Isaac Newton was a famous scientist and mathematician from England who lived long ago, and MacTutor divides his life into three periods: his boyhood up to 1669, his years as Lucasian professor from 1669 to 1687, and a long third period as a highly paid government official in London. He was born in the manor house at Woolsthorpe, in England, where his family were farmers, and his father died before Newton was born. At school, his reports called him idle and inattentive, and his mother took him out of school to run the family farm, but he returned to school and went on to university. He went to Trinity College, part of Cambridge University, where he studied the work of Johannes Kepler, René Descartes and other giants of the Scientific Revolution. As a student he wrote in a notebook, in Latin, 'Plato is my friend, Aristotle is my friend, but my best friend is truth.'

According to de Moivre, Newton's interest in mathematics began in 1663, when he bought an astrology book at a fair in Cambridge and could not understand its mathematics. Then a sickness called the plague closed Cambridge University, so Newton went home to Woolsthorpe. While away from Cambridge because of the plague, Newton began important work in mathematics, light, physics and astronomy in less than two years. He had early versions of his three laws of motion by 1666, and he began working on them in a notebook at the family farm. John Conduitt, who worked with Newton at the Mint, wrote that in 1666 Newton, musing in a garden, thought gravity might reach as far as the Moon. In 1666 Newton imagined that the Earth's gravity reached the Moon, balancing the Moon's outward push, and from this and Kepler's third law he worked out the inverse-square law. Gravity does not give the Moon its speed, but it stops the Moon from running away and keeps it in some orbit.

Every scientist since Aristotle had believed white light was a single basic thing, and the color fringes in a telescope lens convinced Newton otherwise. He shone sunlight through a glass prism and saw a band of colors, split white light into colors with one prism, and then used a second prism to join the colors back into white light. In a key experiment, Newton passed one color from the spectrum through a hole and a second prism, and the second prism bent it by the same amount without changing its color, showing that each color is a pure part of white light. Newton explained the color of an object as the colors it reflects after it absorbs all the others, and he named seven colors in the spectrum, admitting that choosing seven was rather arbitrary. Newton reasoned that lens telescopes would always blur colors, and so built a reflecting telescope, though MacTutor calls that conclusion erroneous.

Others, such as James Gregory in 1663, had described ideas for a reflecting telescope, but Newton was the first to build one, and his used a mirror to gather light and a second mirror to send it to an eyepiece. As of November 2026, reflecting telescopes, which use mirrors as Newton's did, are mainstays of astronomy, including the Hubble Space Telescope. In 1669 Newton became the Lucasian Professor at Cambridge. Newton's first scientific paper, 'New Theory About Light and Colours,' appeared in the Philosophical Transactions of the Royal Society in March 1672, after the Royal Society asked for a written account of his telescope. Robert Hooke and Christiaan Huygens objected to Newton trying to prove by experiment alone that light is made of small particles rather than waves. After critics challenged his light theory, Newton became impatient with hypothetical arguments, and he insisted that science should be mainly mathematical and experimental.

Kepler's third law links a planet's distance from the Sun to the time its orbit takes, and it inspired Newton to come up with three laws of his own to explain how planets move. In 1684 Edmond Halley asked Newton what orbit a body follows under an inverse-square force, and Newton replied at once that it would be an ellipse. Halley persuaded Newton to write out his new physics in full, and the result, the Principia, was published in 1687. Halley also paid to have the Principia printed. A mathematician at the Open University wrote that the Principia made Newton famous even though few people read it and even fewer understood it. The first edition of the Principia did not contain the proof that inverse-square forces give conic-section orbits, and a sketch of it appears in the second and third editions. The proof Newton published for planetary orbits did not use calculus, because it used the properties of ellipses and other conic sections.

In the Principia, Newton's first law says a moving object keeps its speed and direction, and a still object stays still, unless an outside force acts on it, and the law is often called inertia. Newton wrote that a change of motion is proportional to the force pressing on an object and happens in the direction of that force, and people write this second law as F=ma: force equals mass times acceleration. Newton's third law says that when one object pushes on another, the second pushes back just as hard in the opposite direction. Newton's law of universal gravitation says all matter attracts all other matter, and the pull is proportional to the product of the masses and inversely proportional to the square of the distance between them. Newton showed that if gravity gets weaker with the square of the distance, then gravity on Earth's surface correctly predicts how long the Moon takes to orbit.

In the Principia, Newton applied his laws to orbiting bodies, projectiles, pendulums and free-fall near the Earth. It explained the eccentric orbits of comets, the tides and their variations, the wobble of the Earth's axis, and the Moon's motion as pulled by the Sun's gravity. Before Newton, thinkers assigned different causes to different types of motion, according to physicist Stephen Hawking, so by unifying all motion Newton shifted science toward a search for large, unifying patterns in nature. Scientists on the European continent did not accept Newton's idea of action at a distance, and they kept to Descartes's vortex theory, in which forces work through contact. Newton became Warden of the Royal Mint in 1696 and Master of the Mint in 1699, a post he kept until his death in 1727. At the Royal Mint, Newton helped take old coins out of use and replace them with more reliable ones, and he was determined that all coins be made to the correct weight and fineness, varying as little as possible.

In September 1717 Newton, as Master of the Mint, sent the Treasury a report setting a new ratio between silver and gold, which had the effect of moving Britain onto the gold standard. In 1703 Newton was elected President of the Royal Society, a group of scientists, and Queen Anne made him a knight in 1705. His Opticks appeared in 1704, and it covered the theory of light and color, the colors of thin sheets known as Newton's rings, and diffraction of light. Newton measured the colored rings made when a lens is pressed against flat glass, and the gap between lens and glass grows evenly with each ring. Newton's Opticks established a more experimental and quantitative style in science for the eighteenth century, in contrast with the earlier, more speculative approach. Newton's particle theory of light was so influential that it delayed acceptance of the wave theory for nearly a century.

Newton worked out a version of calculus in the 1660s but did not publish it, while Leibniz formulated his own version in the 1670s and published a decade later. As of November 2026, the calculus used in classrooms follows Leibniz's system rather than Newton's. Newton's laws of motion and universal gravitation stood unchallenged for nearly 220 years, until Albert Einstein presented special relativity in 1905. Newton's theory depended on the assumption that mass, time and distance are constant wherever you measure them. As of November 2026, at slow speeds and large scales the differences predicted by relativity are small enough that Newton's laws still work, and they still define the orbits of large, slow-moving satellites. Newton's laws are still used to reach the Moon, Mars and other places beyond Earth, and they became the base of classical mechanics, the study of how large things move. Historian Patricia Fara of the University of Cambridge writes that Newton told the apple story around four times near the end of his life, and that it only became well known in the nineteenth century.

No one knows for sure if an apple really fell the way the story says, and the part where it hits him on the head is called a myth. Newton lived to be 84 years old, and he is buried in Westminster Abbey in London, where his monument was finished in August 1730 and unveiled the following year. The carved scene on the monument shows figures with a telescope, a prism, and a balance weighing the Sun and planets, and Newton's grave carries Latin words that mean 'Here lies that which was mortal of Isaac Newton.' Newton once said that if he saw farther than others, it was because he stood on the shoulders of giants. Near the end of his life Newton said he felt like a boy on the seashore, finding a smoother pebble or prettier shell while the great ocean of truth lay undiscovered.

Words to know

• Principia: Newton's motion book
• Opticks: Newton's light book
• inertia: keeps moving, stays
• diffraction: light bending around
• calculus: math of change
• erroneous: mistaken