The AnalystThe Analyst, subtitled A DISCOURSE Addressed to an Infidel Mathematician, is a book published by George Berkeley in 1734. The infidel mathematician in question is believed to have been either Edmond Halley, or Sir Isaac Newton himself, although the discourse would then have been posthumously addressed as Newton died in 1727.
The Analyst represented a direct attack on the foundations and principles of calculus, and in particular the notion of fluxion or infinitesimal change which Newton and Leibnitz had used to develop the calculus. Berkeley's intention seems to have been to defend religion by showing that the foundations of natural philosophy were equally weak.
As a consequence of the resulting controversy, the foundations of calculus were rewritten in a much more formal and rigorous form using limits. It was not until 1966, with the publication of Abraham Robinson's book Non-standard Analysis, that the concept of the infinitesimal was made rigorous, thus giving an alternative way of overcoming the difficulties which Berkeley discovered in Newton's original approach.