1668 in science
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- Isaac Newton invents the reflecting telescope.
- Francesco Redi publishes Esperienze Intorno alla Generazione degl'Insetti ("Experiments on the Generation of Insects"), disproving theories of the spontaneous generation of maggots in putrefying matter.
- Nicholas Mercator and William Brouncker discover an infinite series for the logarithm while attempting to calculate the area under a hyperbolic segment.
- François Mauriceau publishes Traité des Maladies des Femmes Grosses et Accouchées in Paris, a key text in scientific obstetrics.
- John Mayow publishes a tract on respiration in Oxford, recognising "spiritus nitro-aereus" as a component of air, prefiguring the isolation of oxygen.
- John Wilkins publishes An Essay towards a Real Character and a Philosophical Language proposing a universal language and a uniform system of measurement for international communication between natural philosophers.
- December 31 – Herman Boerhaave, Dutch physician and chemist who makes Leiden a European centre of medical knowledge (died 1738)
- Morton, Leslie T. (1943). A Medical Bibliography; a check-list of texts illustrating the history of the medical sciences. London: Grafton.