The year 1778 in science and technology involved some significant events.

• Lagrange delivers his treatise on cometary perturbations to the Académie française.

• Molybdenum discovered by Carl Wilhelm Scheele.
• Antoine Lavoisier, considered "The father of modern chemistry",^[1] recognizes and names oxygen, and recognizes its importance and role in combustion.^[2]

• January 18 – On his third voyage, Captain James Cook, with ships HMS Resolution and HMS Discovery, becomes the first European to view the Hawaiian Islands in the Pacific Ocean.^[3]
• March 6 – October 24 – Captain Cook explores and maps the Pacific Northwest coast of North America from Cape Foulweather (Oregon) to the Bering Strait.
• James Rennell publishes a chart and memoir of the Agulhas Current, one of the first contributions to scientific oceanography.^[4]

• John Hunter publishes The Natural History of the Human Teeth.
• Samuel-Auguste Tissot begins publication of Traité des nerfs et de leurs maladies, including a classical account of migraine.^[5][6]
• Samuel Thomas von Sömmerring describes the organization of the cranial nerves.
• Publication of Collection of observations on diseases and epidemic constitutions (Collection d’observations sur les maladies et constitutions épidémiques), by Louis Lépecq de La Clôture, work consisting mainly of a 15-year observation of the relations between climate, geography and pathologies in Normandy.^[7][8]

• Joseph Bramah patents an improved design of flush toilet in London.^[9]
• The brothers Hans Ulrich and Johannes Grubenmann complete a bridge across the Limmat at Wettingen in Switzerland, a 60 m span which is the first known use of a true arch in a timber bridge.^[10]

• Petrus Camper publishes On the Points of Similarity between the Human Species, Quadrupeds, Birds, and Fish; with Rules for Drawing, founded on this Similarity, an early work of comparative anatomy.
• Johan Christian Fabricius publishes his Philosophia Entomologica in Hamburg.^[11]

• Copley Medal: Charles Hutton^[12]

• February 4 – A. P. de Candolle, Swiss botanist (died 1841)
• May 18 – Andrew Ure, Scottish industrial chemist and encyclopaedist (died 1857)
• December 6 – Joseph Louis Gay-Lussac, French chemist and physicist (died 1850)
• December 17 – Humphry Davy, English chemist (died 1829)
• December 25 (bapt.) – Joseph Aspdin, English inventor (died 1855)
• Maria Dalle Donne, Bolognese physician (died 1842)
• Anna Maria Walker, Scottish botanist (died 1852)

• January 10 – Carl Linnaeus, Swedish botanist, first to develop standard nomenclature for naming species (born 1707)
• February 20 – Laura Bassi, Italian scientist (born 1711)
• March 7 – Charles De Geer, Swedish industrialist and entomologist (born 1720)
• May 6 – Jean Baptiste Christophore Fusée Aublet, French pharmacist and botanist (born 1720)