Edward Waring
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Edward Waring (15 August 1798) was a British
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 ...
. He entered
Magdalene College, Cambridge Magdalene College ( ) is a constituent college of the University of Cambridge. The college was founded in 1428 as a Benedictine hostel, in time coming to be known as Buckingham College, before being refounded in 1542 as the College of St Mary ...
as a
sizar At Trinity College Dublin and the University of Cambridge, a sizar is an Undergraduate education, undergraduate who receives some form of assistance such as meals, lower fees or lodging during his or her period of study, in some cases in retur ...
and became
Senior wrangler The Senior Wrangler is the top mathematics undergraduate at the University of Cambridge in England, a position which has been described as "the greatest intellectual achievement attainable in Britain". Specifically, it is the person who achiev ...
in 1757. He was elected a Fellow of Magdalene and in 1760
Lucasian Professor of Mathematics The Lucasian Chair of Mathematics () is a mathematics professorship in the University of Cambridge, England; its holder is known as the Lucasian Professor. The post was founded in 1663 by Henry Lucas (politician), Henry Lucas, who was Cambridge U ...
, holding the chair until his death. He made the assertion known as Waring's problem without proof in his writings ''Meditationes Algebraicae''. Waring was elected 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 ...
in 1763 and awarded the
Copley Medal The Copley Medal is the most prestigious award of the Royal Society of the United Kingdom, conferred "for sustained, outstanding achievements in any field of science". The award alternates between the physical sciences or mathematics and the bio ...
in 1784.


Early years

Waring was the eldest son of John and Elizabeth Waring, a prosperous farming couple. He received his early education in
Shrewsbury School Shrewsbury School is a Public school (United Kingdom), public school in Shrewsbury. Founded in 1552 by Edward VI by royal charter, to replace the town's Saxon collegiate foundations which were disestablished in the sixteenth century, Shrewsb ...
under a Mr Hotchkin and was admitted as a
sizar At Trinity College Dublin and the University of Cambridge, a sizar is an Undergraduate education, undergraduate who receives some form of assistance such as meals, lower fees or lodging during his or her period of study, in some cases in retur ...
at
Magdalene College, Cambridge Magdalene College ( ) is a constituent college of the University of Cambridge. The college was founded in 1428 as a Benedictine hostel, in time coming to be known as Buckingham College, before being refounded in 1542 as the College of St Mary ...
, on 24 March 1753, being also Millington exhibitioner. His extraordinary talent for mathematics was recognised from his early years in Cambridge. In 1757 he graduated BA as
senior wrangler The Senior Wrangler is the top mathematics undergraduate at the University of Cambridge in England, a position which has been described as "the greatest intellectual achievement attainable in Britain". Specifically, it is the person who achiev ...
and on 24 April 1758 was elected to a fellowship at Magdalene. He belonged to the Hyson Club, whose members included
William Paley William Paley (July 174325 May 1805) was an English Anglican clergyman, Christian apologetics, Christian apologist, philosopher, and Utilitarianism, utilitarian. He is best known for his natural theology exposition of the teleological argument ...
.


Career

At the end of 1759 Waring published the first chapter of ''Miscellanea Analytica''. On 28 January the next year he was appointed Lucasian professor of mathematics, one of the highest positions in Cambridge. William Samuel Powell, then tutor in
St John's College, Cambridge St John's College, formally the College of St John the Evangelist in the University of Cambridge, is a Colleges of the University of Cambridge, constituent college of the University of Cambridge, founded by the House of Tudor, Tudor matriarch L ...
opposed Waring's election and instead supported the candidacy of William Ludlam. In the polemic with Powell, Waring was backed by John Wilson. In fact Waring was very young and did not hold the MA, necessary for qualifying for the Lucasian chair, but this was granted him in 1760 by royal mandate. In 1762 he published the full ''Miscellanea Analytica'', mainly devoted to the theory of numbers and algebraic equations. In 1763 he was elected to 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 ...
. He was awarded its
Copley Medal The Copley Medal is the most prestigious award of the Royal Society of the United Kingdom, conferred "for sustained, outstanding achievements in any field of science". The award alternates between the physical sciences or mathematics and the bio ...
in 1784 but withdrew from the society in 1795, after he had reached sixty, 'on account of isage'. Waring was also a member of the academies of sciences of
Göttingen Göttingen (, ; ; ) is a college town, university city in Lower Saxony, central Germany, the Capital (political), capital of Göttingen (district), the eponymous district. The River Leine runs through it. According to the 2022 German census, t ...
and
Bologna Bologna ( , , ; ; ) is the capital and largest city of the Emilia-Romagna region in northern Italy. It is the List of cities in Italy, seventh most populous city in Italy, with about 400,000 inhabitants and 150 different nationalities. Its M ...
. In 1767 he took an MD degree, but his activity in medicine was quite limited. He carried out dissections with Richard Watson, professor of chemistry and later bishop of
Llandaff Llandaff (; ; from 'church' and ''River Taff, Taf'') is a district, Community (Wales), community and coterminous electoral ward in the north of Cardiff, capital of Wales. It was incorporated into the city in 1922. It is the seat of the Bisho ...
. From about 1770 he was physician at
Addenbrooke's Hospital Addenbrooke's Hospital is a large teaching hospital and research centre in Cambridge Cambridge ( ) is a List of cities in the United Kingdom, city and non-metropolitan district in the county of Cambridgeshire, England. It is the county to ...
at Cambridge, and he also practised at St Ives, Huntingdonshire, where he lived for some years after 1767. His career as a physician was not very successful since he was seriously short-sighted and a very shy man.


Personal life

Waring had a younger brother, Humphrey, who obtained a fellowship at Magdalene in 1775. In 1776 Waring married Mary Oswell, sister of a draper in Shrewsbury; they moved to Shrewsbury and then retired to Plealey, 8 miles out of the town, where Waring owned an estate of 215 acres in 1797


Work

Waring wrote a number of papers in the ''Philosophical Transactions of the Royal Society'', dealing with the resolution of algebraic equations, number theory, series, approximation of roots, interpolation, the geometry of conic sections, and dynamics. The ''Meditationes Algebraicae'' (1770), where many of the results published in ''Miscellanea Analytica'' were reworked and expanded, was described by
Joseph-Louis Lagrange Joseph-Louis Lagrange (born Giuseppe Luigi LagrangiaGoldbach conjecture Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics. It states that every even natural number greater than 2 is the sum of two prime numbers. The conjecture has been shown to ho ...
(every even integer is the sum of two primes), and also the following conjecture: every odd integer is a prime or the sum of three primes. Lagrange had proved that every positive integer is the sum of not more than four squares; Waring suggested that every positive integer is either a cube or the sum of not more than nine cubes. He also advanced the hypothesis that every positive integer is either a biquadrate (fourth power) or the sum of not more than nineteen biquadrates. These hypotheses form what is known as Waring's problem. He also published a theorem, due to his friend John Wilson, concerning prime numbers; it was later proven rigorously by Lagrange. In ''Proprietates Algebraicarum Curvarum'' (1772) Waring reissued in a much revised form the first four chapters of the second part of ''Miscellanea Analytica''. He devoted himself to the classification of higher plane curves, improving results obtained by
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 ...
, James Stirling,
Leonhard Euler Leonhard Euler ( ; ; ; 15 April 170718 September 1783) was a Swiss polymath who was active as a mathematician, physicist, astronomer, logician, geographer, and engineer. He founded the studies of graph theory and topology and made influential ...
, and
Gabriel Cramer Gabriel Cramer (; 31 July 1704 – 4 January 1752) was a Genevan mathematician. Biography Cramer was born on 31 July 1704 in Geneva, Republic of Geneva to Jean-Isaac Cramer, a physician, and Anne Mallet. The progenitor of the Cramer family i ...
. In 1794 he published a few copies of a philosophical work entitled ''An Essay on the Principles of Human Knowledge'', which were circulated among his friends. Waring's mathematical style is highly analytical. In fact he criticised those British mathematicians who adhered too strictly to geometry. It is indicative that he was one of the subscribers of John Landen's ''Residual Analysis'' (1764), one of the works in which the tradition of the Newtonian fluxional calculus was more severely criticised. In the preface of ''Meditationes Analyticae'' Waring showed a good knowledge of continental mathematicians such as
Alexis Clairaut Alexis Claude Clairaut (; ; 13 May 1713 – 17 May 1765) was a French mathematician, astronomer, and geophysicist. He was a prominent Newtonian whose work helped to establish the validity of the principles and results that Isaac Newton, Sir Isaa ...
,
Jean le Rond d'Alembert Jean-Baptiste le Rond d'Alembert ( ; ; 16 November 1717 – 29 October 1783) was a French mathematician, mechanician, physicist, philosopher, and music theorist. Until 1759 he was, together with Denis Diderot, a co-editor of the ''Encyclopé ...
, and Euler. He lamented the fact that in Great Britain mathematics was cultivated with less interest than on the continent, and clearly desired to be considered as highly as the great names in continental mathematics—there is no doubt that he was reading their work at a level never reached by any other eighteenth-century British mathematician. Most notably, at the end of chapter three of ''Meditationes Analyticae'' Waring presents some partial fluxional equations (partial differential equations in Leibnizian terminology); such equations are a mathematical instrument of great importance in the study of continuous bodies which was almost completely neglected in Britain before Waring's researches. One of the most interesting results in ''Meditationes Analyticae'' is a test for the convergence of series generally attributed to d'Alembert (the 'ratio test'). The theory of convergence of series (the object of which is to establish when the summation of an infinite number of terms can be said to have a finite 'sum') was not much advanced in the eighteenth century. Waring's work was known both in Britain and on the continent, but it is difficult to evaluate his impact on the development of mathematics. His work on algebraic equations contained in ''Miscellanea Analytica'' was translated into Italian by Vincenzo Riccati in 1770. Waring's style is not systematic and his exposition is often obscure. It seems that he never lectured and did not habitually correspond with other mathematicians. After
Jérôme Lalande Joseph Jérôme Lefrançois de Lalande (; 11 July 1732 – 4April 1807) was a French astronomer, freemason and writer. He is known for having estimated a precise value of the astronomical unit (the distance from the Earth to the Sun) using measu ...
in 1796 observed, in ''Notice sur la vie de Condorcet'', that in 1764 there was not a single first-rate analyst in England, Waring's reply, published after his death as 'Original letter of Dr Waring' in the ''Monthly Magazine'', stated that he had given 'somewhere between three and four hundred new propositions of one kind or another'.


Death

During his last years he sank into a deep religious melancholy, and a violent cold caused his death, in Plealey, on 15 August 1798. He was buried in the churchyard at Fitz, Shropshire.


See also

*
Lagrange polynomial In numerical analysis, the Lagrange interpolating polynomial is the unique polynomial of lowest degree that interpolates a given set of data. Given a data set of coordinate pairs (x_j, y_j) with 0 \leq j \leq k, the x_j are called ''nodes'' ...


References


External links

* {{DEFAULTSORT:Waring, Edward 1730s births 1798 deaths 18th-century English mathematicians Alumni of Magdalene College, Cambridge Fellows of Magdalene College, Cambridge Fellows of the Royal Society Lucasian Professors of Mathematics Number theorists Scientists from Shrewsbury Recipients of the Copley Medal Senior Wranglers Date of birth unknown