Niels Nielsen (2 December 1865, in Ørslev – 16 September 1931, in Copenhagen) was a Danish mathematician who specialised in mathematical analysis.

Nielsen was the son of humble peasants and grew up in the western part of the island of Funen.

In 1891 he graduated in mathematics from the University of Copenhagen and in 1895 obtained his doctorate.

In 1909 he succeeded Julius Petersen as Professor of Mathematics at the University of Copenhagen.

From this date onward he became interested in the number theory, Bernoulli numbers, Stirling numbers, and the history of mathematics, writing two books on Danish mathematicians of the time period 1528-1908, and two other books on French mathematicians.