The site on which St Mary’s College now lies is arguably the first piece of property owned by the University of St Andrews. Over six centuries ago, in 1419, Robert of Montrose, rector of Cults, Fife, granted the six-year-old University of St Andrews a building to found “a college of theologians and artists”. This building would go on to become St John’s College, a place for pedagogical study in arts and theology.

Many other St Andrews Colleges went on to be formed within St Andrews before Archbishop James Beaton founded St Mary’s College in the old pedagogy site between 1537 and 1539. Although St Mary’s College was streamlined specifically for the study of Theology since 1579, it has also been home to a rich history in Mathematics.

The Work of James Gregory in St Andrews

Mathematician and astronomer James Gregory (1638-1675) was the first Regius Professor of Mathematics at St Andrews, appointed by Charles II, King of Scotland. His father, Reverend John Gregory, had studied theology at St Mary’s College.

As Gregory was not attached to a specific College in St Andrews, he used the Upper Hall of the University’s library (King James Library) near St Mary’s College as an observatory. There, he also developed one of the most accurate meridian lines nearly 200 years prior to the Greenwich Meridian’s establishment. The line runs roughly 12 minutes behind GMT. He aligned a bracket in one of the windows overlooking the St Mary’s quadrangle with a pillar about 2 miles away which indicated the southern end-point of the meridian. The pillar and bracket were only three one-thousandths of a degree off in longitudinal alignment, a remarkable feat of precision given measurement apparatus at the time. In 2014, a brass meridian bisecting the pavement in South Street was unveiled in commemoration of the line.

Along with his contemporaries Gottfried Wilhelm Leibniz and Sir Isaac Newton (with whom he was quite cordial), Gregory independently developed the study of modern calculus. Gregory constructed the earliest recorded proof of the fundamental theorem of calculus (in his book Geometriæ pars universalis) and had utilized the chain rule prior to Leibniz’s writing on the subject. However, Gregory’s status as a co-inventor of calculus is often underrecognized. This is due to a number of factors including Gregory’s untimely demise at only 37 as well as the costliness and short supply of paper in St Andrews at the time which lead him to sometimes write his work on random scraps of paper. Another likely reason was the fact that publicly laying claim to the discovery of new mathematical techniques was often the cause of acrimonious disputes within the mathematical community, and could risk severe reputation damage (Gregory had already been involved in arguments with Christian Huygens over another mathematical issue to do with his book Vera circuli et hyperbolae quadratura).

Gregory also designed the first reflecting telescope. Gregory made concerted efforts to create a full-fledged observatory at the University. Although he collected many precious mathematical instruments, he left before the observatory reached its full potential. Had this happened, it would have been the first official observatory in Britain. Many of Gregory’s rare possessions are still housed in St Andrews’ Senate Room.

Theology and Mathematics in St Andrews

St Mary’s College has had theologians over the years who played notable roles in the field of Mathematics at St Andrews.

Clergyman Robert Haldane (1772 – 1854) became the sixth successor to James Gregory as the Regius Professor of Mathematics in 1809. Despite being considered as having possibly the best scheme for “mathematical drilling” in Scotland at the time, Haldane’s appointment to Regius Professor of Mathematics was a matter of controversy which received criticism from some of his contemporaries. This was due to the political situation at the time which typically saw high educational positions monopolized by the Church of Scotland. It was generally believed that St Andrews mathematicians James Ivory and William Wallace were far more suitable candidates. Perhaps most notable among the critics of his appointment was former St Andrean John Leslie, who first created artificial ice and produced the first accurate explanation of capillary action. Haldane’s predecessor as principal of St Mary’s College, Professor George Hill, was also a subject of criticism by Leslie for his role in the Church’s monopolization of education.

John Playfair (1748 – 1819) was a Scottish mathematician and parish minister who attended St Mary’s College. Unlike Haldane, however, he was a friend of Leslie. Playfair made great strides in geology and mathematics, his greatest contributions arguably being his developments in the theory of uniformitarianism (the idea that our geological past can be explained by current geological events) and his standardization of many of Euclid’s works. The Playfair axiom is one of Playfair’s most well-known works and was a reformulation of Euclid’s parallel postulate. At the time, geometrical approaches to mathematics were generally favoured by Great Britain, in contrast with the more algebraic style used by their continental counterparts. Playfair, however, often found that many British mathematical works lacked a certain simplicity that could be gained when utilizing some algebra. In 1795, Playfair published Elements of Geometry, a republication of the main British geometry text of the 1700’s. This text was a English translation and adaptation of Euclid’s original works. Playfair wrote a concise version of Euclid’s postulate, which was 38 words shorter than the previous author’s phrasing. Playfair wrote the following:

“two straight lines, which intersect one another, cannot be both parallel to the same straight line”.

It should be noted that while St Mary’s College has long been dedicated to the study of Divinity, it contains the recently-established Logos Institute , which is committed to “scholarship that reflects a concern for: transparency; simplicity in expression; clear, logical argumentation; and rigorous analysis.”, values that all good mathematicians strive towards. St Andrews has also hosted public lectures, called the “James Gregory Lectures”, dedicated to exploring the relationships between science and religion.