MMT

Isaac Newton

I INTRODUCTION

Newton, Sir Isaac (1642-1727), mathematician and physicist, one of the foremost scientific

intellects of all time. Born at Woolsthorpe, near Grantham in Lincolnshire, where he

attended school, he entered Cambridge University in 1661; he was elected a Fellow of

Trinity College in 1667, and Lucasian Professor of Mathematics in 1669. He remained at the

university, lecturing in most years, until 1696. Of these Cambridge years, in which Newton

was at the height of his creative power, he singled out 1665-1666 (spent largely in

Lincolnshire because of plague in Cambridge) as "the prime of my age for invention".

During two to three years of intense mental effort he prepared Philosophiae Naturalis

Principia Mathematica (Mathematical Principles of Natural Philosophy) commonly known as

the Principia, although this was not published until 1687.

As a firm opponent of the attempt by King James II to make the universities into Catholic

institutions, Newton was elected Member of Parliament for the University of Cambridge to

the Convention Parliament of 1689, and sat again in 1701-1702. Meanwhile, in 1696 he had

moved to London as Warden of the Royal Mint. He became Master of the Mint in 1699, an

office he retained to his death. He was elected a Fellow of the Royal Society of London in

1671, and in 1703 he became President, being annually re-elected for the rest of his life.

His major work, Opticks, appeared the next year; he was knighted in Cambridge in 1705.

Isaac Newton

I INTRODUCTION

Newton, Sir Isaac (1642-1727), mathematician and physicist, one of the foremost scientific

intellects of all time. Born at Woolsthorpe, near Grantham in Lincolnshire, where he

attended school, he entered Cambridge University in 1661; he was elected a Fellow of

Trinity College in 1667, and Lucasian Professor of Mathematics in 1669. He remained at the

university, lecturing in most years, until 1696. Of these Cambridge years, in which Newton

was at the height of his creative power, he singled out 1665-1666 (spent largely in

Lincolnshire because of plague in Cambridge) as "the prime of my age for invention".

During two to three years of intense mental effort he prepared Philosophiae Naturalis

Principia Mathematica (Mathematical Principles of Natural Philosophy) commonly known as

the Principia, although this was not published until 1687.

As a firm opponent of the attempt by King James II to make the universities into Catholic

institutions, Newton was elected Member of Parliament for the University of Cambridge to

the Convention Parliament of 1689, and sat again in 1701-1702. Meanwhile, in 1696 he had

moved to London as Warden of the Royal Mint. He became Master of the Mint in 1699, an

office he retained to his death. He was elected a Fellow of the Royal Society of London in

1671, and in 1703 he became President, being annually re-elected for the rest of his life.

His major work, Opticks, appeared the next year; he was knighted in Cambridge in 1705.

As Newtonian science became increasingly accepted on the Continent, and especially after a

general peace was restored in 1714, following the War of the Spanish Succession, Newton

became the most highly esteemed natural philosopher in Europe. His last decades were

passed in revising his major works, polishing his studies of ancient history, and

defending himself against critics, as well as carrying out his official duties. Newton was

modest, diffident, and a man of simple tastes. He was angered by criticism or opposition,

and harboured resentment; he was harsh towards enemies but generous to friends. In

government, and at the Royal Society, he proved an able administrator. He never married

and lived modestly, but was buried with great pomp in Westminster Abbey.

Newton has been regarded for almost 300 years as the founding examplar of modern physical

science, his achievements in experimental investigation being as innovative as those in

mathematical research. With equal, if not greater, energy and originality he also plunged

into chemistry, the early history of Western civilization, and theology; among his special

studies was an investigation of the form and dimensions, as described in the Bible, of

Solomon's Temple in Jerusalem.

II OPTICS

In 1664, while still a student, Newton read recent work on optics and light by the English

physicists Robert Boyle and Robert Hooke; he also studied both the mathematics and the

physics of the French philosopher and scientist Rene Descartes. He investigated the

refraction of light by a glass prism; developing over a few years a series of increasingly

elaborate, refined, and exact experiments, Newton discovered measurable, mathematical

patterns in the phenomenon of colour. He found white light to be a mixture of infinitely

varied coloured rays (manifest in the rainbow and the spectrum), each ray definable by the

angle through which it is refracted on entering or leaving a given transparent medium. He

correlated this notion with his study of the interference colours of thin films (for

example, of oil on water, or soap bubbles), using a simple technique of extreme acuity to

measure the thickness of such films. He held that light consisted of streams of minute

particles. From his experiments he could infer the magnitudes of the transparent

"corpuscles" forming the surfaces of bodies, which, according to their dimensions, so

interacted with white light as to reflect, selectively, the different observed colours of

those surfaces.

The roots of these unconventional ideas were with Newton by about 1668; when first

expressed (tersely and partially) in public in 1672 and 1675, they provoked hostile

criticism, mainly because colours were thought to be modified forms of homogeneous white

light. Doubts, and Newton's rejoinders, were printed in the learned journals. Notably, the

scepticism of Christiaan Huygens and the failure of the French physicist Edme Mariotte to

duplicate Newton's refraction experiments in 1681 set scientists on the Continent against

him for a generation. The publication of Opticks, largely written by 1692, was delayed by

Newton until the critics were dead. The book was still imperfect: the colours of

elaborate, refined, and exact experiments, Newton discovered measurable, mathematical

patterns in the phenomenon of colour. He found white light to be a mixture of infinitely

varied coloured rays (manifest in the rainbow and the spectrum), each ray definable by the

angle through which it is refracted on entering or leaving a given transparent medium. He

correlated this notion with his study of the interference colours of thin films (for

example, of oil on water, or soap bubbles), using a simple technique of extreme acuity to

measure the thickness of such films. He held that light consisted of streams of minute

particles. From his experiments he could infer the magnitudes of the transparent

"corpuscles" forming the surfaces of bodies, which, according to their dimensions, so

interacted with white light as to reflect, selectively, the different observed colours of

those surfaces.

The roots of these unconventional ideas were with Newton by about 1668; when first

expressed (tersely and partially) in public in 1672 and 1675, they provoked hostile

criticism, mainly because colours were thought to be modified forms of homogeneous white

light. Doubts, and Newton's rejoinders, were printed in the learned journals. Notably, the

scepticism of Christiaan Huygens and the failure of the French physicist Edme Mariotte to

duplicate Newton's refraction experiments in 1681 set scientists on the Continent against

him for a generation. The publication of Opticks, largely written by 1692, was delayed by

Newton until the critics were dead. The book was still imperfect: the colours of

diffraction defeated Newton. Nevertheless, Opticks established itself, from about 1715, as

a model of the interweaving of theory with quantitative experimentation.

III MATHEMATICS

In mathematics too, early brilliance appeared in Newton's student notes. He may have

learnt geometry at school, though he always spoke of himself as self-taught; certainly he

advanced through studying the writings of his compatriots William Oughtred and John

Wallis, and of Descartes and the Dutch school. Newton made contributions to all branches

of mathematics then studied, but is especially famous for his solutions to the

contemporary problems in analytical geometry of drawing tangents to curves

(differentiation) and defining areas bounded by curves (integration). Not only did Newton

discover that these problems were inverse to each other, but he discovered general methods

of resolving problems of curvature, embraced in his "method of fluxions" and "inverse

method of fluxions", respectively equivalent to Leibniz's later differential and integral

calculus. Newton used the term "fluxion" (from Latin meaning "flow") because he imagined a

quantity "flowing" from one magnitude to another. Fluxions were expressed algebraically,

as Leibniz's differentials were, but Newton made extensive use also (especially in the

Principia) of analogous geometrical arguments. Late in life, Newton expressed regret for

the algebraic style of recent mathematical progress, preferring the geometrical method of

the Classical Greeks, which he regarded as clearer and more rigorous.

Newton's work on pure mathematics was virtually hidden from all but his correspondents

a model of the interweaving of theory with quantitative experimentation.

III MATHEMATICS

In mathematics too, early brilliance appeared in Newton's student notes. He may have

learnt geometry at school, though he always spoke of himself as self-taught; certainly he

advanced through studying the writings of his compatriots William Oughtred and John

Wallis, and of Descartes and the Dutch school. Newton made contributions to all branches

of mathematics then studied, but is especially famous for his solutions to the

contemporary problems in analytical geometry of drawing tangents to curves

(differentiation) and defining areas bounded by curves (integration). Not only did Newton

discover that these problems were inverse to each other, but he discovered general methods

of resolving problems of curvature, embraced in his "method of fluxions" and "inverse

method of fluxions", respectively equivalent to Leibniz's later differential and integral

calculus. Newton used the term "fluxion" (from Latin meaning "flow") because he imagined a

quantity "flowing" from one magnitude to another. Fluxions were expressed algebraically,

as Leibniz's differentials were, but Newton made extensive use also (especially in the

Principia) of analogous geometrical arguments. Late in life, Newton expressed regret for

the algebraic style of recent mathematical progress, preferring the geometrical method of

the Classical Greeks, which he regarded as clearer and more rigorous.

Newton's work on pure mathematics was virtually hidden from all but his correspondents