The Cambridge History of English and American Literature in 18 Volumes (1907–21).

Volume VIII. The Age of Dryden.

**XV. The Progress of Science**

# § 12. Mathematics: John Wallis and Seth Ward; Newton

In mathematics, John Wallis was, to some extent, a forerunner of Newton. At Felsted school and at Emmanuel college, he received the curiously wide education of his age. He was a skilled linguist; although he had taken holy orders, he was the first of Francis Glisson’s pupils to proclaim in public Harvey’s discovery of the circulation of the blood, but his bent was towards mathematics, and he possessed an extraordinary memory for figures. His *Arithmetica Infinitorum* is described as “the most stimulating mathematical work so far published in England.” It contained the germs of the differential calculus, and it suggested to Newton, who “read it with delight,” the binomial theorem. In it [char] was evaluated, and it must not be forgotten that to Wallis we owe the symbol for infinity, [char]. Living in troublesome times, under many rulers, he contrived, not without some loss of popularity, to remain on good terms with all. His services were, indeed, indispensable to a succession of governments, for he had a power of deciphering which was almost miraculous. Cromwell, who seems to have had a great respect for his powers, appointed him Savilian professor of geometry at Oxford in 1649.

Another mathematical ecclesiastic was Seth Ward, bishop of Exeter and afterwards of Salisbury. Ward was educated at Sidney Sussex college and, in 1643, was chosen as mathematical lecturer to the university at Cambridge. But, like Wallis, he was appointed, and in the same year, to a Savilian professorship, that of astronomy—another instance, not uncommon at the time, of men educated at Cambridge but recognised and promoted at Oxford. He took the place of the ejected John Greaves, who magnanimously used his influence in his successor’s favour. Ward was renowned as a preacher; but his later fame rested chiefly on his contributions to the science of astronomy, and he is remembered in the world of science mainly for his theory of planetary motion. Ward and Wallis—but the burden of the attack was borne by the latter—laid bare Hobbes’s attempted proof of the squaring of the circle; there was also a little controversy “on the duplication of the cube,” and mixed up with these criticisms in the realm of pure reason were political motives. Hobbes had not begun to study Euclid until he was forty; and, after Sir Henry Saville had founded his professorships at Oxford, Wood says that not a few of the foolish gentry “kept back their sons” in order not “to have them smutted by the black art”—so great was the fear and the ignorance of the powers of mathematics. Ward was a pluralist, as was the manner of the times, and Burnet tells us “he was a profound statesman but a very indifferent clergyman.” Yet, what money he got he lavishly spent on ecclesiastical and other purposes.

Like the distinguished mathematicians just mentioned, Isaac Newton took a keen interest in certain forms of theology current in his day; but in his intellectual powers he surpassed not only them but all living mathematicians and those who lived after him. His supreme genius has ensured him a place in the very small list of the world’s thinkers of the first order. He, too, exercised a certain influence in affairs, and, during his later years, he took a keen interest in theological speculations; but his activities in these fields are completely overshadowed by the far-reaching importance of his great discoveries as a natural philosopher and a mathematician. As the discoverer of the decomposition of white light in the spectrum, he may be regarded as the founder of the modern science of optics. His discovery of the law of gravitation, and his application of it to the explanation of Kepler’s laws of planetary motion and of the principal inequalities in the orbital motion of the moon made him the founder of the science of gravitational astronomy. His discovery of the method of fluxions entitles him to rank with Leibniz as one of the founders of mathematical analysis. All these great discoveries gave rise to long and sometimes acrimonious controversies among his contemporaries, relating both to the subjects themselves and to priority of discovery. In a letter to Halley referring to one of these disputes, Newton writes:

**Philosophy is such an impertinently litigious lady, that a man has as good be engaged in lawsuits, as have to do with her. I found it so formerly, and now I am no sooner come near her again, but she gives me warning.**

*Principia,*has been described by dean Peacock as “the greatest single triumph of the human mind.”