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Mathematical Treasure: Berkeley on Various Topics

Frank J. Swetz (Pennsylvania State University)

George Berkeley (1685-1753) was a bishop of the Church of England, best known to mathematicians for his attack on the logical foundations of Newton’s calculus in a pamphlet entitled The Analyst (1734). The images here of Berkeley’s writings are taken from Alexander Fraser’s The Works of George Berkeley (1871), supplied through the courtesy of the Pennsylvania State University Library. Fraser was a bibliographer and great admirer of George Berkeley.

Above is an article by Berkeley based on his Master of Arts thesis, Arithmetica absque Algebra aut Euclide demonstrate (Arithmetic demonstrated without Algebra or Euclid, 1707). Once again, Fraser’s notations are informative.

The article “Miscellanea Mathematica” (1707) was also drawn from Berkeley’s thesis.

In the article, "A Defence of Free-Thinking in Mathematics" (1735), Berkeley responded to criticisms of his 1734 Analyst. His attacks against Newton’s calculus were twofold, concerning (1) the rigor of the calculus as conceived and (2) the climate of “free thinking” scientific rationalism then taking place in England. Berkeley feared that the new scientific movement countered religious beliefs and therefore protested against it. Here, however, he defended free thinking in mathematics. The rigorization of calculus would await the forthcoming contributions of other mathematicians; particularly Euler in the eighteenth century and Cauchy in the nineteenth century, but also the writings of Colin Maclaurin and Thomas Simpson soon to follow Berkeley's. To see the title page and first three pages of the original 1735 edition of Berkeley's A Defence of Free-Thinking in Mathematics, see Mathematical Treasure: Berkeley's Defence of Free-Thinking.

For a sampling of pages from Berkeley's 1734 Analyst in Fraser's volume, see Mathematical Treasure: Berkeley's Critique of Calculus.


Alexander Campbell Fraser, The Works of George Berkeley (4 vols.), Oxford Clarendon Press, 1871

Frank J. Swetz (Pennsylvania State University), "Mathematical Treasure: Berkeley on Various Topics," Convergence (August 2015)