1668 in science

Astronomy

• Isaac Newton invents the reflecting telescope.

Biology

• Francesco Redi publishes Esperienze Intorno alla Generazione degl'Insetti, disproving theories of the spontaneous generation of maggots in putrefying matter.

Mathematics

• Nicholas Mercator and William Brouncker discover an infinite series for the logarithm while attempting to calculate the area under a hyperbolic segment.

Medicine

• 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.

Publications

• 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.

Births

• December 31 – Herman Boerhaave, Dutch physician and chemist who makes Leiden a European centre of medical knowledge