William Neile (7 December 1637 – 24 August 1670) was an English

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

and founder member of the

Royal Society The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...

. His major mathematical work, the rectification of the semicubical parabola, was carried out when he was aged nineteen, and was published by John Wallis. By carrying out the determination of arc lengths on a curve given algebraically, in other words by extending to

algebraic curve In mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective plane of a homogeneous polynomial in three variables. An affine algebraic plane ...

s generally with

Cartesian geometry In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry. Analytic geometry is used in physics and engineerin ...

a basic concept from differential geometry, it represented a major advance in what would become infinitesimal calculus. His name also appears as Neil.

Life

Neile was born at Bishopsthorpe, the eldest son of Sir Paul Neile MP for Ripon and Newark. His grandfather was Richard Neile, the

Archbishop of York The archbishop of York is a senior bishop in the Church of England, second only to the archbishop of Canterbury. The archbishop is the diocesan bishop of the Diocese of York and the metropolitan bishop of the province of York, which covers th ...

. He entered

Wadham College, Oxford Wadham College () is one of the constituent colleges of the University of Oxford in the United Kingdom. It is located in the centre of Oxford, at the intersection of Broad Street and Parks Road. Wadham College was founded in 1610 by Dorothy W ...

as a

gentleman-commoner A commoner is a student at certain universities in the British Isles who historically pays for his own tuition and commons, typically contrasted with scholars and exhibitioners, who were given financial emoluments towards their fees. Cambridge ...

in 1652, matriculating in 1655. He was taught by John Wilkins and Seth Ward. In 1657, he became a student at the

Middle Temple The Honourable Society of the Middle Temple, commonly known simply as Middle Temple, is one of the four Inns of Court exclusively entitled to call their members to the English Bar as barristers, the others being the Inner Temple, Gray's Inn ...

. 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 Gresham College is an institution of higher learning located at Barnard's Inn Hall off Holborn in Central London, England. It does not enroll students or award degrees. It was founded in 1596 under the will of Sir Thomas Gresham, and hosts ove ...

. His demonstration was published by Wallis in ''De Cycloide'' (1659). The general formula for rectification by definite integral was in effect discovered by Hendrik van Heuraet in 1659. In 1673 Wallis asserted that Christiaan Huyghens, who was advancing his own claim to have influenced Heuraet, was also slighting the priority of Neile. Neile was elected a fellow of the Royal Society on 7 January 1663 and a member of the council on 11 April 1666. He entered the debate on the theory of

motion In physics, motion is the phenomenon in which an object changes its position with respect to time. Motion is mathematically described in terms of displacement, distance, velocity, acceleration, speed and frame of reference to an observer and m ...

, as a critic of the empiricist stance of other members. 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. Neile objected to Wren's 1668 work on

collision In physics, a collision is any event in which two or more bodies exert forces on each other in a relatively short time. Although the most common use of the word ''collision'' refers to incidents in which two or more objects collide with great fo ...

as lacking discussion of causality: he asked for discussion of the nature of momentum. His own work was much influenced by ideas drawn from the '' De Corpore'' of

Thomas Hobbes Thomas Hobbes ( ; 5/15 April 1588 – 4/14 December 1679) was an English philosopher, considered to be one of the founders of modern political philosophy. Hobbes is best known for his 1651 book ''Leviathan'', in which he expounds an influ ...

.Jon Parkin, ''Science, Religion and Politics in Restoration England: Richard Cumberland's De Legibus Naturae'' (1999), pp. 136-7. He made astronomical observations with instruments erected on the roof of his father's residence, the “Hill House” (later called Waltham Place) at White Waltham in Berkshire, where he died at the age of 32. 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.

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* {{DEFAULTSORT:Neile, William Original Fellows of the Royal Society 1637 births 1670 deaths People from White Waltham Alumni of Wadham College, Oxford 17th-century English mathematicians