He was born in Eutin, Schleswig-Holstein, Germany and educated at Rostock and Leyden after which he lived from 1642 to 1648 in the Netherlands. 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 was elected a Fellow of the Royal Society. He designed a marine chronometer for Charles II.
Mathematically, he is most well known for his treatise Logarithmo-technia 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. To the field of music he contributed the first precise account of 53 equal temperament, which was of theoretical importance, but not widely practiced.
He died at Versailles in 1687.
- 1676: Institutionum astronomicarum, London (1685, Padua)
- Kinkhuysen (1661) Algebra ofte Stelkonst, translated by N. Mercator, appears 1968 in Mathematical Papers of Isaac Newton II: 295–364 with Newton commentary 364–446.
- 1664: Hypothesis astronomica nova, London
- 1666: "Certain problems touching some points of navigation", Philosophical Transactions of the Royal Society 1: 215–18
- 1668: Logarithmo-technia from HathiTrust or Logarithmtechnia from Internet Archive
- Wallis (1668) Review of Logarithmotechnia, Philosophical Transactions of the Royal Society 3: 753–9, followed by "Some further Illustration" by N. Mercator, pp 759–64.
- 1670: "Some considerations … method of Cassini", Philosophical Transactions of the Royal Society 5: 1168–75.
- Euclid Speidel (1688) Logarithmotechnia: the making of numbers called logarithms from Google Books
- Francis Maseres & Charles Hutton (1791) Scriptores Logarithmici, link from Google Books.
- Benjamin Wardhaugh (July 2010) A Plague of Ratios from Mathematics Association of America
- John Aubrey (1813) Letters and Lives of Eminent Men II: 450,1, 473