Edward Waring

Edward Waring

Edward Waring (* 1736 in Old Heath near Shrewsbury , † August 15, 1798 in Pontesbury , Shropshire ) was an English mathematician .

Life

Waring was the son of a farmer in Mytton, Shropshire . Edward Waring attended school in Shrewsbury and studied from 1753 at Magdalene College at Cambridge University , where he was initially Sizar, so his study stay partly worked off by services to other students or the faculty, but he had also won a scholarship. He stood out for his mathematical talent and was Senior Wrangler (best) in his Bachelor exams in 1757 . In 1754 he became a Fellow of Magdalene College. In the next few years he worked on his major work Meditationes Algebraicae , of which he sent the first chapter to the Royal Society and further parts circulated as Miscellanea Analytica when he sought the position of the Lucasian Chair of Mathematics at Cambridge University to succeed John Colson applied, which he held from 1760 until the end of his life. His appointment at the age of only 23 met with criticism and an exchange of pamphlets ensued (William Samuel Powell attacked the first chapter of the Miscellanea Analytica after Moritz Cantor because of some insignificant errors), but Waring received the support of his friend John Wilson from Peterhouse College. He also received his master’s degree in 1760. When he was appointed to the Lucasian Chair, he gave up his fellowship at Magdalene College. With the publication of his major work in 1762, he proved his position as a mathematician of the first order, which silenced any criticism that still existed.

Waring also studied medicine with the MD 1767 and also practiced briefly in hospitals in London and at the Addenbroke Hospital in Cambridge and most recently in a hospital in St. Ives in Huntingdonshire. In 1770 he gave up. The reasons for this were likely that he was very short-sighted and very reserved by nature. He is said to have privately conducted sections on his premises in Cambridge.

In 1776 he married Mary Oswell, with whom he first lived in Shrewsbury and then on the farm of Waring in Plealey in Pontesbury. According to contemporary accounts, towards the end of his life he fell into a state of deeply religious melancholy with features of madness.

He was on the Board of Longitude .

plant

Waring was considered one of the most important mathematicians of his time in England, albeit at a time when the cultivation of analysis in England itself was in decline. His main work Miscellanea Analytica appeared in 1762 and was renamed in the second edition in Meditationes Algebraicae. It deals with topics from the theory of equations, i.e. algebra, number theory and geometry . In the work, he made an unproven claim known as Waring's problem, which is a generalization of the four-squares theorem . In Waring's formulation: any integer is the sum of no more than nine cubes, likewise any sum of no more than nineteen is fourth powers, and so on. The validity of the assertion made by Waring could only be proven in 1909 by David Hilbert . In the theory of algebraic curves, he classified quarters (curves of the fourth degree), distinguishing between twelve main types with a further subdivision into 84551 cases.

His contributions to the theory of equations are some of the earliest contributions to what later became known as Galois theory ( resolvent equations in algebra, theory of symmetric functions). He proved that rational symmetric equations of the roots of a polynomial can be expressed as a rational equation of the coefficients (construction of symmetric polynomials from elementary symmetric ones ). Formulas in this field were also named after him. He also examined the circular division equation, formulated a forerunner of Bézout's theorem and was the first to publish the Goldbach conjecture (which had previously been formulated by Goldbach in a letter to Euler, but was not published). He gave conditions for the number of imaginary roots of equations of the fourth and fifth degree (after Cantor he was the first to set such conditions for the equation of the fifth degree), using a transformation he had invented. In the Meditationes algebraicae there is also the first (modern) mention of Wilson's theorem ( John Wilson was a student of Waring).

A result of Waring from analysis has a close relation to the theorem of Rolle ( Waring's theorem ). In addition to his main work, Waring also wrote other books. In analysis he followed both Leibniz's and Newton's notation without choosing either side.

Waring did not give any lectures, and his books also show his deficits as a pedagogical mediator of his mathematical knowledge. His algebraic notation was cumbersome and also left a lot to be desired, his books difficult to read and so the reception of his main work was limited in England, which he complained about in a letter to the royal astronomer Nevil Maskelyne . The letter was in response to a comment by Jérôme Lalande in his biography of Condorcet (Mercure de France, January 20, 1796), in which he claimed that there were no top mathematicians in England at the moment. Waring pointed out that his main work contained around 300 to 400 new sentences, more than any other contemporary English mathematician, and that Leonhard Euler , Joseph-Louis Lagrange (who praised the book Meditationes algebraicae of 1770 in the highest terms) and Jean-Baptiste le Rond d'Alembert would have praised his work. In England, on the other hand, according to Waring, no one outside of Cambridge would seem to have noticed.

Waring himself had sent a copy of the Miscellanea Analytica to Euler in 1763 and copies of his Meditationes Algebraicae from 1770 to Euler, Lagrange, D'Alembert, Jean-Étienne Montucla , Étienne Bézout and Paolo Frisi , who was the only one to confirm receipt.

His last book from 1794 was devoted to philosophy.

Honors and memberships

Waring was inducted into the Royal Society in 1763 and was awarded the Copley Medal in 1784 . In 1795, however, he resigned, citing his poverty as the reason. In 1786 he was elected a foreign member of the Göttingen Academy of Sciences . He was also a member of the Academy of Sciences in Bologna.

Works

Miscellanea analytica , 1762

• Miscellanea Analytica, de aequationibus algebraicis et curvarum proprietatibus , Cambridge 1762, Archives
• Meditationes algebraicae , Cambridge 1770, expanded edition 1782, 3rd edition 1783, archives
• Proprietates algebraicarum curvarum , Cambridge 1772
• Miscellanea Analytica , Cambridge 1776, 2nd edition 1785
• On the principles of translating algebraic quantities into probable relations and annuities , Cambridge 1792
• Essays on the principles of human knowledge , Cambridge 1794

He also published in the Philosophical Transactions of the Royal Society, for example, On the general resolution of algebraic equations , Volume 69, 1779, pp. 86-104.

literature

• Moritz Cantor : Lectures on the history of mathematics, Volume 4, Leipzig 1908, pp. 92–94
• D. Weeks: Meditationes algebraicae, an English translation of the work of Edward Waring , American Mathematical Society, Providence / Rhode Island, 1991 (with appendix by Franz X. Mayer)
• JF Scott: Waring, Edward, Dictionary of Scientific Biography , Volume 14, pp. 179-181
• Edward Warren, entry in The Georgian Era: Memoirs of the most eminent persons who have flourished in Great Britain, Volume 3, London 1834
• WP Courtney: Edward Waring, Dictionary of National Biography , 1899
• P. Bhattacharyya, S. Sankar: History of Waring's problem, Math. Student, Vol. 61, 1992, pp. 29-53.
• Isabella Grigoryevna Baschmakowa : Unproblemème de la théorie des equations algébriques chez I. Newton et E. Waring (Russian with French summary), Istor.-Mat. Issled., Vol. 12, 1959, pp. 431-456
• Ian Stewart : The Waring Experience, Nature, Volume 323, Oct 1986, p. 674.
• Franz Xaver Mayer: Eduard Warings Meditationes algebraicae. Inaugural dissertation (University of Zurich). Überlingen (Lake Constance) 1923

Web links

• John J. O'Connor, Edmund F. Robertson :  Edward Waring. In: MacTutor History of Mathematics archive .

Individual evidence

1. ↑ According to Mctutor (see web links). In the Dictionary of Scientific Biography, the date of birth is Shrewsbury, around 1736, and the date of death is Plealey, near Shrewsbury, August 15, 1798
2. ^ Moritz Cantor, History of Mathematics, Volume 4, p. 92
3. ^ ^{A b c} J. F. Scott, Dictionary of Scientific Biography
4. ↑ Tignol, Galois theory of algebraic equations, World Scientific, 2002, p. 100. After that, these results can be found in print for the first time in Waring.
5. ^ Cantor, History of Mathematics, Volume 4, p. 94
6. ^ Cantor, History of Mathematics, Volume 4, p. 93
7. ↑ The term Waring's sentence can be found in S. Gottwald u. a., Lexicon of important mathematicians, Leipzig 1990, p. 482
8. ↑ According to his biographer JF Scott, for example, his notation for exponents was clumsy to the extreme
9. ↑ JF Scott, Dict. Sci. Biogr .: He suffered from an apparent lack of intellectual order that rendered his mathematical compositions so confused that they are almost impossible to follow in manuscript . There were many typographical errors in his books and, according to Scott, his language was obscure at best.
10. ↑ Moritz Cantor, History of Mathematics, Volume 4, p. 93, quoting Lagrange's view of Waring's main work, published in 1770: ouvrage remplit d'excellentes recherches .
11. ^ Cantor, History of Mathematics, Volume 4, p. 93
12. ↑ Holger Krahnke: The members of the Academy of Sciences in Göttingen 1751-2001 (= Treatises of the Academy of Sciences in Göttingen, Philological-Historical Class. Volume 3, Vol. 246 = Treatises of the Academy of Sciences in Göttingen, Mathematical-Physical Class. Episode 3, vol. 50). Vandenhoeck & Ruprecht, Göttingen 2001, ISBN 3-525-82516-1 , p. 252.
13. ↑ After JF Scott, Dict. Sci. Biogr., The most detailed appraisal of Waring as a mathematician up to that time in the 1970s