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The Analytical Society was a group of individuals in early-19th century Britain whose aim was to promote the use of Leibnizian 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 at the lodgings of Edward Bromhead, who suggested it. 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[by whom?] 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.[who?] 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.