Mathematician, born at Ashford, Kent, was trained at Cambridge, and took orders, but in 1648 became Savilian professor of Geometry at Oxford. He sided with the parliament, was secretary to the Westminster Assembly, but strenuously favoured the Restoration. Besides the Arithmetica Infinitorum, he wrote on proportion, mechanics, the quadrature of the circle (against Hobbes), grammar, logic, theology, and the teaching of the deaf and dumb, and edited some of the Greek mathematicians. He was a founder of the Royal Society. His collected works appeared in 1791.

Personal

  The doctor has less in him of the gallant man than Mr. Hobbes; and, if you should see him with his university cap on his head, as if he had a porte-feuille on, covered with black cloth, and sewed to his calot, you would be as much inclined to laugh at this diverting sight as you would be ready to entertain the excellency and civility of my friend [Hobbes] with esteem and affection…. What I have said concerning Dr. Wallis is not intended in the least to derogate from the praises due to one of the greatest mathematicians in the world.

  Dr. Wallis was a man of most admirable fine parts, and great industry, whereby in some years he became so noted for his profound skill in mathematics that he was deservedly accounted the greatest person in that profession of any in his time. He was withal a good divine, and no mean critic in the Greek and Latin tongues.

General

  The book, next to the elements, which was put into his [Isaac Newton’s] hands was Wallis’s “Arithmetic of Infinities,” a work well fitted for suggesting new views in geometry and calling into activity the powers of mathematical invention. Wallis had effected the quadrature of all those curves in which the value of one of the co-ordinates can be expressed in terms of the other without involving either fractional or negative exponents. Beyond this point neither his researches nor those of any other geometer had yet reached, and from this point the discoveries of Newton began…. Wallis appears to have been the first writer who, in his “Mechanics,” published in 1669, founded an entire system of statics on the principle of Galileo, or the equality of the opposite momenta.

  It [“Treatise of Algebra”] is the first work in which a copious history of the subject was mixed with its theory.

  Not [“Institutio Logicæ”] rising above a humble mediocrity, even at the date of its composition.

  The author of many works of great learning, ingenuity, and profoundness on algebra, geometry, and mechanical philosophy. Among the practical subjects to which he devoted himself were the deciphering of secret writing, and the teaching of persons born deaf to speak.

  In mathematical history Wallis ranks as the greatest of Newton’s English precursors. He was as laborious as he was original; and, by the judicious use of his powers of generalisation, he prepared all the subsequent discoveries of that age. The principles of analogy and continuity were introduced by him into mathematical science. His interpretation of negative exponents and unrestricted employment of fractional exponents greatly widened the range of the higher algebra. Finally, he invented the symbol for infinity, ∞. His memory for figures was prodigious. He often whiled away sleepless nights with exercises in mental arithmetic. On one occasion he extracted the square root of a number expressed by fifty-three figures, and dictated the result to twenty-seven places next morning to a stranger. It proved exact. He made use of no special technique in performing such feats, working merely by common rules on the blackboard of his own tenacious mind.