971 and 1986 found no treasure.
Inventions of War and Agriculture
Napier's inventive mind extended beyond pure mathematics. In 1596, he wrote a paper entitled "Secret inventions, profitable and necessary in these days for defence of this island", prompted by fears of Catholic Spanish invasion. In it, he described several ingenious military devices: two types of burning mirrors that could set fire to enemy ships at a distance, a special type of artillery projectile, and a metal-plated chariot driven by men inside that could emit "odious smoke and firepower" through small openings - an early concept remarkably similar to modern tanks.
Napier also applied his creativity to improving agriculture on his estates, developing various methods to increase fertility and productivity, though the details of these agricultural innovations have been largely lost to history.
Final Years at Merchiston
In 1608, following the death of his father, Napier and his large family moved from Gartness to the family seat at Merchiston Castle in Edinburgh. He also maintained a property on Borthwick's Close, just off Edinburgh's Royal Mile. During these final years, Napier continued his mathematical work whilst suffering from increasingly poor health, troubled by gout.
Napier died on 4 April 1617 at Merchiston Castle at the age of 67, never living to see the full impact of his invention. He was buried in the kirkyard of St Giles in Edinburgh. Following the loss of that kirkyard to make way for Parliament House, his remains were transferred to an underground vault on the north side of St Cuthbert's Parish Church at the west end of Edinburgh.
Two years after his death, in 1619, his son Robert published his father's second major work, "Mirifici Logarithmorum Canonis Constructio" (Construction of the Marvellous Canon of Logarithms), with additions by Henry Briggs. This work explained the methods Napier had used to calculate his original logarithmic tables.
An Enduring Legacy
John Napier's impact on mathematics and science cannot be overstated. Logarithms transformed the practice of astronomy, navigation, engineering, and all fields requiring complex calculations. For over 350 years, until the advent of electronic calculators in the 1970s, logarithmic tables based on Napier's work were standard equipment in schools, universities, and workplaces worldwide.
The great astronomers Johannes Kepler and Galileo Galilei recognised the revolutionary nature of Napier's work, with Kepler dedicating his 1620 Ephemeris to Napier and congratulating him on his invention. Isaac Newton's mathematical achievements would have been far more difficult without logarithms. As historian E.W. Hobson wrote in 1914, on the 300th anniversary of Napier's tables: "Probably no work has ever influenced science as a whole, and mathematics in particular, so profoundly as this modest little book. It opened the way for the abolition, once and for all, of the infinitely laborious, nay, nightmarish, processes of calculation."
Napier's legacy lives on in numerous ways. Edinburgh Napier University, built around the site of Merchiston Castle, bears his name and educates thousands of students annually. The Neper crater on the Moon honours his memory. In electrical engineering, an alternative unit to the decibel called the "neper" commemorates his work. In several languages, natural logarithms are still named after him - "Logarithme Népérien" in French, "Logaritmos Neperianos" in Spanish and Portuguese. In Finnish and Italian, the mathematical constant e is called "Neperin luku" and "Numero di Nepero" respectively.
A memorial to Napier stands at St Cuthbert's Parish Church in Edinburgh, and his birthplace, Merchiston Tower, remains a prominent landmark on the university campus that bears his name. The tower stands as a fitting monument to a man who, from his secluded castle, changed the course of mathematics and made the complex calculations of modern science possible.
Conclusion
John Napier was a man of paradoxes - a brilliant mathematician who considered his work merely a hobby, a devout Protestant who was rumoured to practice the occult, a reclusive thinker whose ideas transformed the world. Whether calculating the date of the apocalypse, inventing war machines, or developing the mathematical tools that would unlock the heavens, Napier approached every challenge with the same fierce intelligence and creativity. History has judged which of his contributions truly mattered, and today, more than four centuries after his death, "Marvellous Merchiston" remains one of Scotland's greatest intellectual exports, a testament to the power of patient, focused genius to change the world.
