Joseph Raphson (c. 1668 – c. 1715) was an

English English usually refers to: * English language * English people English may also refer to: Culture, language and peoples * ''English'', an adjective for something of, from, or related to England * ''English'', an Amish ter ...

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, mathematical structure, structure, space, Mathematica ...

and intellectual known best for the

Newton–Raphson method In numerical analysis, the Newton–Raphson method, also known simply as Newton's method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a ...

Biography

Very little is known about Raphson's life. Connor and Robertson give his date of birth as 1668 based on a 1691 book review giving his age as 22; mathematical historian

Florian Cajori Florian Cajori (February 28, 1859 – August 14 or 15, 1930) was a Swiss-American historian of mathematics. Biography Florian Cajori was born in Zillis, Switzerland, as the son of Georg Cajori and Catherine Camenisch. He attended schools firs ...

preferred dates around 1648–1715. His parents were probably Ruth and James Raphson, in which case he is likely to be a Joseph Raphson baptised at

St John the Baptist John the Baptist ( – ) was a Jewish preacher active in the area of the Jordan River in the early first century AD. He is also known as Saint John the Forerunner in Eastern Orthodoxy and Oriental Orthodoxy, John the Immerser in some Baptist ...

Pinner Pinner is a suburb in the London Borough of Harrow, northwest London, England, northwest of Charing Cross, close to the border with Hillingdon, historically in the county of Middlesex. The population was 38,698 in 2021. Originally a mediaeval ...

Middlesex Middlesex (; abbreviation: Middx) is a Historic counties of England, former county in South East England, now mainly within Greater London. Its boundaries largely followed three rivers: the River Thames, Thames in the south, the River Lea, Le ...

in the 1660s. Raphson was made a

Fellow of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the Fellows of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural science, natural knowledge, incl ...

on 30 November 1689, after being proposed for membership by

Edmund Halley Edmond (or Edmund) Halley (; – ) was an English astronomer, mathematician and physicist. He was the second Astronomer Royal in Britain, succeeding John Flamsteed in 1720. From an observatory he constructed on Saint Helena in 1676–77, H ...

. In 1692 he graduated with an

M.A. A Master of Arts ( or ''Artium Magister''; abbreviated MA or AM) is the holder of a master's degree awarded by universities in many countries. The degree is usually contrasted with that of Master of Science. Those admitted to the degree have ...

in 1692 from Jesus College which at the time was primarily a training college for Church of England clergy, however as the degree was awarded Royal warrant he probably did not actually study there. He described himself as "of London" on his Royal Society bond form and from

on the Jesus College register. Raphson's most notable work is ''Analysis Aequationum Universalis'', which was published in 1690. It contains a method, now known as the

, for approximating the roots of an equation.

Isaac Newton Sir Isaac Newton () was an English polymath active as a mathematician, physicist, astronomer, alchemist, theologian, and author. Newton was a key figure in the Scientific Revolution and the Age of Enlightenment, Enlightenment that followed ...

had developed a very similar formula in his ''

Method of Fluxions ''Method of Fluxions'' () is a mathematical treatise by Sir Isaac Newton which served as the earliest written formulation of modern calculus. The book was completed in 1671 and posthumously published in 1736. Background Fluxion is Newton's term ...

'', written in 1671, but this work would not be published until 1736, nearly 50 years after Raphson's ''Analysis''. However, Raphson's version of the method is simpler than Newton's, and is therefore generally considered superior. For this reason, it is Raphson's version of the method, rather than Newton's, that is to be found in textbooks today. Raphson was a staunch supporter of Newton's claim, and not that of

Gottfried Leibniz Gottfried Wilhelm Leibniz (or Leibnitz; – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat who is credited, alongside Isaac Newton, Sir Isaac Newton, with the creation of calculus in ad ...

, to be the sole inventor of calculus. In addition, Raphson translated Newton's ''

Arithmetica Universalis ''Arithmetica Universalis'' ("Universal Arithmetic") is a mathematics text by Isaac Newton. Written in Latin, it was edited and published by William Whiston, Newton's successor as Lucasian Professor of Mathematics at the University of Cambridg ...

'' into

. Raphson coined the word ''

pantheism Pantheism can refer to a number of philosophical and religious beliefs, such as the belief that the universe is God, or panentheism, the belief in a non-corporeal divine intelligence or God out of which the universe arisesAnn Thomson; Bodies ...

'', in his work ''De Spatio Reali'', published in 1697, where it may have been found by

John Toland John Toland (30 November 167011 March 1722) was an Irish rationalist philosopher and freethinker, and occasional satirist, who wrote numerous books and pamphlets on political philosophy and philosophy of religion, which are early expressions ...

, who called Raphson's work "ingenious". In ''De Spatio Reali'', Raphson begins by making a distinction between atheistic ''panhylists'' (from the Greek '' pan'' 'all' and '' hyle'' 'wood, matter'), who believe everything derives from matter, and pantheists who believe in "a certain universal substance material as well as intelligent, that fashions all things that exist out of its own essence." Raphson further believed the universe to be immeasurable in respect to a human's capacity of understanding, and that humans would never be able to comprehend it. A book by Raphson became a part of the long-running

priority dispute In science, priority is the credit given to the individual or group of individuals who first made the discovery or proposed the theory. Fame and honours usually go to the first person or group to publish a new finding, even if several researchers a ...

on who invented calculus after his death. Newton apparently took control of the publication of Raphson's posthumous book ''Historia fluxionum'' and added a supplement with letters from Leibniz and

Antonio Schinella Conti Antonio Schinella Conti (1677–1749), also known by his religious title as Abate Conti, was an Italian writer, translator, mathematician, philosopher and physicist. He was born in Padua on 22 January 1677 and died there on 6 April 1749. Life In ...

to support his position in the dispute. The lack of sources about Raphson's life and background has been described as surprising. He may have been of Irish descent.

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* {{DEFAULTSORT:Raphson, Joseph 1660s births 1710s deaths English mathematicians Alumni of Jesus College, Cambridge Fellows of the Royal Society Place of death unknown English people of Irish descent People from Pinner