Isaac Barrow
Isaac Barrow (1630–1677) was an English mathematician, theologian, and scholar, widely regarded as a precursor of calculus and the first Lucasian Professor at Cambridge. Explore his life, work, ideas, and enduring influence.
Introduction
Isaac Barrow is a key figure in the history of mathematics. Though less celebrated than Isaac Newton, Barrow’s contributions and his teaching shaped the early development of calculus and analysis. He is especially known for his work on tangents and his recognition that integration and differentiation are inverse operations.
He also held the first Lucasian Chair of Mathematics at Cambridge and later devoted himself more fully to theology and classical scholarship.
This article examines Barrow’s life, major works, intellectual influences, famous statements, and the lessons his journey offers to students, mathematicians, and thinkers.
Early Life and Family
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Barrow was born in October 1630 in London, England.
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His father, Thomas Barrow, was a linen draper, and his mother was Ann Buggin (who died circa 1634).
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After his mother’s death, young Isaac was sent to live with his grandfather in Cambridgeshire.
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Barrow had half-siblings from his father’s second marriage.
He attended Charterhouse School as a boy, where he was reportedly troublesome, leading his father to once pray that “if it pleased God to take any of his children, he might take Isaac first.”
Later, he studied at Felsted School, where he learned Latin, Greek, Hebrew, and logic—training that would support both his mathematical and theological work.
Education & Travels
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Barrow entered Trinity College, Cambridge in 1643 (or thereabouts).
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He earned his B.A. in 1648, and shortly thereafter was elected a Fellow of Trinity in 1649.
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He received his M.A. in 1652, under supervision of the classicist James Duport.
In 1655, Barrow refused to sign the Engagement (an oath to uphold the Commonwealth), which blocked him from some university positions. As a result, he spent the next four years traveling across Europe (France, Italy, and the Ottoman territories).
During his travels, he is said to have had a harrowing adventure where he helped save his ship from capture by pirates.
He returned to England in 1659 and took holy orders in 1660.
Academic Career & Major Works
Professorships & Positions
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In 1660, Barrow was appointed Regius Professor of Greek at Cambridge.
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In 1662, he became Professor of Geometry at Gresham College, London.
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In 1663, he was appointed the first Lucasian Professor of Mathematics at Cambridge.
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Around 1669, he resigned the Lucasian Chair, in favor of his protégé Isaac Newton, recognizing Newton’s greater potential.
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In 1672 (or 1673), he became Master of Trinity College, Cambridge, and held that position until his death.
During his tenure, Barrow also contributed to the planning of Trinity’s library (with Christopher Wren).
Mathematical & Scientific Contributions
Barrow’s mathematical work bridges the geometry of his time and the nascent calculus. Some of his notable contributions:
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He developed geometric methods to determine tangents of curves, using what became known as the “characteristic triangle” method.
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He recognized that integration and differentiation are inverse processes—a pivotal insight underlying the Fundamental Theorem of Calculus (though he did not frame it in modern notation).
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In optics, his Lectiones Opticae treated reflection, refraction, and the geometry of images, lenses, and the rainbow.
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He produced critical editions / translations of foundational works: Euclid’s Elements, Apollonius’ Conics, Archimedes’ Works, and Theodosius’ Spherics.
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His Lectiones Geometricae (published posthumously) contain his geometry lectures exploring curves, areas, and foundational reasoning.
Barrow also found the integral of the secant function in closed form, resolving a known conjecture of his time.
While he did not express calculus in the formal symbolic way later developed by Newton and Leibniz, Barrow’s geometric framework and insight about inverse operations laid groundwork for later advances.
Later Years & Theological Focus
After resigning from the Lucasian chair, Barrow devoted himself increasingly to theology, sermons, and classical scholarship.
He was granted a Doctor of Divinity by royal mandate in 1670.
He wrote a series of theological and philosophical works—on the Creed, the Lord’s Prayer, the Decalogue, the Sacraments, and controversial works such as A Treatise on the Pope’s Supremacy.
Barrow died unmarried on May 4, 1677 in London. Westminster Abbey.
His later life is sometimes described as eccentric; some sources suggest he had an opium addiction acquired during his travels in Turkey.
Intellectual Style & Personality
Barrow was known for being learned across disciplines: mathematics, classical languages, theology, and philosophy.
He had a flair for eloquence in sermons, which are considered masterpieces of argument and rhetorical clarity.
Physically, contemporary accounts describe him as small in stature, lean, pale, somewhat careless in dress, and a habitual tobacco smoker.
He was known to be witty and courageous (as in his maritime adventure against pirates).
Barrow had a generous academic spirit: he recognized Newton’s talent and relinquished the Lucasian chair to him rather than cling to it.
Famous Quotes & Thought Fragments
Because much of Barrow’s work is technical or theological, fewer pithy quotes are widely circulated. However, here are some notable statements or ideas tied to him:
“Integration and differentiation are inverse operations.”
— This insight underlies the fundamental theorem of calculus, a concept he grasped though not in modern symbolic form.
"The image of an object is the locus of the geometrical foci of every point on it."
— In his Lectiones Opticae, this expresses a deeper geometrical conception of vision and optics.
“He who knows more mathematics, praise God; but he who remains in ignorance, praise God as well.”
— A sentiment (paraphrased) reflecting his theological humility (found in some of his sermons and writings). (Attributed in theological commentary)
Because much of his writings are in Latin or theological prose, many expressions are embedded in dense texts.
Legacy & Influence
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Bridge to Newton and calculus
Barrow is often seen as the link between classical geometry and Newton’s formal calculus. His methods, teaching, and insight about inverse operations shaped Newton’s development. -
Lucas Chair tradition
He was the first Lucasian Professor of Mathematics at Cambridge, a prestigious post later held by Isaac Newton, Paul Dirac, Stephen Hawking, and others. -
Geometric foundations
His geometric methods for tangents and areas influenced how mathematicians conceptualized the movement from pure geometry to infinitesimal reasoning. -
Optics & vision theory
His optical lectures contributed to the scientific understanding of image formation, lens effects, and the mathematics of light. -
Scholarship & translation work
His annotated editions and translations of Euclid, Archimedes, Apollonius, and Theodosius made classical mathematics more accessible to his contemporaries and successors. -
Theological and intellectual integration
Barrow exemplified a scholar who did not sharply divide science and faith, but integrated mathematical reasoning and religious reflection—a model for later scientific theologians.
Though Barrow may not have invented calculus in the modern form, his influence lives in how he guided a generation toward that horizon.
Lessons from Isaac Barrow
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Pursue deep foundations, not only technique
Barrow’s deep grounding in classical geometry allowed him to see the deeper relations that later became calculus. -
Be interdisciplinary
His work across theology, linguistics, optics, and mathematics enriched each domain. -
Recognize and nurture talent
His willingness to step aside for Newton shows intellectual generosity and humility. -
Translate for posterity
His editions and commentaries helped later scholars access classical and modern ideas. -
Balance humility with ambition
Though capable, Barrow voluntarily shifted his focus toward theology and mentoring rather than clinging to prestige. -
Let insight precede formalism
He understood geometric intuition before symbolic machinery was developed, showing that conceptual clarity matters.
Conclusion
Isaac Barrow may not be as familiar a name as Newton or Leibniz, but his role as a teacher, translator, geometrician, and thinker was pivotal at a turning point in mathematical history. His insights about tangents, his recognition of inverse operations, his intellectual generosity, and his integrated view of science and faith ensure that his legacy continues.
May Barrow’s example encourage us to build bridges between disciplines, teach with humility, and value the foundational insights that precede formal advances.