How a humbleWelshman became a maths pi-oneer
Mathematician William Jones was the first person to use the Greek letter π for pi. Tony Bonnici reflects on the story behind the Welshman’s crucial discovery...
THIS week the world, with the possible exception of children sitting in double maths, celebrates the achievements of William Jones the man who invented pi.
But who was he? And why is this little symbol used to calculate the circumference and area of a circle so important?
William Jones was born sometime around 1675 on the Isle of Anglesey in the parish of Llanfihangel Tre’r Beirdd (The Parish of St Michael, Town of the Bards), about four miles west of Benllech.
The son of Siôn Siôr (John George Jones) and Elizabeth Rowland, he had a humble upbringing on a small farmstead.
However, his talent for mathematics quickly became apparent when he attended a charity school at Llanfechell. It was to be his only formal education.
His aptitude for the subject ensured that he would not follow in the family footsteps. Local squires and landlords, the distinguished Bulkeley family, heard of his skill and took him under their patronage.
They arranged for him to work in a merchant’s counting house in London.
It was only the first of many journeys. Between 1695 and 1702 he served in the Royal Navy, sailing to the West Indies during which time he taught mathematics on board a manof-war, en route learning about navigation.
He was present at the battle of Vigo in October 1702 when the English successfully captured the Spanish treasure fleet as it was returning to the port in north-west Spain under French escort.
Ignoring the obvious riches of silver to be had, he went in search of other booty according to an 1807 memoir by Baron Teignmouth, “...literary treasures were the sole plunder that he coveted”.
On his return, he published A New Compendium of the Whole Art of Navigation which he dedicated to a benefactor John Harris, a writer, scientist and Anglican priest who had taken him under his wing.
Back in the capital, his voyages over, he became a mathematics teacher in coffee houses and as a private tutor to the son of the future Earl of Macclesfield. He also became tutor to Philip Yorke, later 1st Earl of Hardwicke (1690-1764), who became lord chancellor and provided an invaluable source of introductions for his tutor.
It was around this time that Jones first came to the attention of that giant of 17th century mathematics, Isaac Newton.
The great mathematician’s attention was grabbed after reading Jones’s Synopsis, in which the younger man explained Newton’s methods for calculus as well as other mathematical innovations.
In was in this book that Jones first used the Greek symbol ‘π’ to denote the pi, more significantly he used it as a constant number – 3.141...
Before Jones , approximations such as 22/7 and 355/113 had also been used to express the ratio.
Explaining its use, he wrote: “...the exact proportion between the diameter and the circumference can never be expressed in numbers...” Hence, a symbol was required to represent an ideal that can be approached but never reached. For this, Jones recognised that only a pure platonic symbol would suffice.
In 1708 Jones was able to acquire an extensive library and archive, which contained several of Newton’s letters and papers written in the 1670s.
The following year he applied for the mastership of Christ’s Hospital Mathematical School, despite references from Newton and Edmund Halley, the astronomer who calculated the orbit of the comet, now named after him, he was turned down.
Jones went back into private teaching but, thanks to the papers he had acquired, he was able to help his old mentor Newton resolving a dispute with German mathematician Gottfried Leibniz, over which of the men first invented calculus.
In 1712 Jones joined the committee set up by the Royal Society to determine which of them invented calculus. He was now firmly in the mathematical establishment.
He married twice, firstly the widow of his counting-house employer, whose property he inherited on her death.
He remarried in 1731, to Mary, the 22-year-old daughter (30 years his junior) of cabinet-maker George Nix, with whom he had three children.