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

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

• Leonhard Euler introduces the symbol i to represent the square root of −1.^[1]

• probable date – Thomas Arnold of London produces the first watch ("Arnold 36") to be called a chronometer.^[2][3]

• Copley Medal: John Mudge^[4]

• 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)

• 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)