The year 1771 in science and technology involved some significant events.

• Lagrange discusses how numerous astronomical observations should be combined so as to give the most probable result.^[1]

• British apothecary Thomas Henry invents a process for preparing magnesium oxide.

• August 17 – Edinburgh botanist James Robertson makes the first recorded ascent of Ben Nevis in Scotland.

• Lagrange publishes his second paper on the general process for solving an algebraic equation of any degree via Lagrange resolvents; and proves Wilson's theorem that if n is a prime, then (n − 1)! + 1 is always a multiple of n.

• Norfolk and Norwich Hospital founded in England.

• March 15 – Society of Civil Engineers first meets (in London), the world's oldest engineering society.^[2][3]
• December 16 – French chemist Antoine Lavoisier (28) marries Marie-Anne Pierrette Paulze, not yet 14 and daughter of his senior in the Ferme générale.

• Louis Antoine de Bougainville publishes Le voyage autour du monde, par la frégate La Boudeuse, et la flûte L'Étoile.
• Peter Simon Pallas begins publication of Reise durch verschiedene Provinzen des Russischen Reichs, chronicling his ongoing scientific expedition through the Russian Empire.
• Arthur Young publishes The Farmer's Kalendar.

• Copley Medal: Matthew Raper^[4]

• April 13 – Richard Trevithick (died 1833), Cornish mechanical engineer and inventor.
• August 22 – Henry Maudslay (died 1831), English mechanical engineer and inventor.
• September 11 – Mungo Park (died 1806), Scottish explorer.
• October 13 – Gotthelf Fischer von Waldheim (died 1853), Saxon-born naturalist.
• November 6 – Alois Senefelder (died 1834), Prague-born German inventor of lithography.
• December 14 – Regina von Siebold (died 1849), German physician and obstetrician.

• February 20 – Jean-Jacques d'Ortous de Mairan, French geophysicist, astronomer and chronobiologist (born 1678)
• March 17 – Chester Moore Hall, English scientific instrument maker (born 1703)
• March 23 – Henry Hindley, English clock and scientific instrument maker (born c. 1701)
• December 6 – Giovanni Battista Morgagni, Italian anatomist (born 1682)
• December 15 – Benjamin Stillingfleet, English botanist (born 1702)