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.īeyond his first use of the symbol π Jones is of interest because of his connection to a number of key mathematical, scientific and political characters of the 18th century. The irrationality of π was not proved until 1761 by Johann Lambert (1728-77), then in 1882 Ferdinand Lindemann (1852-1939) proved that π was a non-algebraic irrational number, a transcendental number (one which is not a solution of an algebraic equation, of any degree, with rational coefficients). 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. 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. The circumference of a circle was known in those days as the 'periphery', hence the Greek equivalent 'π' of our letter 'π'. 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. 1575-1 660), in his book Clavis Mathematicae (first published in 1631).
The symbol π had been used in the previous century in a significantly different way by the rector and mathematician, William Oughtred (c. For this Jones recognised that only a pure platonic symbol would suffice. Consequently, a symbol was required to represent an ideal that can be approached but never reached. the exact proportion between the diameter and the circumference can never be expressed in numbers.'. Though he did not prove it, Jones believed that π was an irrational number: an infinite, non-repeating sequence of digits that could never totally be expressed in numerical form. In fact it was first used in print in its modern sense in 1706 a year before Euler's birth by a self-taught mathematics teacher William Jones (1675-1749) in his second book Synopsis Palmariorum Matheseos, or A New Introduction to the Mathematics based on his teaching notes.īefore the appearance of the symbol π, approximations such as 22/7 and 355/113 had also been used to express the ratio, which may have given the impression that it was a rational number. It is widely believed that the great Swiss-born mathematician Leonhard Euler (1707-83) introduced the symbol π into common use.
Before this the ratio had been awkwardly referred to in medieval Latin as: quantitas in quam cum multiflicetur diameter, proveniet circumferencia (the quantity which, when the diameter is multiplied by it, yields the circumference). The history of the constant ratio of the circumference to the diameter of any circle is as old as man's desire to measure whereas the symbol for this ratio known today as π ( pi) dates from the early 18th century. A more detailed and comprehensive mathematical chronology can be found at. Where the mathematicians have individual pages in this website, these pages are linked otherwise more information can usually be obtained from the general page relating to the particular period in history, or from the list of sources used. This is a chronological list of some of the most important mathematicians in history and their major achievments, as well as some very early achievements in mathematics for which individual contributions can not be acknowledged. LIST OF IMPORTANT MATHEMATICIANS – TIMELINE