The year 1777 in science and technology involved some significant events.

Exploration March – Third voyage of James Cook: English explorer Captain Cook discovers Mangaia and Atiu in the Cook Islands.

Mathematics Leonhard Euler introduces the symbol i to represent the square root of −1.

Technology probable date – Thomas Arnold of London produces the first watch ("Arnold 36") to be called a chronometer.

Awards Copley Medal: John Mudge

Births February 12 – Bernard Courtois, French chemist (died 1838) April 30 – Carl Friedrich Gauss, German mathematician (died 1855) May 4 – Louis Jacques Thénard, French chemist (died 1857) May 18 – John George Children, English chemist, mineralogist and entomologist (died 1852) August 14 – Hans Christian Ørsted, Danish physicist (died 1851)

Deaths September 22 – John Bartram, naturalist and explorer considered the "father of American botany" (born 1699) September 25 – Johann Heinrich Lambert, Swiss polymath (born 1728) December 7 – Albrecht von Haller, Swiss anatomist and physiologist (born 1708) Celia Grillo Borromeo, Italian scientist and mathematician (born 1684)

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