William Neile, the mathematician, was the eldest son of Sir Paul Neile and the grandson of Richard Neile, Archbishop of York, in whose palace at Bishopsthorpe, he was born on 7th December 1637. Entering Wadham College, Oxford, as a gentleman-commoner in 1652, but not matriculating in the university till 1655, he soon displayed mathematical genius, which was developed by the instructions of Dr. Wilkins and Dr. Seth Ward. In 1657, he became a student at the Middle Temple. In the same year, at the age of nineteen, he gave an exact rectification of the cubical parabola and communicated his discovery - the first of its kind - to Brouncker, Wren and others of the Gresham College Society. His demonstration was published in Wallis' 'De Cycloide' (1669). Neile was elected a fellow of the Royal Society on 7th January 1663 and a member of the council on 11th April 1666. His theory of motion was communicated to the society on 29th April 1669. He pro­secuted astronomical observations with in­struments erected on the roof of his father's residence, the 'Hill House' (now called Waltham Place) at White Waltham in Berkshire, where he died, in his thirty-third year, on 24th August 1670, “to the great grief of his father, and resentment of all virtuosi and good men that were ac­quainted with his admirable parts”. A white marble monument in the parish church of White Waltham commemorates him and an inscribed slab in the floor marks his burial-place. He belonged to the privy council of King Charles II. Hearne says of him, “He was a virtuous, sober, pious man, and had such a powerful genius to mathematical learning that had he not been cut off in the prime of his years, in all probability he would have equalled, if not excelled, the celebrated men of that profession. Deep melancholy hastened his end, through his love for a maid of honour, to marry whom he could not obtain his father's consent.”