John Playfair FRSE, FRS (10[citation needed] March 1748 – 20 July 1819) was a Church of Scotland minister, remembered as a scientist and mathematician, and a professor of natural philosophy at the University of Edinburgh.

In 1766, when only 18, he was a candidate for the chair of mathematics in Marischal College (now part of the University of Aberdeen), and, although he was unsuccessful, his claims were admitted to be high.

By this arrangement Playfair regularly visited Edinburgh and went on to cultivate the literary and scientific society for which the city was at that time specially distinguished.

Through Nevil Maskelyne, whose acquaintance he had first made in the course of the celebrated Schiehallion experiments in 1774, he also gained access to the scientific circles of London.

In 1805 Playfair exchanged the Chair of Mathematics for that of natural philosophy in succession to John Robison, whom also he succeeded as general secretary to the Royal Society of Edinburgh.

He took a prominent part, on the liberal side, in the ecclesiastical controversy that arose in connection with Sir John Leslie's appointment to the post he had vacated, and published a satirical letter (1806).

[12] He died of strangury on 20 July 1819, and, although an eminent man, was buried in an unmarked grave in Old Calton Burial Ground, on Waterloo Place in Edinburgh.

[17] His writings include a number of essays contributed to the Edinburgh Review from 1804 onwards, various papers in the Philosophical Transactions of the Royal Society (including his earliest publication, "On the Arithmetic of Impossible Quantities", 1779, and an "Account of the Lithological Survey of Schehallion", 1811) and in the Transactions of the Royal Society of Edinburgh ("On the Causes which Affect the Accuracy of Barometrical Measurements" and others), the articles "Aepinus" and "Physical Astronomy", and a "Dissertation on the Progress of Mathematical and Physical Science since the Revival of Learning in Europe" in the Encyclopædia Britannica (Supplement to fourth, fifth and sixth editions).

[19] His Elements of Geometry first appeared in 1795 and has passed through many editions; his Outlines of Natural Philosophy (2 vols., 1812–1816) consist of the propositions and formulae which were the basis of his class lectures.

Playfair's contributions to pure mathematics were not considerable, his papers "On the Arithmetic of Impossible Quantities" and "On the Causes which Affect the Accuracy of Barometrical Measurements", and his Elements of Geometry, all already referred to, being the most important.