Analytical Society
Encyclopedia
The Analytical Society was a group of individuals in early-19th century Britain
whose aim was to promote the use of Leibniz
ian or analytical calculus as opposed to Newtonian calculus
. The latter system came into being in the 18th century as an invention of Sir Isaac Newton, and was in use throughout Great Britain for political rather than practical reasons. The Newton system of fluxions
and fluents proved cumbersome to use, and less flexible and usable than Leibnizian calculus
, which was used by the rest of Europe.
The Society was founded in 1812 over a Sunday morning breakfast. Its membership originally consisted of a group of Cambridge students led by Robert Woodhouse
. Woodhouse, a professor at the university, had published a series of papers that promoted Leibnizian calculus as early as 1803. These papers proved difficult to understand and thus failed to promote the idea. Other charter members included Charles Babbage
, Sir John Herschel
and George Peacock
. It soon attracted many new members, predominantly students.
The first solid action by the Society did not take place until 1816, when a French textbook on analytical calculus was translated and distributed. This was followed in 1817 by the introduction, by Peacock, of Leibnizian symbols in that year's examinations in the local senate-house.
Both the exam and the textbook met with little criticism until 1819, when both were criticised by a D.M. Peacock. However, the reforms were encouraged by younger members of Cambridge University. George Peacock successfully encouraged a colleague, Richard Gwatkin of St John's College
at Cambridge University, to adopt the new notation in his exams.
Use of Leibnizian notation began to spread after this. In 1820, the notation was used by William Whewell
, a previously neutral but influential Cambridge University faculty member, in his examinations. In 1821, Peacock again used Leibnizian notation in his examinations, and the notation became well established.
The Society followed its success by publishing two volumes of examples showing the new method. One was by George Peacock on differential and integral calculus; the other was by Herschel on the calculus of finite differences. They were joined in this by Whewell, who in 1819 published a book, An Elementary Treatise on Mechanics, which used the new notation and which became a standard textbook on the subject.
Sir John Ainz, a pupil of Peacock's, published a notable paper in 1826 which showed how to apply Leibnizian calculus on various physical problems.
These activities did not go unnoticed at other universities in Great Britain, and soon they followed Cambridge's example. By 1830, Leibnizian calculus had superseded Newtonian calculus. It soon underwent constructive use, for instance in devising and expressing James Clerk Maxwell
's equations.
In 1832, the Society, which had been renamed the Cambridge Philosophical Society
in 1819, incorporated officially. The members included Peacock and mathematician Oliver Heaviside
. This society still exists today.
United Kingdom
The United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...
whose aim was to promote the use of Leibniz
Gottfried Leibniz
Gottfried Wilhelm Leibniz was a German philosopher and mathematician. He wrote in different languages, primarily in Latin , French and German ....
ian or analytical calculus as opposed to Newtonian calculus
Calculus
Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem...
. The latter system came into being in the 18th century as an invention of Sir Isaac Newton, and was in use throughout Great Britain for political rather than practical reasons. The Newton system of fluxions
Method of Fluxions
Method of Fluxions is a book by Isaac Newton. The book was completed in 1671, and published in 1736. Fluxions is Newton's term for differential calculus...
and fluents proved cumbersome to use, and less flexible and usable than Leibnizian calculus
Calculus
Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem...
, which was used by the rest of Europe.
The Society was founded in 1812 over a Sunday morning breakfast. Its membership originally consisted of a group of Cambridge students led by Robert Woodhouse
Robert Woodhouse
Robert Woodhouse was an English mathematician.-Biography:He was born at Norwich, the son of Robert Woodhouse, linen draper, and educated at Caius College, Cambridge, of which society he was subsequently a fellow...
. Woodhouse, a professor at the university, had published a series of papers that promoted Leibnizian calculus as early as 1803. These papers proved difficult to understand and thus failed to promote the idea. Other charter members included Charles Babbage
Charles Babbage
Charles Babbage, FRS was an English mathematician, philosopher, inventor and mechanical engineer who originated the concept of a programmable computer...
, Sir John Herschel
John Herschel
Sir John Frederick William Herschel, 1st Baronet KH, FRS ,was an English mathematician, astronomer, chemist, and experimental photographer/inventor, who in some years also did valuable botanical work...
and George Peacock
George Peacock
George Peacock was an English mathematician.-Life:Peacock was born on 9 April 1791 at Thornton Hall, Denton, near Darlington, County Durham. His father, the Rev. Thomas Peacock, was a clergyman of the Church of England, incumbent and for 50 years curate of the parish of Denton, where he also kept...
. It soon attracted many new members, predominantly students.
The first solid action by the Society did not take place until 1816, when a French textbook on analytical calculus was translated and distributed. This was followed in 1817 by the introduction, by Peacock, of Leibnizian symbols in that year's examinations in the local senate-house.
Both the exam and the textbook met with little criticism until 1819, when both were criticised by a D.M. Peacock. However, the reforms were encouraged by younger members of Cambridge University. George Peacock successfully encouraged a colleague, Richard Gwatkin of St John's College
St John's College, Cambridge
St John's College is a constituent college of the University of Cambridge. The college's alumni include nine Nobel Prize winners, six Prime Ministers, three archbishops, at least two princes, and three Saints....
at Cambridge University, to adopt the new notation in his exams.
Use of Leibnizian notation began to spread after this. In 1820, the notation was used by William Whewell
William Whewell
William Whewell was an English polymath, scientist, Anglican priest, philosopher, theologian, and historian of science. He was Master of Trinity College, Cambridge.-Life and career:Whewell was born in Lancaster...
, a previously neutral but influential Cambridge University faculty member, in his examinations. In 1821, Peacock again used Leibnizian notation in his examinations, and the notation became well established.
The Society followed its success by publishing two volumes of examples showing the new method. One was by George Peacock on differential and integral calculus; the other was by Herschel on the calculus of finite differences. They were joined in this by Whewell, who in 1819 published a book, An Elementary Treatise on Mechanics, which used the new notation and which became a standard textbook on the subject.
Sir John Ainz, a pupil of Peacock's, published a notable paper in 1826 which showed how to apply Leibnizian calculus on various physical problems.
These activities did not go unnoticed at other universities in Great Britain, and soon they followed Cambridge's example. By 1830, Leibnizian calculus had superseded Newtonian calculus. It soon underwent constructive use, for instance in devising and expressing James Clerk Maxwell
James Clerk Maxwell
James Clerk Maxwell of Glenlair was a Scottish physicist and mathematician. His most prominent achievement was formulating classical electromagnetic theory. This united all previously unrelated observations, experiments and equations of electricity, magnetism and optics into a consistent theory...
's equations.
In 1832, the Society, which had been renamed the Cambridge Philosophical Society
Cambridge Philosophical Society
The Cambridge Philosophical Society is a scientific society at University of Cambridge. It was founded in 1819. The name derives from the medieval use of the word philosophy to denote any research undertaken outside the fields of theology and medicine...
in 1819, incorporated officially. The members included Peacock and mathematician Oliver Heaviside
Oliver Heaviside
Oliver Heaviside was a self-taught English electrical engineer, mathematician, and physicist who adapted complex numbers to the study of electrical circuits, invented mathematical techniques to the solution of differential equations , reformulated Maxwell's field equations in terms of electric and...
. This society still exists today.