1690 in science

• Giovanni Cassini observes differential rotation within Jupiter's atmosphere. • December – Earliest recorded sightings of the planet Uranus, by John Flamsteed, who mistakenly catalogues it as the star 34 Tauri. ==Geography==

• Franciscan Vincenzo Coronelli publishes the first folio of his atlas Atlante Veneto. ==Botany==

• French horticulturalist Jean-Baptiste de La Quintinie's Instruction pour les jardins fruitiers et potagers is published posthumously. ==Mathematics==

• of Osaka publishes Sampo-Hakki (算法発揮), in which he gives the resultant and the Laplace expansion of the determinant for the n×n case. At about this date, also describes and applies the resultant, in Sampo-Funkai (算法紛解). • Michel Rolle publishes ''Traité d'Algebre'', in which he gives the first published description in Europe of Gaussian elimination. ==Medicine==

• Justine Siegemund publishes Die Chur-Brandenburgische Hof-Wehemutter ("The Court Midwife"), the first medical textbook in German written by a woman. ==Technology==

• February 3 – America's first paper money is printed in the Massachusetts Bay Colony. • A rudimentary working model of a liquid compass is introduced by Sir Edmond Halley at a meeting of the Royal Society. • French physicist Denis Papin, while in Leipzig and having observed the mechanical power of atmospheric pressure on his 'digester', builds a working model of a reciprocating steam engine for pumping water, the first of its kind, though not efficient. ==Births==

• March 18 – Christian Goldbach, Prussian mathematician (died 1764) ==Deaths==

• February 3 – Elizabeth Walker, English pharmacist (born 1623) • October 13 – Ole Borch, Danish polymath (born 1626) • October 22 (bur.) – William Ball, English astronomer (born c. 1631)