The year 1691 in science and technology involved some significant events.

• Italian Jesuit scholar Filippo Bonanni publishes the results of his microscopic observations of invertebrates in Observationes circa Viventia, quae in Rebus non-Viventibus.

• Gottfried Leibniz discovers the technique of separation of variables for ordinary differential equations.
• Michel Rolle invents Rolle's theorem.

• Anton Nuck's Adenographia curiosa et uteri foeminei anatome nova is published at Leiden, including a description of the canal of Nuck^[1] and a demonstration that the embryo is derived from the ovary and not the sperm.^[2]

• Edmond Halley devises a diving bell.^[3]
• In music, the "equal temperament scale" used in modern music is developed by organist Andreas Werckmeister.

• November 18 – Mårten Triewald, Swedish mechanical engineer (died 1747)

• January 17 – Richard Lower, English physician who performed the first direct blood transfusion (born 1631)
• December 31 – Robert Boyle, Anglo-Irish chemist (born 1627)^[4]