John Napier: A St Andrean Polymath

Our latest #onthisday blog post comes from volunteer blogger, Glenn Mills, who writes about the world-renown mathematician and St Andrews alumnus, John Napier, who died exactly 401 years ago today.

On the 4th April 1617, the Scottish mathematician John Napier died in his home at Merchiston Castle. Famous for his invention of logarithms and his improvement of decimal notation, Napier stands as an embodiment of the early modern Scottish intelligentsia. Yet, for all his scientific renown, Napier was also a consummate Latinist, a prolific writer of theology and a vehement exponent of Protestantism. More than a scientist, Napier was a polymath in the widest possible sense.


Born in 1550, the first son of Sir Archibald Napier and Janet Bothwell, Napier spent the formative years of his life in Scotland where he enjoyed a noble upbringing. In 1563, at the age of thirteen, he enrolled at the University of St Andrews, where his name appears in the matriculation roll of St Salvator’s College. Here, under the supervision of a master, students would engage in weekly civilized debates on theological matters; a practice which Napier embraced with great enthusiasm. His academic prowess is attested by Mark Napier who, in his Memoirs of John Napier (1834), asserts that the precocious student was ‘able to keep his own… amid the gladiatorship of intellect affected by his youthful competitors’.

This period also marked the point at which Napier adopted the Protestant cause. In the preface to his exegetical commentary, A Plaine Discovery of the Whole Revelation of St John (1593), he expresses his admiration for his St Andrean teacher ‘Maister Christopher Goodman’, a reforming clergyman and Marian exile who preached against ‘the blindness of Papists’ (Memoirs, 87). In the same work, he would employ militant and vitriolic language in his condemnation of Catholicism, warning that those who continued in the creed would ‘be tormented eternallie in the bitter fulphurious fire of hell’. So, Napier was as much a theological reformer as he was a scientific innovator.

Alas, Napier’s time at St Andrews was to be short-lived. At some point before 1566, following the advice of his uncle, Adam Bothwell, who asserted that ‘he can leyr na guid at hame’, Napier abandoned his studies at St Andrews and travelled to the continent where he continued his intellectual pursuits. However, his activity during this period is rife with uncertainty. George Mackenzie, writing over a century later, recounts that Napier ‘stayed for some years in the Low Countries, France and Italy’, before returning to his ‘Native Country’. Where exactly he studied during his time abroad is unclear but the University of Paris has been conjectured as a possibility.  This is certainly a likely possibility, especially given the amicable political relations between Scotland and France at the time. Even so, little can be said with certainty other than that Napier acquired something of the ‘study abroad’ experience.

Napier returned to Scotland no later than 1572 when he married Elizabeth Stirling, with whom he had two children, Archibald and Jane. Following Elizabeth’s death in 1579, Napier got remarried to Agnes Chisholm who bore five sons and five daughters. Despite a less-than-modest family life and his various duties towards his many estates, Napier still found time to pursue his scientific and technological interests. In 1598, he patented an agricultural innovation which involved the manuring of land with salt. Another invention featured a revolving screw and axle used for the draining of mines. More surreal, perhaps, is a document in his Memoirs which contains ‘blue prints’ for an array of military devices. One in particular stands out: ‘a round chariot of mettle made of the proofe of dooble muskett’; in effect, a precursor to the modern tank. Yet, undoubtedly where Napier’s ingenuity was most profound was in his contributions to the field of mathematics. In 1614, he published his Mirifici logarithmorum canonis descriptio in which he propounds his theory of logarithms; a transformative idea which allowed tedious multiplications and divisions to be performed by simple additions and subtractions. Such was the popularity of Napier’s innovation that, within a decade or so, his tables of logarithms became a standard possession among students of mathematics.

A similar calculating device, Napier’s Bones, used the Lattice multiplication method devised by Fibonacci to reduce multiplication to addition and division to subtraction, while more advanced use could extract square roots. Perhaps most importantly, Napier inaugurated the system of decimal notation to which we are now accustomed. Building on the work of the Flemish mathematician Simon Stevin, who first conceived of the notion of distinguishing integers from fractions, Napier simplified and standardised this system by implementing the decimal separator.


When Napier died at the age of sixty-seven, he left behind an intellectual heritage that would change the face of modern mathematics. Today, his remains are interred at the kirkyard of St Giles where an inscription reads: ‘In this place is buried the body of John Napier who, by his marvellous invention of logarithms, won for himself the everlasting remembrance of posterity’. His story is an enduring testament to the intellectual brilliance that characterised (and continues to characterise) the University of St Andrews and its student body.


Brian Rice, Enrique González-Velasco and Alexander Corrigan, The Life and Works of John Napier (Cham, 2017).

Mark Napier, Memoirs of John Napier of Merchiston: his lineage, life, and times, with a history of the invention of logarithms (Edinburgh: London, 1834). Available electronically at <;.

George Molland, ‘John Napier of Merchiston’, Oxford Dictionary of National Biography (2010). Available electronically at <;.

 by Glenn Mills.


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