He was born 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 Frederick Henry, Prince of Orange, to Breda, where he remained till 1652.
From 1654 to 1658 Pell acted as Oliver Cromwell's political agent to the Protestant cantons of Switzerland. On his return to England he took orders and was appointed by King Charles II of England to the rectory of Fobbing in Essex. In 1673 he was presented by Bishop Gilbert Sheldon to the rectory of Laindon in the same county.
His devotion to mathematical science seems to have interfered with his advancement in the Church and with his private life. For a time he was confined as a debtor in the kings bench prison. He lived, on the invitation of Dr Whistler, for a short time in 1682 at the College of Physicians, but died at the house of Mr Cothorne, reader of the church of St Giles-in-the Fields. Many of Pell's manuscripts fell into the hands of Richard 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 Pell's own memoirs, but much of his correspondence with the mathematicians of his time.
The Diophantine equation was a favorite subject with Pell; he lectured on it at Amsterdam; and he is now best remembered for the indeterminate equation , which is known as the Pell equation or Pell's equation. This problem was proposed by Pierre de Fermat first to Bernhard Frenicle de Bessy, and in 1657 to all mathematicians. Pell's connection with the problem simply consists of the publication of the solutions of John Wallis and Lord Brounker in his edition of Breaker's Translation of Rizonius's Algebra (1668).
His chief works are:
- Astronomical History of Observations of Heavenly Motions and Appearances (1634)
- Ecliptica prognostica (1634)
- Controversy with Longomontanus concerning the Quadrature of the Circle (1646?)
- An Idea of the Mathematics, I2iflO (1650)
- A Table of Ten Thousand Square Numbers (fol.; 1672).
- This entry incorporates public domain text originally from the 1911 Encyclopædia Britannica.
- The most recent study of Pell is by Noel Malcolm and Jacqueline Stedall, John Pell (1611-1685) and His Correspondence with Sir Charles Cavendish: The Mental World of an Early Modern Mathematician (Oxford: Oxford University Press, 2005). ISBN 0-19-856484-8
- O'Connor, John J., and Edmund F. Robertson. "John Pell". MacTutor History of Mathematics archive.