1678 in science
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- Edmund Halley publishes a catalogue of 341 southern stars—the first systematic southern sky survey.
- Christiaan Huygens publishes his Traité de la Lumière/Treatise on Light, which states his principle of wavefront sources.
- Robert Hooke discovers the fundamental law of elasticity when he finds that the stress (force) exerted is proportional to the strain (elongation) produced.
- April 14 – Abraham Darby I, ironmaster (died 1717)
- July 16 – Jakob Hermann, mathematician (died 1733)
- October 27 – Pierre Raymond de Montmort, mathematician (died 1719)
- November 26 – Jean-Jacques d'Ortous de Mairan, geophysicist (died 1771)
- December 2 – Nicolaas Kruik (Cruquius), cartographer and meteorologist (died 1754)
- unknown – Pierre Fauchard, physician and "father of modern dentistry" (died 1761)