Isaac Newton was born prematurely on Christmas Day 1642 according to the Julian calendar then in use in England (January 4, 1643, on the Gregorian calendar) at Woolsthorpe Manor in Woolsthorpe-by-Colsterworth, a hamlet in Lincolnshire.¹¹ His father, an illiterate but prosperous yeoman farmer also named Isaac Newton, had died three months before his birth.¹² When Newton was three years old, his mother, Hannah Ayscough, married Barnabas Smith, the well-to-do rector of neighboring North Witham. She moved to her new husband's parish to raise three younger children, leaving Isaac at Woolsthorpe in the care of his maternal grandmother, Margery Ayscough. Biographers have noted Newton's intense resentment toward his mother and stepfather during this nine-year separation, until Smith's death in 1653 brought Hannah back to Woolsthorpe.

From roughly the age of twelve to seventeen, Newton was educated at The King's School in nearby Grantham, where he lodged with the local apothecary, William Clarke, and learned Latin and Greek. In late 1659, his mother withdrew him from school to manage the family estate at Woolsthorpe. Newton proved thoroughly unsuited to farming, preferring to read and construct mechanical models. Persuaded by his maternal uncle, the Reverend William Ayscough, and the schoolmaster at Grantham, his mother allowed him to return to school to prepare for university entrance.

In June 1661, Newton matriculated at Trinity College, Cambridge, entering as a subsizar—a status requiring him to pay his way by performing domestic duties for wealthier students and fellows. Although the official Cambridge curriculum remained centered on the scholastic Aristotelianism of the Middle Ages, Newton immersed himself privately in the works of modern natural philosophers and mathematicians, including René Descartes, Galileo Galilei, Nicolaus Copernicus, Johannes Kepler, and John Wallis.¹³ In 1664, he was elected a scholar of Trinity College, guaranteeing four years of financial support and freeing him from domestic service to pursue his studies.

Newton graduated with a Bachelor of Arts degree in April 1665, shortly before the University of Cambridge closed for nearly two years as a precaution against the Great Plague.¹⁴ Retiring to the isolation of Woolsthorpe Manor between 1665 and early 1667—a period often termed his annus mirabilis or "year of wonders"—the twenty-three-year-old scholar laid the foundations for his most celebrated discoveries.¹⁵ At Woolsthorpe, he developed the generalized binomial theorem, formulated his method of fluxions, began prism experiments on the nature of light and color, and conceived his initial mathematical insights into universal gravitation, later associating this insight with observing the fall of an apple in the manor orchard. Returning to Cambridge when the university reopened in 1667, he was elected a Fellow of Trinity College and received his Master of Arts degree in 1668. In 1669, his mentor Isaac Barrow resigned the Lucasian Professorship of Mathematics and secured the appointment of the twenty-six-year-old Newton as his successor.

Newton's mathematical investigations between 1664 and 1666 transformed early modern analysis.¹⁶ Building upon algebraic geometry and infinite series, he discovered the generalized binomial theorem, extending the expansion of powers of binomials to fractional and negative exponents. This work led directly to his invention of the infinitesimal calculus, which he developed in a manuscript tract of October 1666 and expanded in De analysi per aequationes numero terminorum infinitas (1669) and De methodis serierum et fluxionum (written in 1671, published posthumously in 1736).¹⁷ Conceiving of mathematical quantities as generated by continuous motion—like a point tracing a curve—Newton called the variable quantities "fluents" and their instantaneous rates of change "fluxions". He established that the problem of finding tangents to curves (differentiation) and the problem of finding areas under curves, or quadrature (integration), are inverse operations, a foundational principle known as the fundamental theorem of calculus.¹⁸ He also devised an iterative root-finding algorithm known as Newton's method, classified cubic plane curves, and contributed to the theory of finite differences and algebraic equations.

While lecturing on optics as Lucasian Professor from 1670 to 1672, Newton challenged the prevailing Cartesian and Aristotelian consensus that white light was pure and homogeneous, and that colors resulted from the modification of white light through refraction or reflection. By darkening his chamber and passing a narrow beam of sunlight through a glass prism, he observed an elongated spectrum of colors projected onto the opposite wall. Through his experimentum crucis (crucial experiment), he isolated a single colored ray from the spectrum and passed it through a second prism, demonstrating that it underwent no further change in color. He concluded that white light is a heterogeneous mixture of rays, each possessing a specific degree of "refrangibility" (refractability) corresponding to an immutable spectral color.

Because rays of different colors refract at slightly different angles, Newton realized that any refracting telescope using glass lenses was inherently subject to chromatic aberration, producing fringes of color around images. To bypass this limitation, in 1668 he designed and built the first operational reflecting telescope, using a concave primary mirror ground from a custom alloy of copper and tin (speculum metal) to focus light without chromatic dispersion. When he demonstrated a second, refined model to the Royal Society in London in late 1671, it caused a sensation and prompted his election as a Fellow of the Royal Society in January 1672.

Encouraged by this reception, Newton submitted a paper on his optical discoveries to the Royal Society's Philosophical Transactions in February 1672. The paper sparked protracted criticism from Robert Hooke, the Society's curator of experiments, as well as Christiaan Huygens and several continental Jesuits, who objected to Newton's methodology and his corpuscular hypothesis that light consisted of streams of minute particles. Frustrated by the need to defend his findings, Newton largely withdrew from public scientific debate for over a decade and withheld his comprehensive optical treatise until after Hooke's death in 1703. Published in English in 1704 as Opticks: or, A Treatise of the Reflexions, Refractions, Inflexions and Colours of Light, the book detailed his experiments on dispersion, diffraction (which he termed "inflexion"), and thin-film interference ("Newton's rings"), concluding with a series of speculative "Queries" on matter, chemical affinity, electricity, and the nature of light.

Newton returned to the study of celestial mechanics in the late 1670s and early 1680s. In 1679, an exchange of letters with Robert Hooke concerning the trajectory of a falling body on a rotating Earth prompted Newton to abandon the concept of centrifugal force in favor of a centripetal force directed toward a central focal point. He subsequently proved mathematically that a body moving under a central force behaves according to Kepler's second law, sweeping out equal areas in equal times, and that an elliptical orbit with the center of force at one focus requires the force to vary inversely as the square of the distance.

In August 1684, the astronomer Edmond Halley visited Cambridge to consult Newton on a problem that he, Hooke, and Christopher Wren had been unable to prove: what curve a planet's orbit would describe if the sun attracted it with an inverse-square force. Newton replied immediately that the curve was an ellipse and that he had already calculated it. Having misplaced the original calculation, Newton reconstructed the proof and sent Halley a nine-page treatise, De motu corporum in gyrum (On the Motion of Bodies in an Orbit), in November 1684. Recognizing the importance of the work, Halley urged Newton to expand the tract into a comprehensive volume and personally financed its publication when the Royal Society ran short of funds.

After eighteen months of intense labor, Newton's three-volume Latin masterpiece, Philosophiæ Naturalis Principia Mathematica, was published on July 5, 1687.¹⁹ Written in the rigorous style of classical geometry assisted by his method of first and ultimate ratios (geometric limits), the Principia began by defining mass, momentum, and force within the framework of absolute space and time, followed by the three universal axioms known as Newton's laws of motion.²⁰ The first law (the law of inertia) states that a body remains at rest or in uniform motion in a straight line unless acted upon by an external force. The second law states that the change in motion (momentum) is proportional to the motive force impressed and occurs along the straight line in which that force acts. The third law states that to every action there is always an equal and opposite reaction.

Across the Principia's three books, Newton applied these laws to solve the central problems of terrestrial and celestial physics. Book I analyzed the motion of bodies in free space under various centripetal forces, proving that a uniform spherical shell attracts an external particle as if all the sphere's mass were concentrated at its center. Book II examined motion through resisting media, founding the science of fluid mechanics, calculating the speed of sound in air, and refuting Descartes's theory that the planets were carried around the sun by swirling эфиr vortices. In Book III, titled The System of the World, Newton synthesized astronomical data to formulate the law of universal gravitation: every particle of matter in the universe attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. With this single principle, he derived Kepler's laws of planetary motion, accounted for the ocean tides through the gravitational pull of the Sun and Moon, explained the precession of the equinoxes by demonstrating that the rotating Earth is an oblate spheroid flattened at the poles, and plotted the parabolic and elliptical orbits of comets.²¹ Revised second and third editions of the Principia appeared in 1713 and 1726.

Throughout his years at Cambridge, Newton devoted as much effort to laboratory alchemy (which he termed "chymistry") and biblical scholarship as he did to mathematics and physics. Beginning around 1669, he constructed a brick furnace and chemical laboratory in the garden outside his rooms at Trinity College, where his assistant Humphrey Newton later recalled that the fires rarely went out during six-week stretches of spring and autumn experimentation. Newton amassed a large library of alchemical texts and left behind roughly one million words of handwritten alchemical notes, transcriptions, and laboratory logs. Pursuing the chrysopoeia (the transmutation of base metals into gold) and the preparation of the philosopher's stone, he sought to uncover the active, vegetative principles that animated matter at the particulate level, producing works such as his unpublished treatise Praxis and creating a low-melting-point bismuth alloy known as Newton's metal.²²

Simultaneously, Newton immersed himself in church history, patristic texts, and biblical hermeneutics, composing several million words on theology and ancient chronology. By the early 1670s, his rigorous textual analysis of the New Testament and early church fathers led him to reject the orthodox doctrine of the Trinity. Embracing a view akin to fourth-century Arianism, Newton believed that God the Father alone was the supreme, eternal creator, and that Jesus Christ was a divine mediator created by and subordinate to the Father. In his historical treatise An Historical Account of Two Notable Corruptions of Scripture, he argued that fourth-century church authorities, led by Athanasius, had fraudulently altered biblical manuscripts (such as 1 John 5:7 and 1 Timothy 3:16) to introduce Trinitarian dogma into Christianity.

Because fellows of Trinity College were required by statute to be ordained as priests in the Church of England within seven years of earning their Master of Arts degree—a step that required swearing adherence to the Thirty-Nine Articles and the Trinity—Newton faced the prospect of losing his fellowship in 1675. He avoided resigning only when King Charles II issued a royal dispensation exempting the Lucasian Professor from the requirement of taking holy orders. Newton kept his heretical views strictly private throughout his life, as public denial of the Trinity was punishable by loss of civil office and imprisonment. He also studied the prophetic books of Daniel and Revelation, attempting to align biblical prophecy with secular history and calculating in a 1704 manuscript that the prophetic corruptions of the church would not end before the year 2060.

Newton first entered public affairs in 1687, when he helped lead the University of Cambridge's legal resistance against King James II's attempt to force the university to grant a degree to a Benedictine monk without taking the required Protestant oaths. Following the Glorious Revolution of 1688 that deposed James II, Newton was elected in January 1689 to represent Cambridge University in the Convention Parliament, where he aligned with the Whigs and sat until February 1690; he served a second parliamentary term for the university from 1701 to 1702. In the autumn of 1693, exhausted by years of overwork, chemical experimentation, and anxiety over his career, Newton suffered a severe nervous breakdown characterized by insomnia, delusion, and accusatory letters to friends including Samuel Pepys and John Locke, though he recovered his composure within a few months.

Throughout his career, Newton exhibited an acute sensitivity to criticism and engaged in fierce priority and intellectual disputes with several of Europe's foremost scientists. His earliest major feud was with Robert Hooke. After their clash over the 1672 optics paper, tensions flared again in 1686 when Hooke learned that Newton was completing the Principia and demanded credit for discovering the inverse-square law of gravitation. Newton responded angrily that Hooke had merely guessed at the inverse-square relationship without providing any mathematical demonstration, and he systematically excised almost every mention of Hooke from the Principia manuscript before agreeing, at Halley's urging, to insert a brief scholium acknowledging that Wren, Hooke, and Halley had independently deduced the inverse-square relation for circular planetary motion.

A second protracted conflict involved John Flamsteed, the first Astronomer Royal at the Royal Observatory in Greenwich. Beginning in 1694, Newton repeatedly pressed Flamsteed for unpublished lunar observations needed to perfect the Principia's complex mathematical theory of the Moon's motion.²⁹ Flamsteed, a perfectionist who had paid for his own observational instruments and resented being treated as Newton's subordinate, supplied data reluctantly and complained when Newton shared the preliminary findings with Halley. Using his influence as President of the Royal Society, Newton persuaded Queen Anne and Prince George of Denmark to appoint a Royal Society "Board of Visitors" to oversee the Greenwich Observatory and take control of Flamsteed's star catalogue. In 1712, Newton and Halley published a preliminary, unapproved edition of Flamsteed's observations as Historia Coelestis Britannica without the astronomer's consent; after Queen Anne's death shifted political power, Flamsteed managed to acquire three hundred of the four hundred printed copies and publicly burned the pages edited by Halley.

Newton's most famous and bitter dispute was the calculus priority controversy with Gottfried Wilhelm Leibniz.³⁰ Although Newton had developed his method of fluxions in 1665–1666, he did not publish it, circulating his results only in private manuscripts and two cryptic letters sent to Leibniz via Henry Oldenburg in 1676 (the Epistola prior and Epistola posterior). Leibniz developed his own differential and integral calculus independently during the mid-1670s and published it first, in the journal Acta Eruditorum in 1684 and 1686, introducing the transparent notation ($dx$ and $\int$) that became standard across continental Europe. Beginning in 1699 with accusations by Newton's follower Nicolas Fatio de Duillier and escalating in 1710 through papers by John Keill, English mathematicians accused Leibniz of having plagiarized calculus from Newton's earlier letters.

When Leibniz, himself a Fellow of the Royal Society, formally appealed to the Society in 1711 to clear his name, Newton used his presidency to appoint an ostensibly impartial committee of investigation Packed with his own supporters. Newton privately supplied the historical documents and personally drafted the committee's official 1712 report, the Commercium Epistolicum, which concluded that Newton was the "first inventor" of calculus and implied that Leibniz was a plagiarist. Newton even authored an anonymous review praising the report in the Philosophical Transactions. The dispute, intertwined with broader philosophical disagreements between Leibniz and Newton's spokesman Samuel Clarke over God's role in the cosmos, action at a distance, and absolute space, continued past Leibniz's death in 1716 and isolated British mathematics from continental analytical developments for nearly a century.

In his final decades in London, Newton lived in comfort near Leicester Square with his charismatic niece, Catherine Barton, who served as his hostess and later married his biographer and deputy at the Mint, John Conduitt. He occupied himself with Mint administration, revising the Principia and Opticks, and preparing chronological works such as The Chronology of Ancient Kingdoms Amended (published posthumously in 1728), in which he used astronomical records of the constellations to recalculate the dates of ancient Greek, Egyptian, and Near Eastern history. During the financial frenzy of the South Sea Bubble in 1720, Newton invested heavily in South Sea Company stock and lost approximately £20,000 when the market crashed. In his eighties, he suffered from gout, respiratory ailments, and painful bladder stones, moving in 1725 to Kensington for his health. He died in his sleep in Kensington on March 31, 1727 (March 20, Old Style), at the age of eighty-four. His body lay in state in the Jerusalem Chamber before he was buried with full ceremonial honors in the nave of Westminster Abbey on April 4, becoming the first scientist accorded that distinction. In 1731, an elaborate marble monument designed by William Kent and sculpted by Michael Rysbrack was erected over his grave.

Following his death, Newton's reputation ascended to near-mythic status across Europe. Championed on the continent by Enlightenment thinkers such as Voltaire and the Marquise du Châtelet—who translated the Principia into French—Newtonianism became the model of rational empirical inquiry, inspiring the poet Alexander Pope's famous epitaph: "Nature and Nature's laws lay hid in night: / God said, Let Newton be! and all was light". Throughout the eighteenth and nineteenth centuries, mathematicians including Leonhard Euler, Joseph-Louis Lagrange, and Pierre-Simon Laplace reformulated Newtonian mechanics in the language of Leibnizian calculus, turning it into a powerful analytical system capable of predicting the existence of the planet Neptune and guiding the engineering of the Industrial Revolution. Newtonian mechanics remained the unchallenged foundation of physics until the early twentieth century, when Albert Einstein's theories of special and general relativity and the development of quantum mechanics demonstrated its limits at velocities approaching the speed of light, in intense gravitational fields, and at subatomic scales. Even so, Newton's equations remain an extraordinarily accurate approximation used throughout classical engineering, ballistics, and spaceflight navigation.

Historians' understanding of Newton's intellectual life underwent a major revision in the twentieth century following the dispersal of the Portsmouth Collection—the vast archive of private manuscripts Newton had left at his death to Catherine Barton, whose daughter married into the family of the Earls of Portsmouth.³¹ Whereas the University of Cambridge had accepted Newton's mathematical and scientific papers from the family in 1872, it returned the alchemical and theological manuscripts as scientifically unimportant. In July 1936, Viscount Lymington auctioned these non-scientific papers at Sotheby's in London in 329 lots.³² The British economist John Maynard Keynes acquired roughly half of the alchemical manuscripts and bequeathed them to King's College, Cambridge, while the collector Abraham Yahuda acquired the bulk of the theological papers, now housed at the National Library of Israel in Jerusalem. Studying these texts, Keynes famously remarked in a 1942 essay that Newton "was not the first of the age of reason," but rather "the last of the magicians"—a view that prompted modern historians of science to examine Newton's physics, alchemy, and theology not as contradictory pursuits, but as interconnected facets of a single lifelong quest to comprehend the divine design of the universe.