# John Pell

### Quick Info

Born
1 March 1611
Southwick, Sussex, England
Died
12 December 1685
Westminster, London, England

Summary
John Pell was an English mathematician best known for Pell's equation which in fact he had little to do with.

### Biography

John Pell's father was also named John Pell and his mother was Mary Holland. Mary was from Halden in Kent and her husband was from Southwick where their son John, the subject of this biography, was born. He was the second of his parents two sons but by the time he was six years old he was an orphan, his father dying in 1616 and his mother in the following year. John Pell senior had a fine library and this proved valuable to John junior as he grew up. After attending Steyning School in Sussex, which was a free school, he entered Trinity College, Cambridge in 1624. He received his B.A. in 1628 and his M.A. in 1630. He was by this time an expert in Latin and Greek and, although we know little of his training in mathematics, we do know that he corresponded with Briggs about logarithms in the year in which he graduated with his B.A.

After leaving Cambridge, Pell became a schoolmaster. He worked first in Horsham, as an assistant master at Collyer's School, then in Chichester Academy in Sussex. He married Ithumaria Reginolles on 3 July 1632; they had four sons and four daughters. Pell spent five years from 1638 teaching mathematics in London. He then went abroad becoming Professor of Mathematics at the Gymnasium Illustre in Amsterdam from 1643 until he took up a similar post at the University of Breda in 1646. In 1651 the English brought in the Navigation Act which aimed to prevent the Dutch taking part in the English sea trade. Tensions between the English and the Dutch rose sharply and there was an incident in May 1652 when a Dutch force was defeated. Pell realised that war was imminent and that he would be in an extremely difficult position in Breda once war broke out. He returned to England and indeed the First Anglo-Dutch War did break out on 8 July 1652. After his return, Pell was appointed by Oliver Cromwell to a post teaching mathematics in London.

Pell spent the years 1654 to 1658 holding a government post in Zürich. He had been sent there by Cromwell on a diplomatic mission. The Peace of Westphalia of 1648 that ended the Thirty Years' War saw the Roman Catholicism (at this time identified with French rule) regain some territories which had previously been Lutheran Protestant. Cromwell wanted to split the Protestant cantons of Switzerland off to join a Protestant League, with England at its head. However Pell's negotiations were long drawn out and he returned to England to give his report to Cromwell only shortly before Cromwell's death. He was unable to report as he waited in vain for an audience with Cromwell which could not be arranged. After his return to England Pell was ordained a deacon, then a priest in 1661. He became vicar at Fobbing in Essex, and in 1663 he also became vicar of Laindon and Basildon in Essex. He held these two positions in the church for the last twenty years of his life. His wife Ithumaria died in 1661 and some time before 1669 he remarried.

Malcolm writes in [7]:-
The mathematician John Pell is a significant figure in the intellectual history of 17th century England - significant, however, more because of his activities, contacts and correspondence than because of his published work. His few publications are, nevertheless, valuable sources of information about his intellectual biography.
Pell worked on algebra and number theory. He gave a table of factors of all integers up to 100000 in 1668. Pell's equation $y^{2} = ax^{2} + 1$, where $a$ is a non-square integer, was first studied by Brahmagupta and Bhaskara II. Its complete theory was worked out by Lagrange, not Pell. It is often said that Euler mistakenly attributed Brouncker's work on this equation to Pell. However the equation appears in a book by Rahn which was certainly written with Pell's help: some say entirely written by Pell. Perhaps Euler knew what he was doing in naming the equation.

Pell published a number of works, for example Idea of Mathematics (1638) and the two page A Refutation of Longomontanus's Pretended Quadrature of the Circle (1644) (reprinted in Latin as Controversiae de vera circuli mensura (1647)). M J Klein writes of the Idea of Mathematics:-
Pell made a list of tasks that if executed would promote the progress of mathematics in England. His plans included cataloguing all past works, describing the extent of mathematics, selecting the best of the past, describing the advances already made, delineating the methodologies that would prove helpful, and noting the problems that cannot be solved.
The Refutation was written because of a dispute Pell was involved in over the value of π. Longomontanus (Christian Severin) had published his quadrature of the circle in 1644. In fact Longomontanus died in 1647 but the controversy did not end with his death since others joined in. In [9] van Maanen describes in detail the correspondence between Pell and Charles Cavendish in which Pell is trying to enlist supporters for his side of the argument. Pell also translated Lansberge's tables, which were published in 1632, and worked on astronomy.

Pell was elected to the Royal Society on 20 May 1663. He served on the committee considering mechanical and optical inventions and was elected vice-president in 1675.

He is described in [2] as follows:-
Pell was a striking figure, remarkably handsome, with strong, excellent posture, dark hair and eyes, and a good voice. His temperament was sanguine and melancholic.
When in London, Pell lived for a while with Collins. However in the autumn of 1664 an epidemic of the plague began in the poor outskirts of city. The epidemic died down after the winter but spread again in May 1665. The king and court fled from London in June and that summer Pell also left London being invited to Brereton Hall in Cheshire as the guest of William Brereton whom he had tutored while in the Netherlands. Aubrey writes [3]:-
Never was there greater love between master and scholar then between Dr Pell and this scholar of his, whose death on 17 March 1680 hath deprived this worthy doctor of an ingenious companion and a useful friend.
After this Pell lived [3]:-
... in an obscure lodging, three stories high, in Jermyn Street, next to the sign of the Ship, wanting not only books but his proper manuscripts.
He was now in debt and put in prison. After his release he lived in a number of different places such as the College of Physicians, the house of one of his grandchildren, and a lodgings in Westminster where he died.

### References (show)

1. P J Wallis, Biography in Dictionary of Scientific Biography (New York 1970-1990). See THIS LINK.
2. Biography by Christoph J Scriba, in Dictionary of National Biography (Oxford, 2004). See THIS LINK.
3. J Aubrey, John Pell, Brief lives II (Oxford, 1898), 121-131.
4. J Bernhardt, Une lattre-programme pour 'l'avancement des mathématiques' au XVIIe siècle : L' 'Idée générale des mathématiques' de John Pell, Rev. Histoire Sci. Appl. 24 (4) (1971), 309-316.
5. T Birch, The History of the Royal Society of London 4 (London, 1757), 444-447.
6. H Kangro, Die Unabhängigkeit eines Beweises : John Pells Beziehungen zu Joachim Jungius und Johann Adolph Tassius (aus unveröffentlichten Mss.), Janus 56 (1969), 203-209.
7. N Malcolm, The publications of John Pell FRS (1611-1685) : some new light and some old confusions, Notes and
8. Records of the Royal Society of London 54 (2000), 275-292.
9. C J Scriba, John Pell's English Edition of J H Rahn's Teutsche Algebra, in R S Cohen, J J Stachel, and M W Wartofsky (eds.), For Dirk Struik : scientific, historical, and
10. political essays in honor of Dirk J Struik (Dordrecht, 1974), 261-274.
11. J A van Maanen, The refutation of Longomontanus' quadrature by John Pell, Ann. of Sci. 43 (4) (1986), 315-352.
12. P J Wallis, An early mathematical manifesto - John Pell's 'Idea of Mathematics', Durham Research Review 18 (1967), 139-148.

### Honours (show)

Honours awarded to John Pell

### Cross-references (show)

Written by J J O'Connor and E F Robertson
Last Update February 2005