Even if Berkeley's philosophy of the abstract sciences of arithmetic and algebra had little effect on British mathematics through the mideighteenth century, Newton's bifocal mathematical legacy helped to assure that algebra as well as geometry continued to be cultivated in Great Britain. Probably most early-eighteenth-century British mathematical thinkers were strongly attracted toward the geometric focus of Newtonian mathematics; some, however, felt at least an equal pull toward the arithmetico-algebraic focus.

In Scotland there were two schools of thought on algebra: the somewhat anti-Newtonian school, led by Robert Simson (1687–1768), and the largely Newtonian school, led by Colin MacLaurin (1698–1746). Simson – the “father-figure” of Scottish mathematicians of the first half of the eighteenth century – was primarily attracted to the geometric focus of Newtonian mathematics. By his later years, if not in his early career as well, he came near abandoning early modern algebra. He preferred geometric analysis to analytic geometry; perhaps questioned the symbolical style; and rejected the negative and imaginary numbers. MacLaurin, on the other hand, published first on geometry, then prepared a manuscript on algebra, and next devoted eight years of his life to answering Berkeley's Analyst with his Treatise of Fluxions, a largely geometric work with, however, a significant algebraic section.

By all accounts, MacLaurin was a brilliant mathematician; in many respects, he was the greatest of Newton's mathematical disciples. Early meetings with MacLaurin seem to have convinced Newton that he and the young Scotsman were kindred mathematical souls, who appreciated both the new and the old mathematics.