Yesterday’s post was about the second Lucasian Professor of Mathematics at Cambridge University, Isaac Newton, who was born 25^{th} December 1642. Today we turn our attention to the eleventh holder of the chair, Charles Babbage, who was born 26^{th} December 1791. Of course Babbage is best known for his attempts to construct the world’s first analytical computer but he was far from being a one trick pony. He was an excellent mathematician, cryptologist, and engineer-inventor who amongst other things actually invented a cowcatcher for locomotives. Today I’m going to look at his early activities as a mathematician and his attempts to oust Isaac Newton from Cambridge University. As is often the case with my posts in order to explain the main theme we first have to fill in some of the background.

As I mentioned in my last post throughout the early modern period England lagged far behind the Continent in the propagation and the development of the mathematical sciences. However in the course of the seventeenth century thanks to the efforts of people like Thomas Harriot, William Oughtred, Henry Biggs, Isaac Barrow, John Wallis, Christopher Wren and others England slowly made good on this deficit and by the time Newton was in his prime it could hold its own with any of its European rivals. Newton together with his Newtonians, Colin MacClaurin, Brook Taylor, Abraham de Moirve, James Stirling, David Gregory and others, pushed the development of the calculus along at a pace equal to Leibniz and the Bernoulli brothers on the Continent. However as the first generation passed away further generations of the Bernoullis and Euler in Switzerland and various mathematicians in France continued to develop both the analysis and the mathematical physics whereas in England there were no further developments and the mathematical sciences ossified. By the time Charles Babbage went up to Cambridge in 1810, whereas the continental mathematicians were being taught the latest developments of Laplace, Lagrange, Legendre and Lacroix Cambridge students were still being taught their physics from Newton’s *Principia* and as mathematics the clumsy and difficult to use and comprehend method of fluxions that Newton had developed in the seventeenth century. Why was this? The standard answer is that the English out of nationalist pride in the achievements of Newton refused to accept the continental developments based on the mathematics of Newton’s greatest rival Leibniz. Whilst I think this is part of the answer I think the main reason is that England had never really established mathematics as part of the education system. Whereas both Melanchthon and Clavius in their pedagogical mathematical reforms in the Lutheran and Catholic areas of the Continent in the sixteenth century had establish school curricular as well as supplying teachers and text book to ensure future generations of mathematicians, in his essay *On the Usefulness of Mathematical Learning* from 1705 Newton’s friend, John Arbuthnot, complained there was still not one single school in England that taught mathematics. Also although the Newtonians had ruled the scientific roost in the first quarter of the seventeenth century after Newton’s death the natural historians led by Hans Sloane re-conquered the Royal Society and whereas the eighteenth century saw developments in the biological and the earth sciences in England the mathematical sciences were totally neglected.

Babbage was the son of a wealthy banker and because Charles was a weak and sickly child he was mostly educated by private tutors. By the time he went up to Cambridge he had already read Leibniz, Lagrange and Lacroix and he was horrified to discover how antiquated the teaching of the mathematical sciences at the university were. The young tutor Robert Woodhouse, who would go on to become the eighth Lucasian Professor, had published a book on the Continental methods of analysis in 1803 but it was badly received and had little impact. In 1812 Babbage together with John Herschel and George Peacock and a small group of other undergraduate students of Woodhouse founded the Analytical Society with the express aim of ousting Newton’s mathematics and physics and replacing it with the modern Continental methods. Or as Babbage expressed it in a wonderful series of mathematical puns, the aim of the Society was to promote, “the principles of *d*-ism as opposed to the *dot*-age of the university”. In November 1812 the Society published the first volume of their *Memoirs*, which consisted of two papers by Herschel and one by Babbage as well a preface outlining the history of analysis written by Babbage. Due to their lack of influence the Society was disbanded in 1813 although Babbage and Herschel tried to revive it in 1817 publishing a second volume of the *Memoirs*. In 1819 the Cambridge Philosophical Society arose out of the ashes of the Analytical Society. Later in the 1820s and 30s Woodhouse, Peacock and Babbage’s friend William Whewell introduced many of the reforms that the Analytical Society had demanded. All in all the Analytical Society remains an interesting episode in the history of English mathematics as Charles tried to oust Isaac from Cambridge.

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