The Analytical Society was a group of individuals in early-19th-century Britain whose aim was to promote the use of Leibnizian notation for differentiation in calculus as opposed to the Newton notation for differentiation. The latter system came into being in the 18th century as a convention of Sir Isaac Newton, and was in use throughout Great Britain. According to a mathematical historian:
:In 1800, English mathematics was trapped in the doldrums of fluxional notation and of an intuitive geometric-physical approach to mathematics designed to prepare the student for reading Newton's Principia...The study of any mathematics not pertinent to the traditional questions of Tripos was not only ignored, but actually discouraged. Cambridge was isolated, and its students remained ignorant of continental developments.
The Society was first envisioned by Charles Babbage as a parody on the debate of whether Bible texts should be annotated, with Babbage having the notion that his textbook by Sylvestre Lacroix was without need for interpretation once translated.
Its membership originally consisted of a group of Cambridge students led by Babbage and including Edward Bromhead.
The Cambridge mathematician Robert Woodhouse had brought the Leibniz notation to England with his book Principles of Analytical Calculation in 1803. While Newton's notation was unsuitable for a function of several variables, Woodhouse showed, for instance, how to find the total differential of <math>\phi(p, q),</math> where φ is a function of p and q:
:<math>d\phi = \frac{\partial \phi}{\partial p} dp + \frac{\partial \phi}{\partial q} dq .</math>
The slow uptake of the continental methods in calculus led to the formation of the Analytical Society by Charles Babbage, John Herschel and George Peacock. The evidence of Analytical Society work appeared in 1816 when Peacock and Herschel completed the translation of Sylvestre Lacroix's textbook An Elementary Treatise on Differential and Integral Calculus that had been started by Babbage. In 1817 Peacock introduced Leibnizian symbols in that year's examinations in the local senate-house. 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.
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, Leibniz notation was widely adopted and used alongside the traditional denotation of differentiation by use of dots as Newton had done.
See also
- History of calculus
- Notation for differentiation