The British intellectual tradition produced three major thinkers, in addition to Newton, who published on algebra in the first half of the eighteenth century: George Berkeley, Colin MacLaurin, and Nicholas Saunderson. Berkeley's writings on algebra were the most philosophical of the works produced by the three men and, in their time, the most neglected. Berkeley was also the only of the three to draw significant inspiration from Wallis, for MacLaurin and Saunderson began their algebras as commentaries on Universal Arithmetick. Berkeley wove Wallis's algebraic reflections with the arithmetic insights of Barrow and possibly Hobbes into a coherent philosophy of arithmetic and algebra as sciences of signs, in contrast to his philosophy of geometry as the science of perceptible finite extension.

As Berkeley's general philosophical concerns affected his understanding of early modern mathematics, so mathematics presented him with problems and insights that helped to shape his philosophy. His earliest notebooks referred to Barrow's view of number as a “note” or “sign,” and number, so understood, became one of his stock examples against abstraction. Berkeley, moreover, was the first major British (and perhaps European) philosopher to come to terms with the symbolical style of early modern algebra. His early acceptance of symbolical reasoning and Barrow's view of number helped to raise in him “semiotic consciousness” – or “the explicit awareness of the role of the sign as that role is played in a given respect” – and thus contributed toward his innovative theory of language.