Around the end of the eighteenth century and the beginning of the nineteenth, mathematics and the related natural sciences found themselves considerably backward in relation to the most advanced countries on the continent, especially France. The original reason for this was the infamous priority dispute between the followers of Leibniz and those of Newton over the invention of the differential and integral calculus, which had led to British mathematicians and physicists adopting Newton’s impractical notation.

Added to this, however, was on the one hand, that the political upheavals on the continent and the expansionist policies of Napoleon had increased the nationalist reservations of the British against the continent and particularly against France, and on the other hand that Britain was flourishing economically at this time and was the leading industrial nation, although this industry was to a great extent based on the technical skills of such engineers and technicians as Thomas Newcomen and James Watt and was in no way prepared for the scientific advances in industrial processes that would be necessary for further development.

It should also be noted that in the French universities and numerous institutions of higher education, above all military schools, the most eminent mathematicians of the time were intensively involved in the teaching profession, while in the remaining countries of Europe, in which were also to be found noted mathematicians, these were active primarily in research institutes and observatories, and if they were involved in teaching at all, it was only to a small extent and only grudgingly. In the British universities, the intellectual climate for mathematics and the sciences was particularly backward, and moreover, was politically conservative. However, Robert Woodhouse, a professor of mathematics at Cambridge, published a book in 1803 called Principles of Analytical Calculation, in which he explained and applied the differential notation that had been used by Leibniz. Apparently, though, he had not dared to use this notation in his lectures.

It was in this environment that young men were coming of age at the University of Cambridge who were unwilling to accept the given situation. Three of them would later achieve great renown:

       

George Peacock (1791–1858),   Charles Babbage (1791–1871), John Herschel (1792–1871).
 

George Peacock became a lecturer in mathematics in 1815, and from 1837 was a professor of geometry and astronomy at Cambridge. His main area of research, however, was algebra. John Herschel, son of the astronomer William Herschel, was one of the most famous astronomers of the nineteenth century. Charles Babbage has earned a place in history as a pioneer in the invention of the computer.

The founding by these three, together with some other students, of an “Analytical Society” in 1812 for the purpose of bringing mathematical analysis in Britain up to the European standard began as a typical student prank. At that time, there was a bitter conflict taking place over whether a new English translation of the Bible with explanatory commentaries should be published or whether to do so was a blasphemous attempt to improve on perfection. Babbage was moved by a pamphlet on this topic to write a parody, and he drafted the charter of a society whose task it would be to declare the Gospel according to the Leibniz “d” notation and to condemn to perdition all heretics who adhered to the Newtonian dot. The joke became serious, and today, it must be said that in the situation at the time, when students were forbidden to organize meetings for the purposes of political discussion, casting one’s lot with continental analysis had a thoroughgoing political aspect to it.

The Analytical Society, with at times numerous members and regular membership dues, existed as such for only two years, but in 1819, it was revived under the name of the Cambridge Philosophical Society, under which name it exists to this day. Life within the society was described quite vividly in a letter that Frederick Maule, a member of the society, wrote to Babbage in 1813. The letter speaks of wild debates, cursing, and nonsense [Hyman, p. 44]. It is clear that the professors at the university, with the exception of the sympathetic Woodhouse, followed the whole enterprise partly with scorn and partly with disapproval. The society’s contribution lay above all in the translation of the textbook Traité du calcul différentiel  et du calcul intégral (1797/98) by S. E. Lacroix (1765–1843) into English undertaken by Babbage, Herschel, and Peacock, published in 1816 in Cambridge, and the first (and last) volume of the Memoirs of the Analytical Society, which appeared in 1813 and aside from a programmatic foreword by Babbage and Herschel, contained an article by Babbage on infinite products and two articles by Herschel, on trigonometric series and on differential equations.

While Babbage and Herschel soon turned their attention to their well-known later pursuits, Peacock continued, at least in his Cambridge lectures, to propagate the continental style in analysis. Though the history of the Analytical Society is not a glorious one, in the end, it turns out to have had a great influence. The continental style was disseminated throughout Great Britain, and the following generations of important British mathematicians and physicists such as George G. Stokes (1819–1903) und James Clerk Maxwell (1831–1879) made abundant use of it.

  

References:
Charles Babbage: Passages from the Life of a Philosopher. Autobiography, 1864.
Reprint in Collected Works of Charles Babbage, 11 vols,. ed. M. Campbell-Kelly 1989.
Anthony Hyman: Charles Babbage. Pioneer of the Computer. Oxford University Press,1982.
This book places the life and work of Babbage in the context of a comprehensive presentation of the political, economic, cultural, and scientific milieu of the time based on many sources, some of them not previously utilized.

 

 (By Peter Schreiber, Greifswald, Germany, April 2012; translated by David Kramer)