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Thursday, 3 July 2014

This self-taught mathematician taught in coffee houses for free, yet made his mark with the LIFE OF HIS PI !!!!

William Jones, (1675 – 3 July 1749) was a Welsh mathematician, most noted for his proposal for the use of the symbol π (the Greek letter pi) to represent the ratio of the circumference of a circle to its diameter. He was a close friend of Sir Isaac Newton and SirEdmund Halley. In November, 1711 he became a Fellow of the Royal Society, and was later its Vice-President.

William Jones was born the son of Siôn Siôr (John George Jones) and Elizabeth Rowland in the parish of Llanfihangel Tre'r Beirdd, about 4 miles west of Benllech on the Isle of AngleseyHe attended a charity school at Llanfechell, also on the Isle of Anglesey, where his mathematical talents were spotted by the local landowner who arranged for him to be given a job in London working in a merchant's counting-house. He owed his successful career partly to the patronage of the distinguished Bulkeley family of northWales, and later to the Earl of Macclesfield.

Jones initially served at sea, teaching mathematics on board Navy ships between 1695 and 1702, where he became very interested in navigation and published A New Compendium of the Whole Art of Navigation in 1702, dedicated to a benefactor John Harris. In this work he applied mathematics to navigation, studying methods of calculating position at sea. After his voyages were over he became a mathematics teacher in London, both in coffee houses and as a private tutor to the son of the future Earl of Macclesfield and also the future Baron Hardwicke. He also held a number of undemanding posts in government offices with the help of his former pupils.


Jones published Synopsis Palmariorum Matheseos in 1706, a work which was intended for beginners and which included theorems on differential calculus and infinite series. This used π as an abbreviation for perimeter. His 1711 work Analysis per quantitatum series, fluxiones ac differentias introduced the dot notation for differentiation in calculus. In 1731 he published Discourses of the Natural Philosophy of the Elements.


Before being ascribed a modern name, pi existed under the guise of a bulkier, more antiquated phrase: quantitas in quam cum multiflicetur diameter, proveniet circumferencia—Latin for “the quantity which, when the diameter is multiplied by it, yields the circumference.” While descriptive, the collection of words required to denote pi before “pi” did not lend itself to clear or efficient discussion of the concept. Prior to Jones publishing his bold decision, fractions like 22/7 or 355/113 often served to fill in for the mysterious constant, but gave the erroneous impression that the number was a rational one, which can be fully expressed by one whole number divided into another—an assumption that had not yet been disproved, but with which Jones firmly disagreed. For this reason, only an idealized symbol would suffice to represent the concept, and so the Welshman turned to the Greek alphabet.


π, written in Roman letters as “pi,” is the Greek equivalent to our letter ‘p’. For this reason, 17th-century mathematician William Oughtred used π to denote the “periphery,” or the circumference of any given circle—a value that changed as the circle changed. Jones borrowed this earlier logic and applied it to his theory of an irrational, but universal constant value for the circle’s circumference-to-diameter ratio. Johann Lambert’s definitive proof in 1761 that π was an irrational number justified Jones’s earlier instinct, and once Swiss mathematician Leonhard Euler began to use and widely disseminate the symbol π in correspondence with his contemporaries, π was here to stay.


He married twice, firstly the widow of his counting-house employer, whose property he inherited on her death, and secondly, in 1731, Mary, the 22-year-old daughter of cabinet-maker George Nix, with whom he had two surviving children. His son, also named William Jones and born in 1746, was a renowned philologist who first recognised the existence of the Indo-European language group.

The symbol π had been used in the previous century in a significantly different way by the rector and mathematician, William Oughtred (c. 1575-1 660), in his book Clavis Mathematicae (first published in 1631). Oughtred used π to represent the circumference of a given circle, so that his π varied according to the circle's diameter, rather than representing the constant we know today. The circumference of a circle was known in those days as the 'periphery', hence the Greek equivalent 'π' of our letter 'π'. Jones's use of π was an important philosophical step which Oughtred had failed to make even though he had introduced other mathematical symbols, such as :: for proportion and 'x' as the symbol for multiplication.

On Oughtred's death in 1660 some books and papers from his fine mathematical library were acquired by the mathematician John Collins (1625-83), from whom they would eventually pass to Jones. The irrationality of π was not proved until 1761 by Johann Lambert (172877), then in 1882 Ferdinand Lindemann (1852-1939) proved that π was a nonalgebraic irrational number, a transcendental number (one which is not a solution of an algebraic equation, of any degree, with rational coefficients). The discovery that there are two types of irrational numbers, however, does not detract from Jones's achievement in recognising that the ratio of the circumference to the diameter could not be expressed as a rational number.

Beyond his first use of the symbol p Jones is of interest because of his connection to a number of key mathematicial, scientific and political characters of the 18th century. He was also responsible for developing one of the greatest scientific libraries and mathematical archives in the country which remained in the hands of the Macclesfield family, his patrons, for nearly 300 years.