He lived in the Netherlands from 1642 to 1648. He lectured at the University of Copenhagen during 1648–1654 and lived in Paris from 1655 to 1657. He was mathematics tutor to Joscelyne Percy, son of the 10th Earl of Northumberland, at Petworth, Sussex (1657). He taught mathematics in London (1658–1682). In 1666 he became a member of the Royal Society. He designed a marine chronometer for Charles II, and designed and constructed the fountains at the Palace of Versailles (1682–1687).
Mathematically, he is most well known for his treatise Logarithmo-technica on logarithms, published in 1668. In this treatise he described the Mercator series, also independently discovered by Gregory Saint-Vincent:
It was also in this treatise that the first known use of the term natural logarithm appears, in the Latin form log naturalis. His use of this term is somewhat surprising, since it predates the development of infinitesimal calculus, in which the most natural properties of this logarithm appear.
To the field of music he contributed the first precise account of 53 equal temperament, which was of theoretical importance, but not widely practiced.