Isaac Barrow was an English Christian theologian and mathematician who is generally given credit for his early role in the development of infinitesimal calculus; in particular, for the discovery of the fundamental theorem of calculus. His work centered on the properties of the tangent; Barrow was the first to calculate the tangents of the kappa curve. Isaac Newton was a student of Barrow's, and Newton went on to develop calculus in a modern form.

Memoir of Dr. Isaac Barrow

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ISAAC BARROW, the learned and pious author of the following pages, was born in October, 1630, the son of Thomas Barrow, a respected citizen of London, who was the brother of Isaac Barrow, then Lord Bishop of St. Asaph. Our author was at an early age sent to the Charterhouse School, where he made so small proficiency that he was removed to Felsted, in Essex. His contemporary biographer indeed says, that so little appearance was there of that comfort which his father afterwards received from him, that he often solemnly expressed his wish, if it should please God to take any of his children away, it might be his son Isaac. Very few years elapsed before Thomas Barrow had reason to thank God for having blessed him with a son who proved in after-life to be not only kind and and affectionate and dutiful to his father, but one of the brightest ornaments of his church and his country.

English classical scholar, theologian, and mathematician who was the teacher of Isaac Newton. He developed a method of determining tangents that closely approached the methods of calculus, and he first recognized that what became known as the processes of integration and differentiation in calculus are inverse operations.

Barrow entered Trinity College, Cambridge, in 1643. There he distinguished himself as a classical scholar as well as a mathematician, earning his bachelor’s degree in 1648. He was elected a fellow of the college in 1649 and received his master’s degree in 1652. Such precociousness helped to shield him from Puritan rule, for Barrow was an outspoken Royalist and Anglican. By the mid-1650s he contemplated the publication of a full and accurate Latin edition of the Greek mathematicians, yet in a concise manner that utilized symbols for brevity. However, only Euclid’s Elements and Data appeared in 1656 and 1657, respectively, while other texts that Barrow prepared at the time—by Archimedes, Apollonius of Perga, and Theodosius of Bythnia—were not published until 1675. Barrow embarked on a European tour before the Elements was published, as the political climate in England deteriorated and the Regius professorship of Greek at the University of Oxford, to which he had been elected, was given to another. He spent four years in France, Italy, and Constantinople, returning to England with the restoration of the Stuart monarchy in 1660. On his return to England, Barrow was ordained in the Anglican Church and appointed to a Greek professorship at Cambridge. In 1662 he was also elected professor of geometry, but he resigned both positions after his election as Lucasian Professor of Mathematics at Cambridge in 1663.

Barrow was instrumental in institutionalizing the study of mathematics at Cambridge. From 1664 to 1666, he delivered a set of mathematical lectures—predominantly on the foundations of mathematics—that were published posthumously as Lectiones mathematicae (1683). These lectures treated such basic concepts as number, magnitude, and proportion; delved into the relationship between the various branches of mathematics; and considered the relation between mathematics and natural philosophy—most notably the concept of space. Barrow followed these with a series of lectures on geometry, Lectiones geometricae (1669), that were far more technical and novel. In investigating the generation of curves by motion, Barrow recognized the inverse relationship between integration and differentiation and came close to enunciating the fundamental theorem of calculus. His last series of lectures, on optics, Lectiones opticae (1670), built on the work of Johannes Kepler (1571–1630), René Descartes (1596–1650), and Thomas Hobbes (1588–1679), among others. In these lectures Barrow made major contributions to determining image location after reflection or refraction; opened new vistas for the study of astigmatism and caustics (a collection of rays that, emanating from a single point, are reflected or refracted by a curved surface); and made suggestions toward a theory of light and colours.

Barrow’s tenure as mathematics professor coincided with the maturation of Newton’s mathematical studies, and scholars often debate the exact nature of their relationship. Barrow was not Newton’s official tutor, though they were both members of Trinity College. Newton attended Barrow’s lectures, and it is clear that Barrow encouraged and furthered Newton’s studies. Fully cognizant of the young man’s talents, Barrow resigned his professorship in 1669 in Newton’s favour and accepted a position as royal chaplain in London. In 1673 Barrow was appointed master of Trinity College by King Charles II.

Although Barrow was regarded by his mathematical contemporaries in England as second only to Newton, he was more widely esteemed for his sermons and other writings on behalf of the Church of England, and these were often reprinted well into the 19th century.

Source: https://www.britannica.com/biography/Isaac-Barrow

Science Quotes by Isaac Barrow (7 quotes)

An accomplished mathematician, i.e. a most wretched orator. [Closing remark in an address, referring to himself.]
— Isaac Barrow Source: 'The Prefactory Oration' (address to the University of Cambridge upon being elected Lucasian Professor of Mathematics, 14 Mar 1664). In Mathematical Lectures (1734),

It may be observed of mathematicians that they only meddle with such things as are certain, passing by those that are doubtful and unknown. They profess not to know all things, neither do they affect to speak of all things. What they know to be true, and can make good by invincible arguments, that they publish and insert among their theorems. Of other things they are silent and pass no judgment at all, chusing [choosing] rather to acknowledge their ignorance, than affirm anything rashly. They affirm nothing among their arguments or assertions which is not most manifestly known and examined with utmost rigour, rejecting all probable conjectures and little witticisms. They submit nothing to authority, indulge no affection, detest subterfuges of words, and declare their sentiments, as in a Court of Judicature [Justice], without passion, without apology; knowing that their reasons, as Seneca testifies of them, are not brought to persuade, but to compel. Source: — Isaac Barrow Mathematical Lectures (1734)