Name: sweetestreds

Assignment: Thematic Essay: The

dispute

between Newton and

Leibniz

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Table of ContentsTitle Page

Introduction: 3

Sir Isaac Newton: A Brief Biography 4

Gottfried Wilhelm Leibniz: A brief Biography 8

The Calculus Controversy 10

Conclusion 14

References 16

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Introduction

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Sir Isaac Newton: A brief Biography

The year of 1642 saw many historical events

occurring. It was marked by the death of Galileo as well as

the was between Charles I and the Parliament and, on

Christmas Day (December 25th) of that same year a widow

gave birth to a premature baby named Isaac Newton in the

village of Woolsthorpe, Lincolnshire near Cambridge of

the United Kingdom. The fragile baby’s chances of

survival was estimated at less than fifty percent and yet this

child would not only survive and give remarkable

contributions to the world of politics, mathematics and

physics, but; he would live to be eighty five years old!

The life span of Sir Isaac Newton can be

categorised into three timelines. These are;

1643 – 1669 ; this period of time comprises the childhood days of Newton as well as the

duration of his academic years until his undergraduate days. During this time it was believed

the Newton little enthusiasm or possession of a great expanse of mathematical knowledge.

His course of studies centred on law.

Newton’s first experiment as he would refer to it would be that of trying to

measure the gale force of the wind from the great storm that occurred in England where he first

measured the distance he jumped in the direction of the wind and then compared this

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Figure 1 Sir Isaac Newton (Burton, 2007)

measurement with that of the distance jumped against the direction of the wind. Besides this

experiment, Newton displayed little knack for academic work and instead was fascinated with

mechanical constructions of sundials, clocks and other devices.

Despite his lack of interest on academic work, Newton’s uncle discovered

that he was quite a resilient individual and thus decided to invest in Newton’s future by financing

his attendance to Trinity College, Cambridge where he would go on to pursue a law degree in

1661. It is important to note that mathematics was not an integral part of the curriculum during

this era and would not become part of the curriculum until the Lucasian professorship. Instead

graduates were versed in logic, rhetoric, moral philosophy, Latin and Greek.

Newton’s interest in mathematics was inspired by his need for a challenge

and thus he began reading publications of Euclid and Descartes. Isaac Barrow who was regarded

as one of the world’s foremost mathematicians of that time would then serve as his mentor after

becoming the first Lucasian professor at the university where Newton studied. Postulations that

Barrow made served as precursors for Newton’s invention of calculus.

Newton’s first three significant mathematical contributions would arise

during his seclusion in the time of the bubonic plague that was sweeping through England from

1666 to 1669. It is at this time that Newton was able to:

1. Invent the mathematical method which he called fluxions but today is

known as differential calculus.

2. Separate white light into its constitutional different colours of lights. His

findings however would not be published until 1704 under the title Opticks.

3. Discover the concept of the universal law of gravitation.

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1669 – 1687; Also described as Newton’s Golden years; it was during this

second period of Newton’s life, that he served as a Lucasian professor and also it was the period

in which most of his mathematical discoveries occurred. Accomplishments include:

1. He invented the first reflecting telescope which subsequently led to

valuable contributions in optics. Namely, “He proposed that light was composed of a stream of

tiny particles, or corpuscles, of different sizes (the size corresponding with the colour) and

moving with different velocities.” (Burton, 2007) This postulation would cause controversy

between himself and Robert Hooke who was a foremost personality in the study of Optics.

2. After studying Wallis’ Arithmetica Infinitorium, Newton developed the

expression for binomial expansion (a + b)n for n being a negative or fractional component. This

postulation as well as his work on infinite series was to be shared in letter format in 1676 (The

Epistola Prior) with Leibniz who had requested his Newton’s notes in hope that it would aid his

(Leibniz’s) studies.

3. Working with physicists, Newton began to explore characteristics of gravity.

He published Philosophiae Naturalis Principia Mathematica (The Mathematical Principles of

Natural Philosophy) in 1687. “The Principia consists of three books (containing 53, 42, and 48

propositions, respectively) as well as 25 pages of introductory matter.” (Burton, 2007). His most

memorable contribution in this field was the laws of motions the first two laws of which were

inspired by work done by Galileo but the last one which simply stated; To every action there is

an equal and opposite reaction, was developed by Newton himself.

Besides these works, all of Newton’s work would serve as the foundation for the

work and postulations of proceeding mathematicians, astronomers and physicists until present

day.

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1687 – 1727; these were that latter years of Newton’s life where Newton

worked as a highly paid and ranked Government official in the mint and as a politician. He

battled counterfeiters of British currency and developed a new mixture of alloys that would

subsequently be used to produce British currency. Eventually Newton became afflicted with a

debilitating mental disease and subsequently died in 1727. More of his works would be printed

posthumously.

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Gottfried Wilhelm Leibniz: A brief Biography

Two years prior to the Peace of Westphalia putting an end to the

Thirty Years’ War, Gottfried Wilhelm Leibniz was born in 1646 in

the town in Leipzig in the Continent. In 1652, Leibniz’s father (a

jurist and professor of moral philosophy) died and thus he was left

to learn Latin and Greek by himself. At an early age, Leibniz was

fascinated with the works of Aristotle and Democritus and thus

spent exhaustive amounts of time comparing the work of both

individuals.

Leibniz’s undergraduate studies began concurrently with Newton in the year of 1661,

however, Leibniz studied at the university in his native city. Leibniz’s course of study centred

around orthodox Lutheran doctrine as well as philosophy. Emphasis was also placed on

arithmetic and Euclid’s elements during his course of study. By the year 1664, Leibniz earned

his degree in legal studies and acquired a job at the university at which he had studied.

Leibniz’s first publications were Disputatio Arithmetica de Complexionibus and Ars

Combinatoria (1666), which delved extensively into the theories of permutations and

combinations. He would then later write an essay on the study of law which gained him

employment under the archbishop – elector of Mainz. Leibniz would subsequently develop all

his works in Mainz where he stayed until 1672, and then from there he migrated to Hanover in

1676 where he lived and worked until his death in 1716.

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Figure 2 Showing Gottfried Wilhelm Leiniz (Burton, 2007)

During the years of 1672 to 1676, Leibniz was mentored by one Christopher Huygens of

Paris who realised the ingenious of his German protégé. Among Leibniz’s most notable works,

one remembers the following:

1. Leibniz asserted that he could find the sum of any infinite series whose terms

were formed by some rule (provided only that the series should converge). (Burton, 2007)

2. Leibniz improved or rather developed a working calculating machine based on

a model that had already been invented by Pascal.

3. He developed his own alternating series in 1673 however, Newton brought to

his attention that this series had already been discovered by James Gregory in 1671.

4. After delving onto the works of Descartes, Leibniz created his version of

calculus during the years 1672 to 1676.

Besides becoming a member of the Royal Society, Leibniz lived an adventurous life filled

with many other accomplishments and positions of employment. His life ended in the year of

1716 when he took a noxious potion while suffering with gout. However, there has been

speculation that tired of being accused of plagiarism and having his life’s work constantly

scrutinized and demeaned by his peers, Leibniz decided to commit suicide.

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The Calculus Controversy

Due to Newton’s aversion to controversy over his publications as was the case with

Robert Hooke, he never showed much enthusiasm to publish his works for approval by all.

Newton was rather content to circulate his findings among friends. One of whom happened to act

as an intermediate between Newton and Leibniz, that is, Mr. Henry Oldenburg; permanent

secretary of the Royal Society which Leibniz was a member of. Despite this fact, it has been

confirmed that Newton’s fluxions / differential calculus method had been developed between

1665 and the 1670s. It has also been noted that after development of his method, with much

hesitation on Newton’s part and even trying to disguise his fluxions method through use of

anagrams, he was encouraged to share his findings with Leibniz who took an interest in

Newton’s writings and sought further information on them through Oldenburg.

Within a few years time, Leibniz would then develop his own method of calculus and

much to his bereavement, although his work was formally published before Newton’s, Leibniz is

accused of plagiarism of Newton’s method. This dispute would last for years with no resolution

being derived seemingly in the near future. Even Newton himself would allude to Leibniz’s work

as plagiarism of his own.

The first suggestion of plagiarism was alleged by Nicolas Fatio deDuiller who stated; “I

am now fully convinced by the evidence itself on the subject that Newton is the first inventor

of this calculus, and the earliest by many years; whether Leibniz, its second inventor, may have

borrowed anything from him, I should rather leave to the judgement of those who had seen the

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letters of Newton, and his original manuscripts.” (Burton, 2007) An irate Leibniz would then

retort to friends by simply pointing out that he (Leibniz) had been given credit for the findings in

Newton’s first publication of the Principia. Feeling however unsatisfied that Newton would not

support Leibniz’s claims, Leibniz went on to further publish a letter in an attempt to vindicate

himself.

Approximately five years would pass and when all believed that the dispute had ended,

the controversy would be propelled by the following statement released by Sir Isaac Newton: “In

a letter written to Mr. Leibniz in the year 1676, and published by Dr. Wallis [in volume III

(1699) of the Opera], I mentioned a method by which I found some general theorems about

squaring curvilinear figures. . . . And some years ago I lent out a manuscript containing such

theorems; and having since met with some things copied out of it, I have on this occasion made

it public.” (Burton, 2007) Leibniz would then counter by critiquing Newton’s works and

releasing the following statement in January under an anonymous guise; “The elements of this

calculus have been given to the public by its inventor, Dr. Wilhelm Leibniz,

in these Acts. . . . Instead of the Leibnizian differences, then, Dr. Newton employs, and has

always employed, fluxions, which are very much the same as the arguments of fluents produced

in the least intervals of time; and these fluxions he has used elegantly in his Mathematical

Principles of Nature and in other later publications, just as Honoratus Fabri, in his Synopsis of

Geometry substituted progressive motions for the methods of Cavalieri.” (Burton, 2007)

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This newfound innuendo which had been hurled asserted that Newton was in fact just like

his disciple Fabri who was a proven plagiarizer of the works Cavalieri. Wrath would be

widespread throughout England as these allegations were hurled by Leibniz against Newton.

This seemingly childish banter of accusations would continue for years with other

mathematicians like John Keill, rallying to the support of Newton in 1708 by citing him as the

first and true inventor of calculus in his publication The Laws of Centripetal Force, which was

an essay addressed as a letter to Halley. Keill’s statement; “All these laws follow from that very

celebrated arithmetic of fluxions which, without any doubt, Dr. Newton invented first, as can

readily be proved by anyone who reads the letters about it published by Wallis; yet the same

arithmetic afterwards, under a changed name and method of notation, was published by Dr.

Leibniz in Acta Eruditorum.’ (Burton, 2007) would only serve to infuriate Leibniz further and

demand an apology and rebuttal from Keill. However what would follow would be extensive

investigations by committees appointed by the Royal Society as well as other recognised bodies

into who was the first inventor of calculus.

After years of extensive research, members of the committee concluded in 1712 that

Newton was in fact the first inventor of calculus. “The committee’s conclusion runs:

That the differential method is one and the same with the method of fluxions, excepting the

name and the mode of notation; Mr. Leibniz calling those quantities differences, which Mr.

Newton calls moments or fluxions; and marking them with the letter d, a mark not used by Mr.

Newton. And therefore we take the proper question to be, not who invented this or that

method, but who was the first inventor of the method. And we believe that those who reputed

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Mr. Leibniz the first inventor, knew little or nothing of his correspondence with Mr. Collins

or Mr. Oldenburg long before; nor of Mr. Newton’s having the method above fifteen years

before Mr. Leibniz began to publish it in the Acta Eruditorum of Leipzig.

For which reasons, we reckon Mr. Newton the first inventor; and are of the opinion, that

Mr. Keill, in asserting the same, has been no ways injurious to Mr. Leibniz.’ (Burton, 2007)

Appeals of the decision by Leibniz led to more investigations which were viewed as biased

based on the actions of some of the research who gave preference to Newton even before the

verdict. The outcome would never – the – less be the same.

This dispute would continue weaken Leibniz’s reputation and strengthen Newton’s who

by now was viewed as a British hero. This would subsequently be detrimental to Leibniz’s

career as he would only be employed to do menial research projects and his publications would

no longer be recognised in the public forum except for the Theodicy which his published is 1710

where he disputed religious doctrine rather than mathematics. Sadly, even after the death of

Leibniz in 1716, Newton continued to pursue the cause of verifying that he Newton was the first

inventor of calculus and that Leibniz had plagiarised his work. It is key to note however, that

during his life Leibniz never disputed that Newton had written and developed fluxions /

differential calculus, he had however only disputed the fact that he had plagiarised Newton’s

work and always asserted that his development of calculus was independent of Newton’s

method. In spite of the this, no vindication would be provided for Leibniz and the needless

dispute also affected political and social ties between the homelands of the respective

mathematicians for years to come.

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ConclusionIn sum, the current resolution of this controversy culminated in both men being given

credit as the co-inventors of calculus. However, after consideration of all the facts involved in

the controversy, absent of all innuendo, it is still unclear whether Leibniz’s method of calculus

was that of his own discovery independent of Newton’s work or if it was inspired by Newton’s

work. This controversy may have been avoided completely had Newton published his work from

the time it was developed. However, one can never truly understand the way the mind of any

other individual works.

What is certain though is that this dispute was the basis for the spreading of acrimony,

slander and innuendo between what should have been exemplary men of that decade. The need

for glory corrupted men as well as the need for revenge in some cases. One cannot therefore help

but wonder if the physical meeting of both parties involved with an extensive discussion and

demonstration of how each method was developed among a congregation of UNBIASED peers

would have maybe abated the situation. Or, could not both parties be content with sharing the

priority for the development of calculus? Where was the need to make this relationship work

through compromise?

This dispute not only impacted the lives of the two individuals at the centre of the

controversy but also the society and nations in which each individual resided. The unnecessary

escalation of this matter as well as the tarnishing of each individual’s character is in our opinion

a tragedy that has greatly affected the history of mathematics as well as its development. It is

therefore hoped that should any type of controversy arise within the mathematics world between

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mathematics that the individuals involved would learn from the mistakes of Newton and Leibniz

and find a peaceful resolution.

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References1. Burton, David (2007), The History of Mathematics: An Introduction. Mc Graw-Hill,

Boston (6th Edition)

2. Newton vs Leibniz; the Calculus controversy. Retrieved 1st November, 2011 from:

http://www.angelfire.com/md/byme/mathsample.html

3. Sastry, S.S. The Newton-Leibniz controversy over the invention of the calculus.

Retrieved 1st November, 2011 from:

http://pages.cs.wisc.edu/~sastry/hs323/calculus.pdf

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