Niven completed the solution of most of
Waring's problem in 1944. This problem, based on a 1770 conjecture by
Edward Waring, consists of finding the smallest number g(n) such that every positive integer is the sum of at most g(n) n-th powers of positive integers.
David Hilbert had proved the existence of such a g(n) in 1909; Niven's work established the value of g(n) for all but finitely many values of n. Niven gave an elementary proof that \pi (
pi) is
irrational in 1947.
Niven numbers,
Niven's constant, and
Niven's theorem are named for Niven. He has an
Erdős number of 1 because he coauthored a paper with
Paul Erdős, on partial sums of the
harmonic series. ==Recognition==