John Pell - Academic and Diplomat

Academic and Diplomat

His reputation and the influence of Sir William Boswell, the English resident, with the States-General procured his election in 1644 to the chair of mathematics in Amsterdam, after an earlier attempt immediately after Martin van den Hove left for Leiden had failed. From 1644 he worked on a polemical work, against Longomontanus. For this he put in a large effort soliciting help and testimonials: from Bonaventura Cavalieri, his patron Sir Charles Cavendish, René Descartes, Thomas Hobbes, Mersenne, Claude Mydorge, and Gilles de Roberval. It finally appeared as Controversy with Longomontanus concerning the Quadrature of the Circle (1647).

Pell moved in 1646, on the invitation of Frederick Henry, Prince of Orange, to Breda, and remained there until 1652.

From 1654 to 1658 Pell acted as Oliver Cromwell's political agent to the Protestant cantons of Switzerland; he co-operated with Samuel Morland at Geneva. A mathematical pupil and disciple there, from 1657, was Johann Heinrich Rahn, known as Rhonius. Rahn is credited with the invention of the division sign ÷ (obelus); it has also been attributed to Pell, who taught Rahn a three-column spreadsheet-style technique of tabulation of calculations, and acted as editor for Rahn's 1659 book Teutsche Algebra in which it appeared. This book by Rahn also contained what would become known as the "Pell equation". Diophantine equations was a favorite subject with Pell; he lectured on them at Amsterdam. He is now best remembered, if perhaps erroneously, for the indeterminate equation

which is known as Pell's equation. This problem was in fact proposed by Pierre de Fermat first to Bernard Frénicle de Bessy, and in 1657 to all mathematicians. Pell's connection with the problem is through Rahn. It consisted of the publication of the solutions of John Wallis and Lord Brouncker, in his edition of Thomas Branker's Translation of Rhonius's Algebra (1668); added to his earlier editorial contributions, whatever they were, to the 1659 algebra book written by Rahn (i.e. Rhonius). This new edition of what was essentially Rahn's work, by Pell, included a great deal of additional material on number theory, amounting to a reply to the 1657 book Exercitationes mathematicae by Frans van Schooten. It is also notable for its inclusion of a Table of Incomposits, an early large factor table.