Barrow, Isaac

(1630-1677), mathematician and theologian

by Mordechai Feingold

© Oxford University Press 2004 All rights reserved

Barrow, Isaac (1630-1677), mathematician and theologian, was born in London in October 1630, the son of Thomas Barrow, from a Cambridgeshire family, and his wife, Anne Buggin. Following the death of his mother in 1634 Isaac was sent to his grandfather's house where he remained until his father, already becoming a successful linen-draper, married Katherine Oxinden in 1636. Having baulked at his own father's attempt to make him a scholar, Thomas Barrow was nevertheless determined to make Isaac one, and to that end enrolled him at the Charterhouse, paying the master, Robert Brook, twice the going rate of £2 for his promise to supervise the boy's education. Two years later, to Thomas's chagrin, he learned that his son's education had been grossly neglected and that the lad distinguished himself only by 'being much given to fighting, and promoting it in others'. Isaac was quickly transferred to Felsted School in Essex, the renowned headmaster of which, Martin Holbeach, proved far more successful in discovering Barrow's precocity and instilling in him a love of learning.

The civil war years
The coming of the civil war proved disastrous for Thomas Barrow. The Irish rising precipitated the collapse of his trade with Ireland and resulted in a loss of some £1000. At the same time his strong royalist sympathies, which recently had been rewarded by his appointment as linen-draper to the king, made his position in London increasingly untenable, so that by June 1642 he had removed his family to Cambridgeshire. As a consequence of these difficulties Thomas Barrow was forced to inform Holbeach that he could no longer afford to pay for Isaac's education. The good headmaster, however, was loath to lose his exceptional student, and in response removed Isaac to his own house and appointed him 'little Tutor' to William Fairfax, third Viscount Fairfax of Emley. A last ditch effort to secure Isaac's future was made on 15 December 1643, when he was admitted as a foundation scholar at Peterhouse, Cambridge, owing to the efforts of his uncle Isaac Barrow, a fellow of Peterhouse. However, within a few weeks the elder Isaac was ejected by the parliamentary visitors of the university, and the nephew remained in Felsted. There he became involved in the amorous affairs of Fairfax, who soon eloped with a local girl, taking along his young tutor to London. However, it did not take Fairfax long to exhaust his wife's dowry, and Barrow, not wishing to burden his friend, on the one hand, and refusing Holbeach's kind offer to return to Felsted and become his heir on the other, began wandering in England. At last he arrived at the Norfolk house of a former schoolfellow, Edward Walpole, and the latter, about to go up to Cambridge, resolved on taking Barrow along, promising to support him there.

Barrow was admitted a pensioner in Trinity College on 25 February 1646 with James Duport as tutor, but when, several months later, Walpole went down, Barrow was once again faced with uncertainty. By then Oxford had fallen and Thomas Barrow, who had been stranded at Oxford for the duration of the siege, sought out his son and pledged him £20 per annum toward his maintenance. Duport pitched in as well, offering his tuition gratis as well as providing his charge with free lodgings. Barrow's fortunes further improved the following year thanks to his election to a college scholarship. He graduated BA in March 1649 and shortly thereafter was elected fellow. Such academic success was based on merit alone, as Barrow never disguised his royalist and Anglican sympathies. Indeed, he put his fellowship on the line in October 1649 when he decided, after a momentary acquiescence, against subscribing to the Engagement (Charles I's treaty with the Scots to allow presbyterianism to be established in England). Almost certainly he was spared expulsion thanks to the patronage of the master, Thomas Hill, who is reputed to have once laid his hands over Isaac's head and said: 'Thou art a good lad: 'tis pity thou art a Cavalier' (Pope, 140). Barrow would remain in need of further help from Hill as he became increasingly vocal in his religious and political convictions. Thus, on 5 November 1651, Barrow availed himself of the opportunity that arose with his appointment as the orator commemorating the anniversary of the Gunpowder Plot to articulate a forceful panegyric on the Stuart monarchy. Small wonder that several infuriated fellows conspired to effect Barrow's expulsion, but once again Hill intervened, this time by silencing the indignant fellows with the claim 'Barrow is a better man than any of us' (Pope, 140-41). Barrow's conflicts with some of his colleagues at Trinity, however, should not obscure the fact that his choice as the Gunpowder orator was indicative of the growing recognition of his exceptional literary skills and wit. Six months earlier, still a bachelor of arts, he had also been chosen moderator in the schools, an office which, as he himself remarked in an engaging Latin oration, required its occupant to excel at once in being serious and facetious.

Mastering the 'new philosophy'
The exercises performed by Barrow to satisfy the MA requirements in the summer of 1652 also give first proof of his mastery of the 'new philosophy'. During the early 1650s Barrow devoted much time to the natural sciences, not only because they were part of the regular course of study but also because, like so many royalists at the time, he considered making medicine his profession. Accordingly his studies of astronomy and mathematics were supplemented by those of botany, anatomy, and chemistry, at least some of which were undertaken in the company of John Ray. That he ultimately did not persist in medicine can be attributed to Barrow's realization that 'that profession [was] not well consistent with the oath he had taken when admitted Fellow, to make Divinity the end of his studies' (Napier, l.xli). During this period Barrow also participated in the work of the lively scientific group that was formed in Trinity College and included, in addition to himself and Ray, Walter Needham, John Nidd, Alexander Akehurst, and Francis Willughby.

Barrow was enthusiastic about Cartesianism, though not without qualification. He approved of Descartes's mathematics and much of his physics, but he criticized him for neglecting experiments and was averse to the Frenchman's metaphysics. In time his early concern with the deleterious implications of Cartesianism for religion became increasingly pronounced, providing a development analogous in many ways to Henry More's own evolving reaction to Descartes. At no time, however, was Barrow's endorsement of the new science incompatible with his continued respect for Aristotle and other ancients. Truth, he believed, must be garnered from whatever source, and those in pursuit of truth should be careful to avoid all partisanship and dogmatism, whether ancient or modern. Likewise, he cautioned against permitting the rejection of an obsolete natural philosophy to lead to a rejection of classical literature; and it was with just such a concern that Barrow urged his Cambridge students to allow Aristotle to refine their language even if they rejected him as the source of all knowledge.

It was also during this period of the early 1650s that Barrow seriously embarked on his mathematical studies. The immediate results were the publication of compact editions of Euclid's Elements and Data in 1656 and 1657 respectively, and the composition of the equally compact editions of Apollonius, Archimedes, and Theodosius, published, however, only in 1675. More important still, it was during this same period that Barrow obtained his deep insights into higher mathematics, including the formulation of his method of tangents, which would form the more original part of his Geometrical Lectures a decade and a half later.

Barrow's studies were rudely interrupted in 1654. A new wave of anti-university propaganda--against which Barrow made an impassioned Oratio ad academicos in commitiis--produced a nervous mood at the university. It had already claimed as one of its victims James Duport, who was forced to forfeit his Greek professorship for persisting in his refusal to sign the Engagement. The ousted professor, however, nearly succeeded in arranging to have Barrow succeed him, ensuring to this end the support of Benjamin Whichcote, provost of King's College, and John Worthington, master of Jesus College. Indeed, Barrow may have actually been elected by the university, as he performed, with great success, the required probationary exercise. This time, however, his reputation as a scholar was insufficient to outweigh his politics. The ambitious and irascible Ralph Widdrington of Christ's College, brother of the speaker of the House of Commons, succeeded in obtaining in January 1655--in explicit violation of the statutes of the chair--an injunction from Cromwell himself to force his own induction. Heeding the handwriting on the wall, Barrow applied immediately for a Trinity travelling fellowship, and on 4 April 1655 was granted the necessary passport to travel abroad for three years.

Travel abroad
After selling his books to supplement the £16 stipend attached to the fellowship, in June 1655 Barrow headed for Paris. There he met his father, whom he had not seen for almost a decade, and shared his meagre assets with him. Barrow's mocking description of the French capital, as both devoid of its former renown and inferior in every respect to Cambridge, should not obscure the fact that he much enjoyed his eight-month sojourn. He travelled next, in mid-February 1656, to Florence where he not only delighted in the city and in the company of many local scholars but also, owing to plague in Rome, remained for longer than he had intended. Through the instruction of one Fitton, the English curator of the Medicis' collection of coins and medals, Barrow also became proficient in numismatics.

At length, in November 1656, Barrow decided to travel east and embarked on a ship headed for Smyrna. On the way they were attacked by a Barbary corsair and Barrow distinguished himself in defending the ship. He stayed in Smyrna for seven months, enjoying the most generous hospitality of the English consul there, Spencer Bretton. At length he continued on to Constantinople where, again, his learning and engaging character recommended him to the English ambassador, Sir Thomas Bendish, as well as to the merchant Jonathan Dawes, future mayor of London. Barrow's animosity toward Islam was confirmed while in Constantinople, and despite his great linguistic skills--he was fluent in eight languages--he made little effort to master Arabic. Instead he studied the Greek fathers, especially Chrysostom, and served as agent to James Stock, a young merchant who supported Barrow and to whom the edition of Euclid's Data was dedicated, and Abraham Hill, both of whom were in the process of forming coin collections. Barrow left Constantinople in mid-December 1658, and, after taking a return route by way of Venice, Germany, and the Netherlands, arrived back at Trinity in September 1659 only to discover that a new master, John Wilkins, had just been installed. Although Wilkins would remain but briefly at Trinity, he would prove a valuable patron to Barrow in the coming years. Barrow's immediate concern, however, was to seek Anglican ordination, which he received from Bishop Ralph Brownrigg shortly before the latter's death in December 1659, mystifying Brownrigg's chaplain by 'rhyming answers to moral questions' (Feingold, 99).

Multiple professorships
The Restoration catapulted Barrow into multiple academic positions. In 1660 Widdrington quickly vacated the Greek professorship into which he had been intruded five years earlier and Barrow was elected without competition. Within a year, the new professor obtained a royal patent that granted both himself and future incumbents the freedom to enjoy the income and privileges of a Trinity fellowship in addition to the meagre stipend attached to the chair. Barrow's first course was devoted to Sophocles but, as it attracted few students, he opted to proceed with a course on Aristotle's Rhetoric, which indeed proved far more successful. Unfortunately, the manuscript copy of these lectures was lent to a friend and never returned. At the same time Barrow made his first forays into the domain of theology. In 1661 he was granted the degree of BD honoris causa and invited to deliver the prestigious commencement sermon, which he did on 30 June 1661--his first public sermon. Two years later, on 5 July 1663, Barrow also preached at Westminster Abbey during his uncle's consecration sermon as bishop of Sodor and Man.

On 16 July 1662, on the recommendation of John Wilkins, Barrow was elected Gresham professor of geometry. His brief tenure also included substituting for the astronomy professor, Walter Pope, who went travelling on the continent. Barrow's lectures included a course on the projections of the sphere and another on perspectives. The text of the former was apparently prepared for publication, but alas it, too, was lent out and subsequently lost. On 17 September 1662 Barrow was elected fellow of the Royal Society but, with the exception of the odd meeting he attended while living in London, he never participated in its activities.

Following the foundation of the Lucasian professorship of mathematics at Cambridge in 1663 Barrow was elected its first incumbent, again on Wilkins's recommendation. Turning down an offer to become librarian of the Cottonian Library made at about the same time, Barrow returned to Cambridge and in 1664 resigned both the Greek and Gresham professorships he had held concurrently. He read three sets of lectures during his five years' tenure as Lucasian professor, and though they were subsequently published, their published form does not entirely reflect the order in which they were read. Delivery of the Mathematical Lectures, for example, was stretched over the period 1664-6, partly because Barrow injected what would become lectures one to five of the Geometrical Lectures--to which perhaps were added his lectures on Archimedes--during the winter and spring of 1665, and partly because the plague forced the university to close for several months thereafter. Barrow completed his delivery of the mathematical lectures in spring 1666 and, following another plague-related closure of the university, delivered the rest of the geometrical lectures either in the spring or autumn of 1667. He concluded his tenure as Lucasian professor by delivering the optical lectures in 1668-9, and these were the first to be published.

Having resigned his chair, however, Barrow would have nothing to do with the printing of his lectures, and were it not for the persistence of John Collins, the geometrical and optical lectures might have remained unpublished. The mathematical lectures languished until 1683, when the demand for Barrow's theological works must have led the publisher to believe they were saleable as well. Barrow displayed an even greater indifference toward the publication of Archimedes, Apollonius, and Theodosius. Although he consented to Collins's solicitation, he refused to revise them, thus leaving it to Collins and his associates to check the two-decade-old manuscripts and correct the proofs. As for his Gresham lectures on perspective, although Barrow agreed to allow Collins to publish them, he refused to attach his name to them and ultimately Collins gave up the idea.

Theological works
Barrow's lack of concern with the fate of his mathematical works is puzzling until viewed as a consequence of his resolve to proceed at last with what had always been his intended vocation: divinity. Barrow claimed that he accepted the Greek professorship as a caretaker, and only until a qualified and more willing person came along. Likewise, he was induced to substitute the regius professorship of Greek with the Lucasian chair not only because he found the mathematical sciences more congenial but also because he was intent on securing the institutionalization of the mathematical sciences at Cambridge. Thus, having found a most worthy successor in Isaac Newton, Barrow resigned the professorship in 1669 and abandoned mathematics for good. His sentiments were expressed by his friend Abraham Hill: '[Barrow] had vowed in his ordination to serve God in the Gospel of his Son, and he could not make a bible out of his Euclid, or a pulpit out of his mathematical chair' (Feingold, 80-81). Thereafter Barrow remained a mere fellow of Trinity, for though he intended to make theology his calling, he was reluctant to leave Cambridge, still less to become a church functionary. He did consent, however, to accept a small sinecure in Wales, bestowed on him by his uncle, now bishop of St Asaph, but the income was used solely for charity. On 16 May 1671 Barrow was also installed prebendary of Yetminster, a position he accepted, according to Walter Pope, simply because he needed to raise the sum of £500 for his half-sister Rebecca, 'for a portion, that would procure her a good husband' (Feingold, 82). Once the terms of the lease he had set out expired, however, Barrow resigned the prebend. As a consequence his friends conspired to obtain for Barrow--who had been in the meantime made DD and appointed in 1670 as royal chaplain--the one position he truly wished for: the mastership of Trinity College, then held by John Pearson.

Following John Wilkins's death in November 1672, the vacant bishopric of Chester was quickly secured for Pearson, and on 27 February 1673 Barrow was admitted as the new master of Trinity. His short tenure proved a happy one for both Barrow and Trinity. Admissions remained high, and little, if any, dissension plagued the society. Most important for the long-term prosperity of the college, however, was Barrow's contribution to the construction of the college's new library, which he did not live to see completed. According to Roger North, while serving as vice-chancellor (1675-6) Barrow attempted to press the Cambridge heads of house to contribute toward the building of a public theatre that would rival the Sheldonian Theatre in Oxford. His colleagues, however, proved too cautious and Barrow decided to build the library at Trinity instead, and to this end managed to secure, gratis, the good services of Sir Christopher Wren as architect. It was also Barrow who personally wrote numerous letters to potential benefactors, helping raise a not insignificant portion of the ultimate cost of over £16,000.

In April 1677, while in London for the annual election of Westminster scholars, Barrow contracted a 'malignant fever'. He tried to cure himself, as he had done once before, by fasting and taking opium, but this could well have aggravated his condition and he died on 4 May 1677. Three days later he was buried in Westminster Abbey where, some time later, his friends erected a monument to commemorate him.

Posthumous reputation
Barrow's reputation has metamorphosed over the centuries. For the two centuries following his death it was chiefly as a consummate preacher and controversial theologian that he was remembered. Though the often unreliable Walter Pope claimed that certain urban congregations found Barrow's sermons too 'academic', the fact remains that they were highly regarded by many contemporaries. Indeed, Charles II jested that Barrow was an 'unfair' preacher because 'he exhausted every subject, and left no room for others to come after him'. A more serious threat to Barrow's reputation as a preacher arose from its essentially oral foundation, as only two of the sermons he delivered in London were published during his lifetime. However, as Barrow died intestate, his papers fell into the hands of his father, who was instrumental in ensuring the publication of his son's work. Thomas Barrow appointed John Tillotson and Abraham Hill as executors and the former published three volumes of Barrow's sermons between 1678 and 1680, followed in 1680 by an edition of A Treatise of the Pope's Supremacy, the only work which Barrow, on his deathbed, explicitly requested Tillotson to publish. In 1681 the publisher Brabazon Aylmer bought the copyright of all these works, as well as Barrow's manuscripts, from Thomas Barrow for the staggering price of £470, and proceeded to publish further editions. Thus was established Barrow's posthumous reputation, with collections of his sermons being published at regular intervals well into the nineteenth century. Not surprisingly, numerous readers, including Jean Leclerc, Henry Fielding, and the elder Pitt, expressed their great admiration of Barrow's eloquence no less than his power of reasoning.

As a mathematician Barrow was also highly regarded during the seventeenth and early eighteenth centuries. Henry Pemberton, in the preface to his A View of Isaac Newton's Philosophy (1728), wrote: 'he may be esteemed as having shewn a compass of invention equal, if not superior, to any of the moderns ... [Newton] only excepted'. Late twentieth-century scholars, in contrast, have found it difficult to credit him with being more than just a well-read contemporary in mathematical literature and an elegant codifier. In part, this is due to the juxtaposition of Newton's and Barrow's careers, so that even while Barrow's lectures were being printed, their content was being rendered obsolete by his young protégé, Newton. Nor is there any allowance for the virtually unrevised publication of Barrow's university lectures, the assumption being that they represent both the sum total of his mathematical knowledge and the genesis of his mathematical ideas. Only when, and if, Barrow's one surviving manuscript notebook, once in the hands of William Jones--in all likelihood the very one into which, Barrow told Collins in early 1667, he 'used to cast some things that came into [his] head' (Rigaud, 2.47)--becomes available will it be possible to evaluate the scope and depth of his knowledge. Whatever the ultimate verdict on his originality, however, Barrow remains one of the last Renaissance universal scholars, capable of distinguishing himself as a theologian, classical scholar, and mathematician. He himself articulated the ideal to which he strived in one of his sermons when he wrote: 'he can hardly be a good scholar, who is not a general one'.


M. Feingold, ed., Before Newton: the life and times of Isaac Barrow (1990)
The theological works of Isaac Barrow, ed. A. Napier, 9 vols. (1859)
Brief lives, chiefly of contemporaries, set down by John Aubrey, between the years 1669 and 1696, ed. A. Clark, 1 (1898), 87-93
S. P. Rigaud and S. J. Rigaud, eds., Correspondence of scientific men of the seventeenth century, 2 vols. (1841)
P. H. Osmond, Isaac Barrow, his life and times (1944)
W. Pope, The life of the right reverend father in God, Seth, lord bishop of Salisbury (1697); repr. as The life of Seth, Lord Bishop of Salisbury, ed. J. B. Bamborough (1961)
D. T. Whiteside, 'Patterns of mathematical thought in the later seventeenth century', Archive for History of Exact Sciences, 1 (1960-62), 179-388

RS, papers presented to the Royal Society
Trinity Cam. |  BL, letters to John Collins, Add. MS 4293

D. Loggan, drawing, 1676, NPG [see illus.]
L. F. Roubiliac, marble bust, 1756, Trinity Cam.; terracotta model, BM
R. Earlom, mezzotint, pubd 1811 (after D. Loggan), BM, NPG
B. Holl, line engraving (after portrait, Trinity Cam.), NPG
bust, Wesminster Abbey
oils, Trinity Cam.
print, NPG

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