The year 1671 in science and technology involved some significant events.

• Completion of Paris Observatory, the world's first such national institution.^[1]
• February 27 – The Ortenau meteorite lands in Germany.
• October 25 – Italian-born French astronomer Giovanni Domenico Cassini discovers Iapetus, the second known moon of the planet Saturn.

• James Gregory develops a series expansion for the inverse tangent function and discovers Taylor's theorem.
• Sawaguchi Kazuyuki (沢口 一之) publishes Kokin-Sanpo-Ki (古今算法之記), in which he gives the first comprehensive applied account of Chinese algebra in Japan.

• Publication of Les secrets de la medecine des Chinois, the first Western book on traditional Eastern medicine, in Grenoble.
• Publication of Jane Sharp's The Midwives Book: or the Whole Art of Midwifry Discovered, the first on the subject to be written by an Englishwoman.^[2]

• Jacques Rohault publishes Traité de physique in Paris, disseminating Cartesian physics.

• March 31 – The English Royal Navy launches HMS Royal James at Portsmouth Royal Dockyard, its first warship to have a frame reinforced by iron bars rather than an all wooden ship, an innovation by naval architect Anthony Deane.

• October 1 – Guido Grandi, Italian mathematician (died 1742)

• June 25 – Giovanni Battista Riccioli, Italian astronomer (born 1598)