Who was Isaac Newton? Gravity, light and calculus

Isaac Newton was an English mathematician and physicist, born in 1643 and died in 1727, who showed that one law of gravity governs a falling apple and the orbiting Moon. In his Principia of 1687 he set out the laws of motion and universal gravitation. He also showed that white light is a mixture of colors, built the first working reflecting telescope and, independently of Gottfried Leibniz, invented calculus.

In short

• Newton's Principia (1687) explained the planets, the Moon, the tides and falling bodies with three laws of motion and one law of gravity.
• He found that white light splits into colors that were in it all along, and he invented calculus, which led to a bitter fight with Leibniz over who came first.
• He also spent decades on alchemy and Bible prophecy, and worked at the Royal Mint for the last 31 years of his life, most of them as its Master.

Who was Newton, in brief?

Newton was born at Woolsthorpe Manor in Lincolnshire on 25 December 1642 by the calendar England then used, which is 4 January 1643 by the modern one. His father died before he was born, and his mother left him with his grandmother when she remarried. He entered Trinity College, Cambridge, in 1661 and took his degree in 1665, just as the Great Plague closed the university.

The two years he then spent at home, 1665 and 1666, are the most famous in his story. In them he worked out the beginnings of calculus, experimented with prisms, and started thinking about gravity reaching as far as the Moon. Back in Cambridge he became Lucasian Professor of Mathematics in 1669, at 26. He left for London in 1696 as Warden of the Royal Mint, becoming its Master in 1699, was president of the Royal Society from 1703 until his death, and was knighted by Queen Anne in 1705. He died in Kensington on 20 March 1727 by the old calendar, 31 March by the new, and was buried in Westminster Abbey.

Year	Event
1643	Born at Woolsthorpe, Lincolnshire (25 December 1642, old calendar)
1661–65	Student at Trinity College, Cambridge
1665–66	The plague years at home: calculus, prisms, the first thoughts on gravity
1669	Lucasian Professor of Mathematics at Cambridge
1672	Fellow of the Royal Society; publishes his theory of light and colors
1687	Principia published, paid for by Edmond Halley
1696	Warden of the Royal Mint; Master from 1699
1703	President of the Royal Society
1704	Opticks published
1712	A Royal Society committee rules for him against Leibniz
1727	Dies in Kensington; buried in Westminster Abbey

What did the Principia show?

The Philosophiæ Naturalis Principia Mathematica, published on 5 July 1687, began with a question. In 1684 the astronomer Edmond Halley asked Newton what path a planet would follow if the Sun pulled it with a force that weakens with the square of distance. Newton said an ellipse, and that he had worked it out. Halley pressed him to write it up, and then paid to print the result.

The book opens with the three laws, explained in what Newton's laws of motion say, and then adds universal gravitation. Every piece of matter attracts every other piece, with a force that grows with their masses and falls with the square of the distance between them. In modern notation that is F = G m₁m₂/r², though Newton wrote it in geometry, not in that formula. With it he derived Kepler's laws of planetary motion, explained the tides as the pull of the Moon and Sun, and accounted for the paths of comets.

The Moon test, worked through

The test Newton ran in the plague years can be checked with modern numbers. If gravity weakens with the square of distance, then at the Moon, about 60 Earth radii away, it should be 60 × 60 = 3,600 times weaker than at the ground.

• At the ground, a falling apple accelerates at about 9.81 meters a second, every second.
• Divided by 3,600, that predicts about 0.00272 m/s² at the Moon's distance.
• Now the Moon itself. It circles at about 384,400 km, once every 27.32 days, or about 2.36 million seconds, so it moves at about 1,023 meters a second.
• Anything moving in a circle accelerates toward the center by its speed squared divided by the radius: 1,023² ÷ 384,400,000 ≈ 0.00272 m/s².

The two numbers match. In one second the Moon falls toward Earth by about 1.4 millimeters while an apple falls about 4.9 meters, a ratio of 3,600. The same force holds both. Newton's own figure for the Earth's size was off, so his match in 1666 was only "pretty nearly," and he published the full argument two decades later.

Did an apple really fall on his head?

No apple hit his head. The story comes from Newton himself, late in life. William Stukeley, a younger friend, wrote that on 15 April 1726, after dinner in a garden in Kensington, Newton told him the idea of gravity had come to him years before as he sat in a contemplative mood and saw an apple fall: "why should that apple always descend perpendicularly to the ground," he had asked himself. Stukeley's memoir, written in 1752, is transcribed by the Newton Project.

So the apple has a source, but a late one: an old man's memory of his youth, told 60 years on, and a story Newton evidently enjoyed telling. Historians accept that an apple may well have set him thinking. The idea that the insight arrived complete is legend; the real work took 20 years.

What did Newton discover about light?

Most people in Newton's day thought a prism colored white light. Newton showed the colors were in the light already. He split sunlight into a spectrum with one prism, picked out a single color, and sent it through a second prism. It bent again but stayed the same color. White light, he concluded, is a mixture of rays that bend by different amounts, which he reported to the Royal Society in 1672.

That finding explained why lenses blur colors at the edges, and it led him to build a telescope with a curved mirror instead, which reflects all colors alike. He made the first one in 1668, about 15 cm long, and a copy went to the Royal Society, which elected him a fellow. His Opticks of 1704 collected the work. He thought light was a stream of particles; the 19th century favored waves, and modern physics says light is both, in a sense neither side imagined.

Who invented calculus, Newton or Leibniz?

Both, independently. Calculus is the mathematics of change: how fast something varies at an instant, and how small changes add up. Newton developed his version, which he called the method of fluxions, in 1665 and 1666, but he did not publish it. Leibniz, a German philosopher and mathematician, developed his own in the 1670s and published first, in 1684.

The quarrel turned ugly. Newton's supporters accused Leibniz of stealing from Newton's unpublished papers. In 1712 the Royal Society, with Newton as its president, set up a committee that ruled in Newton's favor, and its report was largely drafted by Newton himself. Historians now credit both men. Leibniz's notation, the dx and ∫ students write today, won out over Newton's dots.

What else did Newton spend his life on?

The scientist known today is one part of the man. Of an estimated 10 million words in Newton's papers, about a million are on alchemy, the search for the hidden workings of matter, and a large share are on theology. When the economist John Maynard Keynes bought many of the alchemical papers at auction in 1936, he concluded that Newton "was not the first of the age of reason. He was the last of the magicians."

Newton's faith was intense and unorthodox. He privately rejected the Trinity, a view that could have cost him his career had it been known. He studied the Books of Daniel and Revelation for dates, and in a manuscript of 1704 reckoned that the world would not end before 2060, adding that he said so to stop "rash conjectures" by people who kept predicting it sooner.

At the Mint he was no figurehead. He oversaw the Great Recoinage of 1696, which replaced England's worn and clipped silver coins, and hunted counterfeiters himself, questioning informers and witnesses in person. One of them, William Chaloner, was hanged in 1699. Newton was also twice a member of Parliament for Cambridge University, in 1689–90 and 1701–02.

Why does Newton still matter?

Newton showed that the heavens and the Earth obey the same rules, and that those rules can be written as mathematics and tested against measurement. That idea is the backbone of how science works. His physics still steers spacecraft and designs bridges.

It has limits, and later physics found them. Near the speed of light, in very strong gravity and at the scale of atoms, Newton's laws give the wrong answers. Albert Einstein replaced Newton's gravity with curved spacetime in 1915, and the theory of relativity reduces to Newton's for everyday speeds and masses. Newton himself admitted he could not say what gravity was, only how it behaved: "I frame no hypotheses," he wrote in the 1713 edition of the Principia.

Check yourself

• Without looking back, explain how the Moon's orbit told Newton that gravity weakens with the square of distance.
• What did the two-prism experiment show that a single prism couldn't?
• Why do historians credit both Newton and Leibniz with calculus?

Sources

• Isaac Newton — Stanford Encyclopedia of Philosophy, George Smith, 2007
• Newton's Philosophiae Naturalis Principia Mathematica — Stanford Encyclopedia of Philosophy, George Smith, 2007
• Memoirs of Sir Isaac Newton's Life, by William Stukeley — The Newton Project, University of Oxford, 2004
• Papers of Sir Isaac Newton — Cambridge Digital Library, Cambridge University Library
• Isaac Newton — Wikipedia