The Tercentenary of the birth of James Gregory

The Tercentenary of the birth of James Gregory (1638-1675), Professor of Mathematics in the University of St Andrews (1668-1674) was celebrated in St Andrews in July 1938. On Tuesday, 5th July 1938, at St Andrews, in the Upper Hall of the University Library, a Graduation Ceremonial took place, at which Sir James Irvine, F.R.S., Principal and Vice-Chancellor of the University, conferred the Honorary Degree of LL.D. on:

Professor George David Birkhoff, A.M., Ph.D., Sc..D., Harvard University, U.S.A.

Professor Arthur William Conway, M.A., D.Sc., F.R.S., University College, Dublin, Eire.

Professor Otto Neugebauer, Copenhagen University, Denmark.

Professor Roland Weitzenböck, Amsterdam University, Holland.

Professor Vito Volterra, Rome (in absentia).

Congratulatory addresses were presented to the University by delegates from the Royal Society of London, the Royal Society of Edinburgh, the University of Edinburgh, the London Mathematical Society, the Edinburgh Mathematical Society, and from Professor Volterra. Among the many guests present were the Minister of Drumoak, the birthplace of James Gregory, and the Rector of the Grammar School, Aberdeen, where Gregory was educated.

Professor H W Turnbull delivered the address James Gregory (1638-1675) at the Tercentenary celebrations, 5th July 1938, in the Upper Library Hall, University of St Andrews. We give the address:-

James Gregory (1638-1675)

In the year 1638 two epoch-making books appeared - the Discorsi e dimonstrazioni matematiche of Galileo who had already become famous for the invention of the telescope, and the Discourse on Method by Descartes. The one revolutionised mechanics, and the other, geometry. They made possible, fifty years later, that crowning achievement of the seventeenth century, the Principia of Isaac Newton. Since the days of Ancient Greece no parallel to the brilliancy of that half century of scientific thought can be found. Within those memorable years James Gregory lived and died, achieving in the brief span of his life a reputation among his peers second only to that of Newton.

Three hundred years ago James Gregory was born at the Manse of Drumoak, a small parish on Deeside, eleven miles from Aberdeen. He came of a family already noted for mathematics. His grandfather, David Anderson, commonly known as "Davie do a' thing", was the Archimedes of Aberdeen who, we are told, had constructed the spire of St Nicholas Church, affixing its weather cock with his own hands, and had removed "Knock Maitland," a dangerous submerged rock, from the fairway of the Aberdeen harbour mouth by harnessing it to the tide. His daughter Janet married John Gregory of Aberdeen, who had studied at St Mary's College in this University; and thereafter for two hundred years their descendants occupied Scottish Chairs of Mathematics, Medicine, Chemistry, History or Philosophy in an almost unbroken sequence. James Gregory, their third son, received his first lessons in geometry from his mother. His brother, David, some ten years his senior, directed his education after his father's death in 1651, gave him a copy of Euclid's Elements, which he eagerly mastered, and sent him to the Grammar School and later to Marischal College, Aberdeen, where he graduated. For a year and a half he suffered from the quartan ague: but, as he wrote several years later, "It is a disease I am happily acquainted with, for since that time I never had the least indisposition; nevertheless that I was of a very tender and sickly constitution formerly." Encouraged by his brother, who was himself a gifted mathematical scientist, James wrote his first book, entitled Optica Promota, being a masterly account of mirrors and lenses, and containing a description of the earliest reflecting telescope, which brought him fame at the age of 24.

Reflecting telescopes contain both mirrors and lenses, so combined as greatly to reduce the length of the tube, in contrast to the usual refractive pattern which consisted of lenses alone. Also, to gain magnifying power it was customary in those days to lengthen the tubes to hundreds of feet. Even the small Galilean telescope which Gregory brought to St Andrews, and perhaps set up in this very room, was 24 feet long, whereas a reflector of six feet or less could be equally powerful.

In 1663 Gregory went to London, where his book was published, and met Collins, who put him in touch with Reive a celebrated optician. But though a large object mirror was actually made, it failed to give satisfaction, and the project was abandoned. But the attempt had interested that prince of experimenters, Hooke, who ten years later succeeded in making such a telescope, and during the eighteenth century it became the standard astronomical pattern. Meanwhile, a young man working independently at Cambridge, Isaac Newton, four years junior to Gregory, had invented a reflecting telescope which was exhibited at the Royal Society in 1672 and brought fame to the maker. It was only six inches long, and differed from Gregory's original design much as a flute differs from an oboe. The observer gazes directly into Gregory's and sideways into Newton's instrument.

Gregory spent the next three years in Italy, visiting Flanders and Rome in his tour and returning by Paris, but settling for most of the time at Padua, where Galileo had taught. He lodged in the house of his fellow countryman, Dr Caddenhead, the Professor of Philosophy in that city: it was there that Gregory was brought into contact with the great Italian school of geometers, particularly that of Cavalieri whose method of indivisibles led, through Gregory, to the integral calculus. At Padua, Gregory wrote two imperishable little volumes, one called the Vera Quadratura - the true quadrature of the circle and hyperbola - and the other the Geometriae Pars Universalis, which enhanced his reputation as a brilliant thinker, and gained for him at once the disapproval of the great Flemish physicist, Huygens, and a Fellowship at the recently-founded Royal Society.

In the Vera Quadratura Gregory sought to prove a property about the transcendental nature of those mysterious numbers commonly called and e, an investigation which was only finally completed at the close of the nineteenth century by Lindemann of Munich. Gregory's work contained a subtle fallacy: it was none the less a supreme achievement both in concept and in fertility of resource. The boldness of the thought raised a storm of opposition. Huygens and Wallis attacked his arguments remorselessly, but Gregory never admitted defeat: he gave way, now here now there, and anticipating the fighting spirit of his later kinsman, Rob Roy, he inevitably reappeared undaunted, to renew the attack from some fresh quarter.

It is difficult for us to realise the atmosphere of fear and distrust which haunted those pioneers in science. Men of genius were afraid to be thought stealing ideas from one another. When Collins, the booklover, eagerly wrote to Gregory to procure particulars of certain rare books in Italy for the use of the Royal Society, Gregory replied, "I believe none knoweth what papers of Soverus there are in the library here: for those that can understand them will not go to see them, fearing that, if they should publish any thing of their own, it should be thought stolen from Soverus." When therefore, Huygens accused Gregory of using his own results without acknowledgment - some of which Gregory had never even seen - the taunt stung the sensitive Highlander to the quick. He retaliated by inserting in his next book, the Exercitationes, a few pages which advanced this work of Huygens beyond all recognition: "I shall here try to bring the squaring of the circle and hyperbola to such perfection that Huygens will scarcely recognise his offspring." In this work Gregory crosses the Great Divide that separates mediaeval thought from the modern world: here also he is thinking the same thoughts as Isaac Newton, when as yet neither had heard of the other. Unfortunately, to heighten the challenge against Huygens Gregory deliberately concealed his method, and thus a brilliant advance in the analytics was hidden from the world. This took place during the four months of 1668 which Gregory spent at London in the society of Collins, whose modest sympathetic friendship was a balm to wounded feelings at the turning point of Gregory's mathematical life. Moreover, Collins made known to him the newest discoveries, and passed on to him also several unsolved problems.

Such a discovery was that of Nicolaus Mercator who had found the logarithmic series. Gregory at once granted that it was better than his own, adding that "it was a hard matter in this age to write a book which should not presently be rendered naught!" Nevertheless, it elicited in return from Gregory the answer to a problem which Mercator himself had failed to solve, and cleared up a seventy year old mystery concerning Sea Charts.

During the summer Gregory attended the meetings of the Royal Society to which he had been elected Fellow on 11th June 1668, where he read several short papers on gravitation and mechanics, which revealed his versatility and resource. One of his friends was Sir Robert Moray, a founder of the Royal Society, a former graduate of St Andrews, a chemist, a mathematician, a student of music, a friend of the learned, and perhaps the most attractive Scot of his generation. It was probably through his influence that Charles Il established in the University of St Andrews a new Chair of Mathematics to which James Gregory was nominated as the first Professor. It seems likely that the Chair was expressly instituted to give Gregory an opportunity for his researches. He was not attached to any of the three colleges, but his work was done in this upper room of the University Library where we are gathered today.

We can picture Gregory at the age of 30, coming a stranger to St Andrews on a late Autumn day, to a University already 250 years old and wrapped in mediaeval tradition - this young firebrand, who was so ready to seize on a new mathematical idea with avidity, bursting into the cloistered calm where the new learning of Kepler, Galileo and Descartes was still unknown.

"I am now much taken up," he writes, "and have been so all this winter by past, both with my public lectures, which I have twice a week, and resolving doubts which some gentlemen and scholars propose to me. This I must comply with, nevertheless I am often troubled with great impertinences: all persons here being ignorant of these things to admiration." Throughout his six years' sojourn in St Andrews he quietly made his discoveries, keeping in touch with the outside world through the letters of the faithful Collins. But for these letters, which he carefully preserved, and the occasional book which Collins so thoughtfully sent, Gregory would have been, as he put it, dead to all the world. We do not know where he lived, but the first letter to Gregory was directed to be left at the Palace of the Archbishop there - Archbishop Sharp, who met his tragic end on Magus Muir in 1679.

In 1669 Gregory married Mary, daughter of George Jamesone, the painter, and widow of Peter Burnet of Elrick, Aberdeen. They had two daughters and a son, James, afterwards professor of physic in King's College, Aberdeen.

In Mary, his wife, James Gregory found a true helpmeet who shares in the honour paid to those who launched such a remarkable family, so conspicuous for their inherited scientific and literary genius. Mary Jamesone - we are told - inherited her mother's beauty and the artistic tastes and character of her father, a man of pronounced individuality and pacific disposition, a difficult combination in those days of lurking barbarism. Mary Jamesone herself worked and designed tapestries which possess artistic and technical merit. The characters of both father and daughter doubtless contributed towards the greatness of the man we are thinking of today, and of his children.

Gregory had seen his father persecuted for making a stand against the Covenanters, his eldest brother had been treacherously slain; even his books had been suppressed at Venice in misguided ecclesiastical zeal or unjustly disparaged by men of learning; and his outward means were narrow. But he was happy. "I am at home," he writes, "in a settled condition, by which I can live. I have known many learned men, far above me upon every account, with whom I would not change my condition."

We can picture Gregory at work in this old room with its unbroken view of the open country towards the south, uninterrupted by the buildings which were added at a later date. It was here that Gregory carried out his astronomical observations. We can picture him laying plans for his observatory, gaining the confidence and friendship of men of goodwill who provided means for gathering the necessary instruments; his occasional journey to Edinburgh or London or homewards to the north: the famous occasion when he persuaded his townsfolk to hold a church door collection throughout Aberdeen to supply instruments for the observatory at St Andrews! Here stands his own pendulum clock, made by Joseph Knibb of London, with its large dial curiously divided into 60 parts for the seconds, a reminder that, only a few years before, Huygens had discovered the secret of the pendulum. This was indeed one of the very earliest clocks to be constructed in England or Scotland. It is a reminder too that Gregory and Huygens were once more good friends and that Huygens had recommended Gregory to Louis XIV of France for a pension and a call to Paris in token of his genius.

Across the floor towards that window runs the meridian line, slightly askew but truly north and south. The floor boards have perished upon which the original line was marked, but the position has been preserved. It points to the iron bracket firmly fixed to the wall beside the window upon which Gregory mounted his quadrant or his telescope. The instruments have long disappeared but the bracket still carries the screw adjustment whereby Gregory brought the axis to a true level. A mile away, behind a thicket of trees on the hilltop, there stands an iron trident affixed to a tall stone. In those days the hilltop was bare, and Gregory placed the trident in full view of this window, in order to make his transit observations. How carefully he awaited the eclipse of 9th April 1670, which had been foretold by another young enthusiast, Flamsteed of Derby, and what was his disappointment when that very day a mighty snowstorm swept all Scotland! We can share his joy one night four years later when he and his friends in Paris made simultaneous observations of a lunar eclipse which enabled him to work out the longitude of St Andrews, a difficult feat in days before the invention of the chronometer. We can picture Gregory walking on our broad sands, watching the sea birds and idly picking up a feather and using it to discover a new phenomenon of light. "Let in the sun's light," he says, "by a small hole to a darkened house, and at the hole place a feather (the more delicate and white the better for this purpose), and it shall direct to a white wall or paper opposite to it a number of small circles and ovals (if I mistake them not) whereof one is somewhat white (to wit, the middle which is opposite the sun) and all the rest severally coloured. I would gladly hear Mr Newton's thoughts of it." This is the earliest recorded example of a diffraction grating.

It was here that Gregory first learnt, through a letter of Collins, about the geometrical methods of Barrow, the Lucasian Professor at Cambridge, and the analytics of his still more wonderful pupil, Isaac Newton, to whom Barrow relinquished his Chair. Here Gregory also learnt of the fame that the reflecting telescope brought to Newton and of his remarkable discoveries in light, the breaking up of white light into colours. All of this acted as so much fuel to kindle his own genius into activity. Barrow and Newton had discovered the differential calculus, but within a month of receiving Barrow's book Gregory poured out such a volley of equations in his next letter that Collins was convinced beyond a doubt that Gregory had made the same discovery too. The climax to this creative activity occurred in the first fortnight of February 1671 when he hit on one of the most important theorems in all mathematics, and thereby anticipated Brook Taylor, to whom it is attributed, by over 40 years. Although Gregory withheld the actual method he sent the results to Collins in a letter dated the 15th of February 1671: but by wonderful fortune the actual rough notes which led to these results are here upon the blank sheets of a letter written on the 30th of January by one Gideon Shaw, a bookseller who lived at the foot of the Ladies' Steps, Edinburgh. These rough notes, written, who knows? in this very room, are the silent but inevitable witness giving Gregory the right to take his place with Barrow, Newton and Leibniz as a principal discoverer of the differential calculus: indeed in this one aspect of the subject he attained a result which neither of the others are known to have found. Little wonder that Collins, in alluding to Gregory, described his work (with that of Barrow) as being "so exceeding general and performing all such difficulties that other methods relinquish, that it seems . . . like Moses Serpent that devoured the Serpents of the Egyptian Magi." Yet Gregory never published this, his crowning achievement: for on learning from Collins that Newton had in actual date anticipated him and modestly assuming that Newton had attained at least as far as he himself, Gregory decided to withhold his work until his young rival had published his own - which did not in fact take place until many years after the death of Gregory.

As he waited for Newton to break the silence Gregory turned once more to Astronomy. There, beyond the boundary wall of the college grounds, once stood a small building, Gregory's observatory. It was the first of its kind in England or Scotland, and it remained until about a hundred years ago when the old Lade Braes path was widened and it was demolished. Whether Gregory ever worked in it we do not know: probably he left St Andrews for his Edinburgh Chair before the project was fulfilled.

He tells us why he left in a letter to a friend at Paris : "I was ashamed to answer, the affairs of the Observatory of St Andrews were in such a bad condition; the reason of which was, a prejudice the masters of the University did take at the mathematics, because some of their scholars, finding their courses and dictats opposed by what they had studied in the mathematics, did mock at their masters, and deride some of them publicly. After this, the servants of the colleges got orders not to wait on me at my observations: my salary was also kept back from me; and scholars of most eminent rank were violently kept from me, contrary to their own and their parents' wills, the masters persuading them that their brains were not able to endure it. These, and many other discouragements, obliged me to accept a call here to the College of Edinburgh, where my salary is nearly double, and my encouragements otherwise much greater."

The old letters, upon the backs of which he wrote his rough notes during the seven years spent at St Andrews and Edinburgh, passed into the possession of his family, and were carefully treasured: but after many years they were lost to be found again by Sir Peter Scott Lang in 1887, a successor two centuries later in the Chair of James Gregory, who bequeathed them to this Library about ten years ago. These papers, which contain vivid historical matter written by Collins together with some fifty rough notes of Gregory, have lately been deciphered. The work was begun by Sir John Smith and continued by the present Librarian and myself. During the last six years it has been a rare privilege, as line upon line, here a little, there a little, the mathematics of Gregory were disclosed, once more to share his first groping thoughts, to laugh with him at his mistakes, to disagree one day and next to find him right after all, to be thrilled at finding that this, his shattered masterpiece, could, after 260 years, be restored.

Deep in the heart of Gregory lay that love of truth which led him to follow with disinterested devotion the bent of his genius. He died at the height of his powers, leaving friends at home and abroad, the warmth of whose affection or respect was expressed in words sometimes startling in their depth; friends in Italy, Flanders, France, Germany, England, Scotland. Today, in this room where Gregory worked so long, we have their mathematical descendants, distinguished guests from the world of science, from the Cambridge of Newton, the Paris of Cassini, the Germany of Leibniz and the Flanders of Huygens, assembled in a Scotland where mathematics is still pursued for its beauty and its truth. Let us, in our respective Universities, hold fast to this tradition of fellowship and of devotion to learning, and thus honour the name of James Gregory.

For other items relating to the celebrations for the Tercentenary of the birth of James Gregory on Tuesday 5th July 1938 see:

Gregory's Observatory
The Upper Hall of the University Library
Gregory's Clock

Last Updated March 2006