It was not until this stage in his schooling that his attention came to
be directed to mathematics, by a book on astrology picked up at the
Stourbridge Fair.
As a consequence, he first read Euclid's Elements, which he
found too obvious, and then Descartes, La geometrie, which he found somewhat
difficult. He also read Oughtred's Clavis, works of Kepler and Viete, and
the Arithmetica infinitorum by wallis. From reading mathematics he turned to
creating it, early discovering the generalized binomial theorem and creating his
method of fluxions, as he called what today is known as differential calculus.
From late summer of 1665 until late summer of 1667, except for a brief
temporary reopening from mid-March to mid-June of 1666, Cambridge University
essentially closed down bevause of the rampant bubonic plague. It has been
generally reported that it was in 1665, during the first year of this closing of the
university and while living at home in Woolsthorpe, that Newton developed his
calculus (to the point where he could find the tangent and radius of curvature at
an arbitrary point of a curve), became interested in various physical questions,
performed his first experments in optics, and formulated the basic principles of
his theory of gravitation. Recent research, however, has shown that this account is
a myth, later promulgated by Newton himself to help assure him of
primacy in the discovery of the calculus, and that these discoveries were actually
not made until he was at cambridge in 1666 during the university's brief,
temporary reopening.
Newton returned to Camvridge in 1667 and for two years occupied himself
with optical researches. In 1669, Barrow resigned the Lucasian professorship,
to be succeeded by Newton, who began his eighteen years of university lecturing
His tremendous dislike of controversy, which seems to have bordered on the pathological,
had an important bearing on the history of mathematics, for the result
was that most all of his findings remained unpublished until many years after
their discovery. This postponement of publication later led to the undignified
dispute with Leibniz concerning priority of discovery of the calculus. It was
owing to this controversy that the english mathematiciians, backing Isaac
Newton as their leader, cut themselves off from continental developments, and
mathematical progress in England was retarded for practically one hundred
years.
Newton's university lectures from 1673 to 1683
were devoted to algebra and the theory of equations. It was in this period, in
1679, that he verified his law of gravitation by using a new meawurement of the
earth's radius in conjuction with a wtudy of the motion of the moon. He also
establlished the compatibility of his law of gravitation with Kepler's alws of
planeltary motion, on the assumption that the sun and the planets may be
regarded as heavy particles.
In 1703, he was elected president of the Royal Soeiety, a position to
which he was snnually reelected until his death; in 1705, he was knighted. The
last part of his life was mad unhappy by the unfortunate controversy with
Leibniz. He died in 1727 when eighty-four years old after a lingering and painful
illness, and was buried in Westminister Abbey.
Of course, Newton's greatest work is his Principia, in which there appears
for the first time a complete system of dynamics and a complete mathematical
formulation of the principal terrestrial and celestial phenomena of motion. It
proved to be the most influential and most admired work in the hisrory of
science. It is interesting that the theorems, although perhaps some may have
been discovered by fluxional methods, are all masterfully established by classical
Greek geometry adided, here and there, with some simple notions of limits.
Until the development of the theory of relativity, all physics and astronomy
rested on the assumption, made by Newton in this work, of a privileged frame
of reference.
Newton was never beaten by any of the various challenge problems that
circulated among the mathematicians of his time. In one of these, proposed by
Leibniz, he solved the problem of finding the orthogonal trajectories of a family
of curves.
Newton was a skilled experimentalist and a superb analyst. As a mathematician,
he is ranked almost universally as the greatest the world has yet produced.
His insight into physical problems and his ability to treat them mathematically has
probably never been excelled. One can find many testimonials by
competent judges as to his greatness, such as the noble tribute paid by Leibniz,
who said, "Taking mathematics from the beginning of the world to the time
when Newton lived, what he did was much the better half." And there is the
remark by Lagrange to the effect that Newton was the greatest genius that ever
lived, and the most fortunate, for we can find only once a system of the universe to be
established.
In contrast to these eulogies is Newton's own modest estimate of his work :
"I do not know what I may appear to the world; but to myself I seem to have
been only like a boy playing on the seashore, and diverting myself in now and
then finding a smoother pebble or a prettier shell than ordinary, whilst the great
ocean of truth lay all undiscovered before me." In generosity to his predecessors
he once explained that if he had seen farther than other men, it was only
because he had stood on the shoulders of giants.
It has been reported that Newton often spent eighteen of nineteen hours a
day in writing, and that he possessed remarkable powers of concentration.
Amusing tales, perhaps apocryphal, are told in testimony to his absent-mindedness
when engaged in thought.
There is the story that, when giving a dinner to some friends, Newton left
the table for a bottle of wine and, becoming mentally engaged, forgot his errand,
went to his room, donned his surplice, and ended up in chapel.
On another occasion, Newton's friend Dr. Stukeley called on him for a
chicken dinner. Newton was out, but the table was already laid with the cooked
fowl in a dish under a cover. Forgetful of his dinner engagement, Newton
overstayed his time, and Dr. Stukeley finally lifted the cover, removed and ate
the chicken, and then replaced the bones the bones in the bovered dish. When Newton
later appeared, he greeted his friend and sitting down he, too, lifted the cover,
only to discover the remains. "Dear me," he said. "Ihad forgotten that we had
already dined."
And then there was the occasion when, riding home one day from grantham,
Newton dismounted from his horse to walk the animal up Spittlegate
Hill, just beyond the town. Unknown to Newton the horse slipped away on the
way up the hill leaving only the empty bridle in his master's hands a fact theat Newton
discovered only when, at the top of the hill, he endeavored to vault
into the saddle.
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