Mathematics at Aberdeen 1

Betty Ponting published a two-part article on the history of Mathematics at Aberdeen in The Aberdeen University Review. Both parts appeared in volume XLVIII (1979-80), the first part on pages 26-35 and the concluding part on pages 162-176. We give a version of the article below. We have divided the article into four web pages. On this page we give the first part of the first of the two articles. Here are links to the other parts:

Mathematics at Aberdeen, Part 2
Mathematics at Aberdeen, Part 3
Mathematics at Aberdeen, Part 4

Developments, Characters and Events, 1495-1717

The University in Old Aberdeen

In 1495 Pope Alexander VI issued a Bull for the erection of a university in Aberdeen to supply much needed culture for the remote parts of northern Scotland. The University, based on those at Paris and Bologna, was to be under the control of the Roman Catholic Church with Bishop Elphinstone and his successors in the office of Chancellor. The Foundation Charter published in 1505 provided for four faculties, Arts, Theology, Law and Medicine. Initially there were only thirty-six members, thirteen of them bursars in Arts. These received financial support from bursaries, and thus the University was from the beginning open to students from poor homes. They were taught by regents, Divinity students who were to teach for a maximum of six years. As in the other universities of Europe, the teaching was dominated by the Logic, Theoretical Physics and Metaphysics of Aristotle. A regent would take his class through its entire course. The small amount of Mathematics given would probably include a little Arithmetic, the Sphere and Astronomy. Arithmetic was needed to calculate dates of Church festivals, the other two for navigation. De Sphera Mundi by Sacrobosco, a thirteenth-century mathematician, was a standard textbook. This was a treatise on the terrestrial and celestial spheres based on the Ptolemaic system. It finished with the motions of the planets and causes of eclipses and was used as an introduction to astronomy.

In the early years of the sixteenth century the University flourished. A new constitution was introduced in 1529 under Bishop Dunbar and the numbers increased to forty-two, but after his death standards and discipline rapidly declined. A visitation, headed by the rector Alexander Galloway in 1549, found attendance by both teachers and taught unsatisfactory and the buildings neglected. Recommendations included examination of bursars by the Principal and regents before entry and a requirement that each regent should take his class through the Arts course in three and a half years. He should teach Logic in the first year, Physics, Natural Philosophy and the Treatise on the Sphere in the second. The remaining one and a half years were to be devoted to Arithmetic, Geometry, Cosmography and Moral Philosophy. During the upheavals of the Reformation the numbers dropped so that by 1562 there were only about fifteen or sixteen members. The Principal and four of his colleagues were deprived of their offices in 1569 for refusing to sign the Confession of Faith, required by the Protestant General Assembly.

The new foundation

A section on higher education in the First Book of Discipline, produced by the General Assembly of 1562, recommended reform of university curricula to include a wider spread of subjects and more Mathematics, but changes came very slowly. Aberdeen's first post Reformation principal, Alexander Arbuthnot, appointed in 1569 was in favour of the new ideas. He became a friend and supporter of the famed Andrew Melville who led the university reform movement in Scotland. Arbuthnot was a man of great ability, 'In all sciences expert: a good poet, mathematician, philosopher, theologue, lawyer and in medicine skilful', but he was unable to make any headway against the traditionalism of the majority of the masters at King's College.

A Parliamentary Commission of 1578 reported three years later on a new foundation for Aberdeen. This scheme, which aimed at a complete reorganization, was also considered and approved by a Commission of the General Assembly set up in 1582. The offices (established at the foundation) of Canonist, Civilist and Mediciner were to be abolished. The Arts curriculum was to be widened with greater emphasis on Arithmetic and Geometry and to include teaching of Greek, Latin, Hebrew, Physiology, Geography, Astronomy and History, whilst Philosophy played a more minor role. A major reform was the introduction of more specialized teaching, by requiring each master to take a particular year of the course.

The plan met with bitter opposition from the University. An appeal to the King obtained his support for the old foundation. Despite another Parliamentary Commission in 1584 no progress was made for the next thirteen years. One of the members of the 1582 commission was the Earl Marischal, a keen supporter of Melville's ideas. Frustrated by the lack of reform at King's College he took steps to set up a rival University in New Aberdeen based on the ideas of the new foundation.

Marischal College

Marischal College, founded in 1593 with only an Arts Faculty, initially had a Principal, three regents and six students. The foundation required that each member of staff should be fixed to one year's course. The three regents took the first three years. The first year was occupied by Latin, Elementary Greek and Logic; the second mainly Logic with the writing and declaiming of Latin and Greek. Mathematics did not appear until the third year when Arithmetic and Geometry shared the course with Physics from Aristotle, Ethics and Politics. The Principal was to teach the fourth year, in addition to supervising the whole establishment. He was to be well informed in the Scriptures and Learned Languages, particularly Hebrew and Syriac. He had to give instruction in Theology, Anatomy, the more difficult parts of Physiology, Geography, Chronology, Astronomy and Hebrew.

The foundation of the Chair of Mathematics

The establishment of distinct Mathematics classes at Marischal was encouraged by a bequest in 1613 from Duncan Liddell. Liddell was a mathematician, astronomer and physician, born and educated in Aberdeen, who spent most of his professional life on the Continent. He worked at universities in Frankfurt, Breslau and Helmstadt where he held chairs in Mathematics and Medicine. Towards the end of his life he returned to Scotland where, in 1612, he executed a settlement upon the University to support six bursars from the revenues of his lands at Pitmedden. This was confirmed in his will of a year later, made just before his death, in which he also left 6,000 merks to found a Chair of Mathematics. Hoping to avoid abuse of his benefits he vested the patronage in the Town Council. He set out in great detail how the bursars and professor were to be chosen and imposed conditions on their work.

One bursar was to be elected each year and to receive 'fourteine bolls victuall halfe meill halfe malt' annually for the four years of his ordinary course. Then, if he were able, he would stay for another two years to acquire further learning and to teach the students of the first two years some Arithmetic, The First Book of Euclid and the Sphere. For this his bursary would be augmented by twelve merks in the first and fifteen merks in the second year. Preference was to be given to Liddell's own close relatives.

The man chosen for the Chair had to be well versed in Euclid, Ptolemy, Copernicus, Archimedes and other Mathematics. For a salary of 400 merks he was to instruct the third and fourth years in Astronomy, Trigonometry, Ecclesiastical and Geographical calculations and supervise the Pitmedden Bursars. Until one of them was ready to assume his teaching duties the professor should also have the income from a bursary and teach five or six times a week. If however the Town Council were unable to find the 'perfyit mathematicus', Liddell required them to appoint one of 'meaner gifts', but in that case his stipend was to be only two or three hundred merks. For every lesson the professor omitted to teach he was to lose twenty shillings.

As a further encouragement to Mathematics, Liddell left his collection of books and instruments to the College together with a maximum of twenty merks a year to maintain and augment them. He also left money to provide two monuments to himself, both of which are still in existence, one a stone obelisk on his lands at Pitmedden and the other a brass in the West Church of St Nicholas, Aberdeen. This, designed by George Jamesone and executed in Antwerp in 1622, shows Liddell in his professor's robes with his books and instruments.

The first professor at Marischal

Although the Town Council received the money in 1615 they failed to find a suitable man for many years, despite repeated advertisement. They claimed that with 'such a laborious and toilsome task being injoyned to the professour be wertew of the fundatioun, Viz. to teache fywe or sex tymes everie week, no scolar of any worth wald condisend to accept of the charge for so meane a stipend as the most that wes allowed be the fundatioun'.

By 1626 the original capital had increased to 10,000 merks. Dr William Johnstone of Caskieben, a brother of the Latin poet Arthur Johnstone was appointed to the Chair at a salary of 800 merks. For this he was only required to teach the college students and any others as might want to attend, twice a week. He was not allowed to hold any other office in the college. Johnstone, a mathematician and physician who also wrote good Latin poetry, came to Marischal College from Sedan where he had been teaching Philosophy. He seems to have taken his duties very seriously. The University has in its possession a set of notes of his lectures, written by a student in the session 1633-4, which must surely represent more than two periods a week.

The course started sometime in October with the first book of Euclid, followed by Elementary Arithmetic. This covered the basic operations of addition, subtraction, multiplication and division of integers; going on to fractions, proportion and the extraction of square and cube roots. The students were then subjected to Chronology, a list of dates from the time of the Creation (roughly 4000 B.C.) to 1629 with a brief history of each period. This stage was reached by 10 November. For the next six weeks they studied Cosmography and Geography, the latter confined mainly to Europe, Asia and North Africa with a brief mention of America. Hydrography followed with an account of winds, tides, points of the compass and the use of some navigational instruments.

In the New Year they started trigonometry. Sine, tangent and secant were defined and their use in practical calculations, particularly surveying discussed. A little spherical trigonometry was included with the idea of plane projections of the sphere. A section on the sphere preceded one on Astronomy. Various ancient beliefs were mentioned and the theories of Ptolemy, Copernicus and Tycho Brahe considered. The session finished with 'Practical Geometry'. This included geometrical constructions, the use of instruments in surveying, more spherical trigonometry and solid geometry with nets for some regular solids.

The system of postgraduate tutors envisaged by Liddell was apparently not entirely successful. A Town Council minute of 21 December 1636 shows that two of the regents were to receive the Pitmedden emoluments whilst teaching the principles of Mathematics under Johnstone's direction, since not one of those who had held bursaries was qualified to teach.

It is perhaps not surprising to find that in March 1638 the professor was called before the Town Council and earnestly entreated to spread his course over four years. He is said to have agreed most willingly, 'albeit to his gryter paines as being most profitable for the schollares and studentis of mathematiques'. He died in office in 1640, his books and instruments being given to the college after his death by his widow.

The period 1641-1717

The Troubles of the seventeenth century necessarily affected college life. Professor Johnstone, in 1639, had been one of two commissioners sent by the town to a Covenanters Convention at Montrose. His successor, William Moir, appointed in 1641 was a stern Covenanter, a former baillie and prominent in local politics. As a baillie again, he was chosen to go to Edinburgh in 1644 in an attempt to obtain redress from the Committee of Estates for damage done in the town by raiding King's men. Afterwards he sought refuge at Dunnottar since he dared not return to Aberdeen until the Covenanters were again in control.

Little is known of Moir as a mathematician. He is reported to have written on Geometry and the mechanical parts of Mathematics. It was about 1642 that Marischal adopted the regenting system recently reintroduced at King's so it is doubtful whether Moir taught at all. About a hundred and thirty years later one of his successors, Professor Trail, making out a case for the augmentation of his own salary, claimed that, 'The Professorship after Dr Johnstone's death was given to one Baillie Moir and it has always been understood that it became a kind of sinecure'. (The well known mathematician James Gregory, inventor of the reflecting telescope, later Professor of Mathematics at St. Andrews and Edinburgh was a student at this time, graduating in 1657.)

Moir became Principal of Marischal in 1649, the Town Council conveniently passing an amendment to allow him to combine this with the offices of Professor of Mathematics and town baillie, despite the conditions laid down for the posts. He was deposed at the Restoration of 1661.

At the time of Moir's original appointment there had been some support for another candidate for the Chair, Duncan Liddell, namesake and nephew of the Founder. Sir Thomas Urquhart tells us in his Tracts that Liddell was rejected, not for mathematical incompetence, but on the grounds that he 'hath committed the hainous sin of fornication and begot a young lass with child'. Urquhart holds that the Town Council had thereby ignored the wishes of the Founder, that preference should be given to his own kinsmen. In fact this appears only to have been specifically stated with reference to the allocation of bursaries. Urquhart further points out that, if the Town Council's criterion had been generally accepted, the world would have lost the services of Socrates and hence also of Plato, Aristotle and Euclid.

Liddell, who had taught Geometry, Navigation and Gunnery in London, now (1661) stepped into his old rival's shoes, being appointed on a recommendation from the King. He held the Chair for twenty-six years. It seems likely that for part of this time at least he ran separate Mathematics classes. Trail's letters referring to his salary claim (mentioned above) state that the post continued as a sinecure except for the period 1673-83 when the professor chose to teach six times a week and drew a bursar's duty from Pitmedden. 'After that the professors except for one or two years gave over teaching. The bursary was withdrawn and Dr Liddell's Bursars were appointed to teach the elements of Arithmetic as formerly. Thus did matters continue till 1717.'

In the Knight manuscripts there is a list of mathematical instruments in the library in 1670, many of which probably came from the Johnstone collection and other bequests. The list includes globes, sea chart, compasses, lodestone, quadrants, astrolabes, nocturnlabes, planisphere, theodolite, surveying table, Gunter's Cross staff (an ancestor of the modern sextant), graphometer and analemma (an instrument on which a projection of a sphere on the plane of the meridian is drawn, or a graduated scale on a terrestrial globe showing the daily declination of the sun). It does suggest that the Mathematics at that time included practical instruction in Navigational and Astronomical calculations and Surveying.

Duncan Liddell was succeeded in 1687 by his own son George, appointed 'in respect of his Father's present inhabilitie'. George Liddell had entered Marischal College in 1681 and had already shown himself capable as a Liddell tutor from 1685 to 1687. He was appointed after giving public evidence of his ability in the presence of the Principal, masters, magistrates, 'the most part of the doctors and ministers of the said burgh and many others', who gave their unanimous approval.

Whatever his teaching abilities, he was to cause the Town Council considerable trouble. Two years after his appointment he was amongst some seventeen Aberdonians who were seized as Jacobite suspects and imprisoned for about three weeks in Dunnottar Castle. In 1706 he was deposed for 'frequently being guiltie of scandals and keeping scandalous company together with his present confessione of fornicatione with Jean Bisset'. An edict was issued for potential successors to come to dispute for the post, but Liddell appealed to the King's Advocate and was reinstated. This narrow escape does not seem to have produced any great reform. Ten years later the Town Council decided to prosecute him for 'several crymes and misdemanners'.

Before they could proceed the matter was taken out of their hands. The uprising of 1715 had found a good deal of support amongst the University staff. Marischal was closed for two years. A University Commission of 1716-17 removed all except one of the masters from office. In deposing George Liddell they reported that he 'did alwayes frequent the Church during the Rebellion, where the Episcopal Intruders prayed for the Pretender by the name of King James the Eight, did not take the Oaths till after the Rebellion, and has been guilty of such gross immorality as render him of Dangerous and Scandalous Example to the Youth'.

The next part of Mathematics at Aberdeen is here:

Mathematics at Aberdeen, Part 2

JOC/EFR April 2007

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