WARING, EDWARD

born 1734, Old Heath, near Shrewsbury, Shropshire, Eng. died Aug. 15, 1798, Pontesbury, Shropshire English mathematician who was the first to set forth a method of approximating the values of imaginary roots. Waring practiced medicine in various London hospitals and later at Addenbrooke's, Cambridge, St. Ives, and Huntingdonshire hospitals. From 1760 he served as Lucasian professor of mathematics at Cambridge University, and in 1770 he gave up his medical practice. In 1776 Waring proposed the Cauchy ratio test. In 1909 the solution of Waring's problem marked a new era in analysis and led to far-reaching theorems in arithmetic. Besides his classification of quartic curves into 12 main divisions with 84,551 species, he gave proofs of Descartes's rule of signs and set forth the theory of symmetrical functions of algebraic roots. He presented a series of propositions in number theory concerning the decomposition of a number into a sum of cubes and biquadratics and suggested a method (unproven) for decomposing any even number into the sum of two prime numbers. His published works include Miscellane analytica . . . (1762; "Miscellany of Analysis . . ."), Meditationes algebraicae (1770; "Thoughts on Algebra"), Proprietates algebraicarum Curvarum (1772; "The Properties of Algebraic Curves"), Meditationes analyticae (1776; "Thoughts on Analysis"), On the Principle of Translating Algebraic Quantities into Probable Relations and Annuities (1792), and An Essay on the Principles of Human Knowledge (1794).