I | INTRODUCTION |

Isaac
Newton (1642-1727), English physicist, mathematician, and natural
philosopher, considered one of the most important scientists of all time. Newton
formulated laws of universal gravitation and motion—laws that explain how
objects move on Earth as well as through the heavens (

*see*Mechanics). He established the modern study of optics—or the behavior of light—and built the first reflecting telescope. His mathematical insights led him to invent the area of mathematics called calculus (which German mathematician Gottfried Wilhelm Leibniz also developed independently). Newton stated his ideas in several published works, two of which,*Philosophiae Naturalis Principia Mathematica*(Mathematical Principles of Natural Philosophy, 1687) and*Opticks*(1704), are considered among the greatest scientific works ever produced. Newton’s revolutionary contributions explained the workings of a large part of the physical world in mathematical terms, and they suggested that science may provide explanations for other phenomena as well.
Newton took known facts and formed mathematical
theories to explain them. He used his mathematical theories to predict the
behavior of objects in different circumstances and then compared his predictions
with what he observed in experiments. Finally, Newton used his results to
check—and if need be, modify—his theories (

*see*Deduction). He was able to unite the explanation of physical properties with the means of prediction. Newton began with the laws of motion and gravitation he observed in nature, then used these laws to convert physics from a mere science of explanation into a general mathematical system with rules and laws. His experiments explained the phenomena of light and color and anticipated modern developments in light theory. In addition, his invention of calculus gave science one of its most versatile and powerful tools.II | EARLY LIFE AND EDUCATION |

Newton was born in Woolsthorpe, Lincolnshire,
in England. Newton’s father died before his birth. When he was three years old,
his mother remarried, and his maternal grandmother then took over his
upbringing. He began his schooling in neighboring towns, and at age ten was sent
to the grammar school at nearby Grantham. While at school he lived at the house
of a pharmacist named Clark, from whom he may have acquired his lifelong
interest in chemical operations. The young Newton seems to have been a quiet boy
who was skilled with his hands. He made sundials, model windmills, a water
clock, a mechanical carriage, and flew kites with lanterns attached to their
tails. However, he was (as he recounted late in his life) very inattentive at
school.

In 1656 Newton’s mother, on the death of her
second husband, returned to Woolsthorpe and took her son out of school in the
hope of making him a farmer. Newton showed no talent for farming, however, and
according to legend he once was found under a hedge deep in study when he should
have been in the market at Grantham. Fortunately, Newton’s former teacher at
Grantham recognized the boy’s intellectual gifts and eventually persuaded
Newton’s mother to allow him to prepare for entrance to University of Cambridge.
In June 1661 Trinity College at Cambridge admitted Newton as a subsizar (a
student required to perform various domestic services). His studies included
arithmetic, geometry, trigonometry, and, later, astronomy and optics. He
probably received much inspiration at Trinity from distinguished mathematician
and theologian Isaac Barrow, who was a professor of mathematics at the college.
Barrow recognized Newton’s genius and did all he could to cultivate it. Newton
earned his bachelor’s degree in January 1665.

III | EARLY SCIENTIFIC IDEAS |

When an outbreak of bubonic plague in 1665
temporarily shut down University of Cambridge, Newton returned to Woolsthorpe,
where he remained for nearly two years. This period was an intellectually rich
one for Newton. During this time, he did much scientific work in the subjects he
would spend his life exploring: motion, optics, and mathematics.

At this point, according to his own account,
Newton had made great progress in what he called his mathematical “method of
fluxions” (which today we call calculus). He also recorded his first thoughts on
gravitation, inspired (according to legend) by observing the fall of an apple in
an orchard. According to a report of a conversation with Newton in his old age,
he said he was trying to determine what type of force could hold the Moon in its
path around Earth. The fall of an apple led him to think that the attractive
gravitational force acting on the apple might be the same force acting on the
Moon. Newton believed that this force, although weakened by distance, held the
Moon in its orbit.

Newton devised a numerical equation to
verify his ideas about gravity. The equation is called the inverse square law of
attraction, and it states that the force of gravity (an object’s pull on another
object) is related to the inverse square of the distance between the two objects
(that is, the number 1 divided by the distance between the two objects times
itself). Newton believed this law should apply to the Sun and the planets as
well. He did not pursue the problem of the falling apple at the time, because
calculating the combined attraction of the whole Earth on a small body near its
surface seemed too difficult. He reintroduced these early thoughts years later
in his more thorough work, the

*Principia.*
Newton also began to investigate the nature
of light. White light, according to the view of his time, was uniform, or
homogeneous, in content. Newton’s first experiments with a prism called this
view of white light into question. Passing a beam of sunlight through a prism,
he observed that the beam spread out into a colored band of light, called a
spectrum. While others had undoubtedly performed similar experiments, Newton
showed that the differences in color were caused by differing degrees of a
property he called refrangibility. Refrangibility is the ability of light rays
to be refracted, or bent by a substance. For example, when a ray of violet light
passes through a refracting medium such as glass, it bends more than does a ray
of red light. Newton concluded through experimentation that sunlight is a
combination of all the colors of the spectrum and that the sunlight separates
when passed through the prism because its component colors are of differing
refrangibility. This property that Newton discovered actually depends directly
on the wavelengths of the different components of sunlight. A refracting
substance, such as a prism, will bend each wavelength of light by a different
amount.

A | The Reflecting Telescope |

In October 1667, soon after his return to
Cambridge, Newton was elected to a minor fellowship at Trinity College. Six
months later he received a major fellowship and shortly thereafter was named
Master of Arts. During this period he devoted much of his time to practical work
in optics. His earlier experiments with the prism convinced him that a
telescope’s resolution is limited not so much by the difficulty of building
flawless lenses as by the general refraction differences of differently colored
rays. Newton observed that lenses refract, or bend, different colors of light by
a slightly different amount. He believed that these differences would make it
impossible to bring a beam of white light (which includes all the different
colors of light) to a single focus. Thus he turned his attention to building a
reflecting telescope, or a telescope that uses mirrors instead of lenses, as a
practical solution. Mirrors reflect all colors of light by the same amount.

Scottish mathematician James Gregory had
proposed a design for a reflecting telescope in 1663, but Newton was the first
scientist to build one. He built a reflecting telescope with a 1.3-in (3.3-cm)
mirror in 1668. This telescope magnified objects about 40 times and differed
slightly from Gregory’s in design. Three years later, the Royal Society,
England’s official association of prominent scientists and mathematicians,
invited Newton to submit his telescope for inspection. He sent one similar to
his original model, and the Society established Newton’s dominance in the field
by publishing a description of the instrument.

B | Calculus (Newton’s “Fluxional Method”) |

In 1669 Newton gave his Trinity mathematics
professor Isaac Barrow an important manuscript, which is generally known by its
shortened Latin title,

*De Analysi*. This work contained many of Newton’s conclusions about calculus (what Newton called his “fluxional method”). Although the paper was not immediately published, Barrow made its results known to several of the leading mathematicians of Britain and Europe. This paper established Newton as one of the top mathematicians of his day and as the founder of modern calculus (along with Leibniz). Calculus addresses such concepts as the rate of change of a certain quantity, the slope of a curve at a given point, the computation of maximum and minimum values of functions, and the calculation of areas bounded by curves. When Barrow retired in 1669, he suggested to the college that Newton succeed him. Newton became the new professor of mathematics and chose optics as the subject of his first course of lectures.C | Newton’s First Published Works |

In early 1672 Newton was elected a Fellow
of the Royal Society. Shortly afterward Newton offered to submit a paper
detailing his discovery of the composite nature of white light. Much impressed
by his account, the Society published it. This publication triggered a long
series of objections to Newton’s scientific views in general, mostly by European
scientists from outside England. Many of the criticisms later proved unsound.
The strongest criticism of Newton’s work, however, concerned his work on the
theory of gravity and came from English inventor, mathematician, and curator of
the Royal Society Robert Hooke. Hooke insisted that he had suggested fundamental
principles of the law of gravitation to Newton. Newton answered these objections
carefully and at first patiently but later with growing irritation. These public
arguments aggravated Newton’s sensitivity to criticism, and for several years he
stopped publishing his findings.

IV | THE PRINCIPIA MATHEMATICA AND LAWS
OF MOTION |

By 1679 Newton had returned to the problem
of planetary orbits. The idea of a planetary attraction based on the inverse
square of the distance between the Sun and the planets (which he had assumed in
his early calculations at Woolsthorpe) ignited wide debate in the scientific
community. This law of attraction follows, in the simple case of a circular
orbit, from German astronomer Johannes Kepler’s Third Law, which relates the
time of a planet’s revolution around the Sun to the size of the planet’s orbit
(

*see*Kepler’s Laws). The law of attraction also takes into account the centripetal acceleration of a body moving in a circle, given by Dutch astronomer Christiaan Huygens in 1673. The problem of determining the orbit from the law of force had baffled everyone before Newton, who solved it in about 1680.*See also*Mechanics:*Newton’s Three Laws of Motion*.
In August 1684 English astronomer Edmond
Halley visited Cambridge to consult with Newton on the problem of orbits. During
a discussion with Halley about the shape of an orbit under the inverse square
law of attraction, Newton suggested that it would be an ellipse. Unable to find
the calculation from which he had derived the answer, Newton promised to send it
to Halley, which he did a few months later. On a second visit Halley received
what he called “a curious treatise de motu” (

*de motu*means “on motion”), which at Halley’s request was registered with the Royal Society in February 1685.
This tract on the laws of motion formed the
basis of the first book of

*Philosophiae Naturalis Principia Mathematica*. Scientists and scholars consider this work a milestone of scientific inquiry, and its composition in the span of about 18 months was an intellectual feat unsurpassed at that time. Halley played a substantial role in the development of the*Principia*. He tactfully smoothed over differences between Newton and Hooke, who insisted that Newton had stolen some of his ideas. Newton angrily decided to suppress the third section of this work, but Halley persuaded Newton to publish it. Halley managed Newton’s work through publication and underwrote the cost of printing.
The

*Principia*finally appeared in the summer of 1687. The scientific community hailed it as a masterpiece, although Newton had intentionally made the book difficult “to avoid being baited by little smatterers in mathematics.” The book’s grand unifying idea of gravitation, with effects extending throughout the solar system, captured the imagination of the scientific community. The work used one principle to explain diverse phenomena such as the tides, the irregularities of the Moon’s motion, and the slight yearly variations in the onset of spring and autumn.V | NEWTON’S LATER WORK |

A few months before publication of the

*Principia*, Newton emerged as a defender of academic freedom. King James II, who hoped to reestablish Roman Catholicism in England, issued a mandate to Cambridge in February 1687. This mandate called on the university to admit a certain Benedictine monk, Alban Francis, to the degree of Master of Arts without requiring him to take the usual oaths of allegiance to the Crown. The university saw this mandate as a request to grant preferential treatment to a Catholic and as a threat both to tradition and standards, so it steadfastly refused. Newton took a prominent part in defending the university’s position. The university senate appointed a group (including Newton) to appear before a government commission at Westminster, and they successfully defended the university’s rights. After the downfall of James II in the Glorious Revolution of 1688, Newton was elected a representative of the university in the Convention Parliament, in which he sat from January 1689 until its dissolution a year later. While he does not appear to have taken part in debate, Newton continued to be zealous in upholding the privileges of the university.
Newton’s public duties brought a change to
his retiring mode of life and required frequent journeys to London, where he met
several prominent writers and intellectuals, most notably philosopher John Locke
and diarist and civil servant Samuel Pepys. In the early 1690s, possibly in
response to the intellectual exertion of writing the

*Principia*, Newton suffered a period of depression. Opinions differ among Newton’s biographers as to the permanence of the effects of the attack.
In the years after his illness, Newton
summoned the energy to attack the complex problem of the Moon’s motion. This
work involved a correspondence with John Flamsteed, England’s first Astronomer
Royal, whose lunar observations Newton needed. However, misunderstandings and
quarrels marred their relationship, which ended sourly. In 1698 Newton tried to
carry his lunar work further and resumed collaboration with Flamsteed, but
difficulties arose again and Newton accused Flamsteed of withholding his
observations. The two scientists had not resolved the dispute when Flamsteed
died in 1719.

In 1696 Newton’s friends in the government
secured a paying political post for him by appointing him warden of the mint.
This position required that he live in London, where he resided until his death.
Newton’s work at the mint included a complete reform of the coinage. In order to
combat counterfeiting, he introduced the minting of coins of standard weight and
composition. He also instituted the policy of minting coins with milled edges.
Newton successfully carried out these tasks, which demanded great technical and
administrative skill, in the three years leading up to November 1699. At that
time his peers promoted him to the mastership of the mint. This position was a
well-paid post that Newton held for the rest of his life.

In 1701 Newton resigned his chair and
fellowship at Cambridge and in 1703 was elected president of the Royal Society,
an office to which he was reelected annually thereafter. In 1704, a year after
the death of his rival Hooke, he brought out his second great treatise,

*Opticks,*which included his theories of light and color as well as his mathematical discoveries. Unlike the*Principia*, which was in Latin,*Opticks*was written in English, but Newton later published a Latin translation. Most of Newton’s work on*Opticks*was done long before he relocated to London. One of its most interesting features is a series of general speculations added to the second edition (1717) in the form of “Queries,” or questions, which bear witness to his profound insight into physics. Many of his questions foreshadowed modern developments in physics, engineering, and the natural sciences.
In 1705 Queen Anne knighted Newton. By this
time Newton was the dominant figure in British and European science. In the last
two decades of his life, he prepared the second and third editions of the

*Principia*(1713, 1726) and published second and third editions of*Opticks*(1717, 1721) as well.
During these last two decades Newton was
entangled in a lengthy and bitter controversy with Leibniz over which of the two
scientists had invented calculus. This controversy embittered Newton’s last
years and harmed relations between the scientific communities in Britain and on
the European continent. It also slowed the progress of mathematical science in
Britain. Most scholars agree that Newton was the first to invent calculus,
although Leibniz was the first to publish his findings. Mathematicians later
adopted Leibniz’s mathematical symbols, which have survived to the present day
with few changes.

VI | NEWTON’S IMPACT ON SCIENCE |

Newton’s place in scientific history rests
on his application of mathematics to the study of nature and his explanation of
a wide range of natural phenomena with one general principle—the law of
gravitation. He used the foundations of dynamics, or the laws of nature
governing motion and its effects on bodies, as the basis of a mechanical picture
of the universe. His achievements in the use of calculus went so far beyond
previous discoveries that scientists and scholars regard him as the chief
pioneer in this field of mathematics.

Newton’s work greatly influenced the
development of physical sciences. During the two centuries following publication
of the

*Principia*, scientists and philosophers found many new areas in which they applied Newton’s methods of inquiry and analysis. Much of this expansion arose as a consequence of the*Principia*. Scientists did not see the need for revision of some of Newton’s conclusions until the early 20th century. This reassessment of Newton’s ideas about the universe led to the modern theory of relativity and to quantum theory, which deal with the special cases of physics involving high speeds and physics of very small dimensions, respectively. For systems of ordinary dimensions, involving velocities that do not approach the speed of light, the principles that Newton formulated nearly three centuries ago are still valid.
Besides his scientific work, Newton left
substantial writings on theology, chronology, alchemy, and chemistry. In 1725
Newton moved from London to Kensington (then a village outside London) for
health reasons. He died there on March 20, 1727. He was buried in Westminster
Abbey, the first scientist to be so honored.

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