Edward Waring (obsolete: Waring , English; Edward Waring ; c. 1736 , Shrewsbury - August 15, 1798 , Pointesbury , Shropshire ) - English mathematician .
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| Edward waring | |
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| Scientific field | mathematician |
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| Alma mater | Magdalen College |
| Awards and prizes | member of the Royal Society of London Copley Medal ( 1784 ) |
His extraordinary mathematical abilities were noted during his studies at the College of St. Magdalen University of Cambridge. [3]
E. Waring dealt mainly with number theory and algebraic equations. In 1760, he became a professor at Cambridge University . In 1782, the scientist published his work “ Meditationes algebraicae ”, in which the so-called Waring problem for number theory was formulated. The question is whether for each positive integer n there exists a number g ( n ) such that any positive integer n is the sum of at most g ( n ) terms that are the nth powers of the positive integers. It is known, for example, that g (2) = 4, and g (3) = 9. Thus, any natural number can be represented by a sum of not more than 4 squares ( Lagrange's theorem on the sum of four squares ) or a sum of not more than 9 cubes. No less important is the question of the function G ( n ) - the number of terms necessary to represent all sufficiently large numbers.
The proof of this theorem using complex analytical methods was first carried out in 1909 by the German scientist David Hilbert . In 1942, the Soviet mathematician Yu. V. Linnik found evidence based on elementary methods.
In 1763, E. Waring became a member of the Royal Scientific Society , and in 1784 he was awarded the Copley Medal of Honor .
Notes
- ↑ 1 2 Archive for the history of mathematics MacTyutor
- ↑ Encyclopædia Universalis - Encyclopædia Britannica Inc. .
- ↑ Waring, Edward in Venn, J. & JA, Alumni Cantabrigienses , Cambridge University Press, 10 vols, 1922–1958.
Literature
- Waring // Encyclopedic Dictionary of Brockhaus and Efron : in 86 volumes (82 volumes and 4 additional). - SPb. , 1890-1907.