The Analyst; or, a Discourse Addressed to an Infidel Mathematician

The Analyst; or, A Discourse Addressed to an Infidel Mathematician is a work by philosopher George Berkeley, published in 1734. In this text, Berkeley critiques the logical foundations of calculus, which had been independently developed by Isaac Newton and Gottfried Wilhelm Leibniz.12

Berkeley questioned the nature of infinitesimals and fluxions, the core concepts of calculus at the time. He famously described them as "the ghosts of departed quantities," highlighting their lack of clear logical definition. His work raised significant philosophical questions about the rigor of mathematical reasoning, suggesting that mathematicians, while precise in religious matters, might be less so in their own science.1

Berkeley's criticisms were not fully addressed until the 19th century with the development of the concept of limits, and later in the 20th century with Abraham Robinson's work on nonstandard analysis, which demonstrated the logical consistency of infinitesimals.1