William Neile (7 December 1637 – 24 August 1670) was an English mathematician and founder member of the Royal Society.
His major mathematical work, the rectification of the semicubical parabola, was carried out when he was aged nineteen, and was published by John Wallis.
In the same year he gave his exact rectification of the semicubical parabola and communicated his discovery to William Brouncker, Christopher Wren and others connected with Gresham College.
In 1673 Wallis asserted that Christiaan Huyghens, who was advancing his own claim to have influenced Heuraet, was also slighting the priority of Neile.
His own theory of motion was held up from publication by unfavourable peer review by Wallis, in 1667; a revision was communicated to the society on 29 April 1669.