Bartholin, the son of Caspar and brother of Thomas Bartholin, who were both distinguished anatomists, was born in Roskilde, Denmark, and educated in Leiden and Padua, where he obtained his MD in 1654. After further travel in France and England he returned to Denmark in 1656 and held chairs in mathematics and medicine at the University of Copenhagen from 1657 until his death.

Bartholin worked on the theory of equations and with Olaus Romer made an unsuccessful attempt to calculate the orbits of the comets prominent in the late 1660s. He is however best remembered for his discovery of double refraction announced in his Experimenta crystalli Islandici disdiaclastici (1669). In it he described how Icelandic feldspar (calcite) produces a double image of objects observed through it. This discovery greatly puzzled scientists and was much discussed by Newton and Christiaan Huygens, who tried unsuccessfully to incorporate the strange phenomenon into their respective theories of light.

Double refraction proved remarkably recalcitrant to all proposed explanations for well over a century and it was only with the work of Etienne Malus on polarized light in 1808, and that of Augustin Fresnel in 1817, that Bartholin's observations could at last be understood.