1739 in science
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- January 1 – Bouvet Island is discovered by French explorer Jean-Baptiste Charles Bouvet de Lozier in the South Atlantic Ocean.
- Leonhard Euler solves the general homogeneous linear ordinary differential equation with constant coefficients.
- Euler invents the tonnetz (German for "tone-network"), a conceptual lattice diagram that shows a two-dimensional tonal pitch space created by the network of relationships between musical pitches in just intonation.
- Émilie du Châtelet publishes Dissertation sur la nature et la propagation du feu.
- June 2 – The Royal Swedish Academy of Sciences is founded in Stockholm by Linnaeus, Mårten Triewald and others.
- April 19 – Nicholas Saunderson, English scientist and mathematician (born 1682)
- April 27 – Nicolas Sarrabat, French scientist, astronomer and mathematician (born 1698)