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 Zurich. 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 y2 = ax2 + 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 p. 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 who 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.



"JOHN PELL." LoveToKnow 1911 Online Encyclopedia. © 2003, 2004 LoveToKnow.

PELL, JOHN (1610-1685), English mathematician, was born on the 1st of March 1610 at Southwick in Sussex, where his father was minister. He was educated at Steyning, and entered Trinity College, Cambridge, at the age of thirteen. During his university career he became an accomplished linguist, and even before he took his M.A. degree (in 1630) corresponded with Henry Briggs and other mathematicians. His great reputation and the influence of Sir William Boswell, the English resident, with the states-general procured his election in 1643 to the chair of mathematics in Amsterdam, whence be removed in 1646, on the invitation of the prince of Orange, to Breda, where he remained till 1652.

From 1654 to 1658 Pell acted as Cromwells political agent to the Protestant cantons of Switzerland. On his return to England he took orders and was appointed by Charles II. to the rectory of Fobbing in Essex, and in 1673 he was presented by Bishop Sheldon to the rectory of Laindon in the same county. His devotion to mathematical science seems to haye interfered alike with his advancement in the Church and with the proper management of his private affairs. For a time he was confined as a debtor in the kings bench prison. He lived, on the invitation of Dr \Vhistler, for a short time in 1682 at the College of Physicians, but died on the 12th of December 1685 at the house of Mr Cothorne, reader of the church of St Gilcs-in-the Fields. Many of Pells manuscripts fell into the hands of Dr Busby, master of Westminster School, and afterwards came into the possession of the Royal Society; they are still preserved in something like forty folio volumes, which contain, not only Pells own memoirs, but much of his correspondence with the mathematicians of his time.

The Diophan tine analysis was a favorite subject with Poll; he lectured on it at Amsterdam; and he is now best remembered for the indeterminate equation ax+I =y, wInch is known by his name. This prcblcm was proposed by Pierre (10 Fermat first to Bernhard Frenicle de Bessv, and in 1657 to all mathematicians. Pells connection with the problem simply consists of the ptiblication of the folutions of John \Vallis and Lord Brounker in his edition of Breakers Translation of Rlzoniuss Algebra (1668). His chief works are: Astronomical History of Observations of Heavenly Motions and Appearances (1634); Ecliptica prognostica (1634); Controversy wit/f Longoinon/anus concerning the Quadrature of the Circle (1646?); An Idea of the Mathematics, I2iflO (1650); A Table of Ten Thousand Square Numbers (fol.; 1672).

More references:


John Pell (1611-1685) and His Correspondence with Sir Charles Cavendish
The Mental World of an Early Modern Mathematician

Noel Malcolm and Jacqueline Stedall

Price: £90.00 (Hardback)
Publication date: 25 November 2004
664 pages, 234mm x 156mm


  • A superb work of scholarship containing new and detailed biographical material
  • Essential reading for historians of mathematics and science, social and political historians and early modern intellectual historians
  • Penetrating and absorbing reconstruction of the life and times of a central figure in seventeenth century England
  • First complete edition of the Pell-Cavendish correspondence
  • Contains extensive footnotes

The mathematician John Pell was a member of that golden generation of scientists Boyle, Wren, Hooke, and others which came together in the early Royal Society. Although he left a huge body of manuscript materials, he has remained an extraordinarily neglected figure, whose papers have never been properly explored. This book, the first ever full-length study of Pell, presents an in-depth account of his life and mathematical thinking, based on a detailed study of his manuscripts. It not only restores to his proper place in history a figure who was one of the leading mathematicians of his day; it also brings to life a strange, appealing, but awkward character, whose failure to publish his discoveries was caused by powerful scruples. In addition, this book shows that the range of Pell's interests extended far beyond mathematics. He was a key member of the circle of the 'intelligencer' Samuel Hartlib; he prepared translations of works by Descartes and Comenius; in the 1650s he served as Cromwell's envoy to Switzerland; and in the last part of his life he was an active member of the Royal Society, interested in the whole range of its activities. The study of Pell's life and thought thus illuminates many different aspects of 17th-century intellectual life. The book is in three parts. The first is a detailed biography of Pell; the second is an extended essay on his mathematical work; the third is a richly annotated edition of his correspondence with Sir Charles Cavendish. This correspondence, which has often been cited by scholars but has never been published in full, is concerned not only with mathematics but also with optics, philosophy, and many other subjects; conducted mainly while Pell was in the Netherlands and Cavendish was also on the Continent, it is an unusually fascinating example of the correspondence that flourished in the 17th-century 'Republic of letters'. This book will be an essential resource not only for historians of mathematics, science, and philosophy, but also for intellectual and cultural historians of early modern Europe.

Readership: Historians of science and mathematics; philosophers; social and political historians; and early modern intellectual historians

  • Part 1. The life of John Pell (1611-1685)
  • Part 2. The mathematics of John Pell
  • Part 3. The Pell-Cavendish correspondence.