Ivan M. Niven

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Ivan Niven

Ivan Morton Niven (October 25, 1915 – May 9, 1999) was a Canadian-American mathematician, specializing in number theory. He was born in Vancouver. He did his undergraduate studies at the University of British Columbia and was awarded his doctorate in 1938 from the University of Chicago.[1] He was a member of the University of Oregon faculty from 1947 to his retirement in 1981. He received the University of Oregon's Charles E. Johnson Award in 1981.

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) nth 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.

He was president of the Mathematical Association of America (MAA) from 1983 to 1984.[2] He received the MAA Distinguished Service Award in 1989.

He died in 1999 in Eugene, Oregon.

He was honored by being selected to write the Carus Monograph Number 11, entitled Irrational Numbers.[3] He won a Lester R. Ford Award in 1970.[4] Niven numbers, Niven's constant, and Niven's theorem are named in his honor; also, in 2000, the asteroid 12513 Niven, discovered in 1998, was named after him. He has an Erdős number of 1 because he has coauthored a paper with Paul Erdős [5] .

Popular works by Niven[edit]

  • (1959) Mathematics: A house built on sand?
  • (1960) (with Herbert S. Zuckerman) An Introduction to the Theory of Numbers, Wiley[6]
  • (1961) Calculus: An Introductory Approach, Van Nostrand
  • (1961) Numbers: Rational and Irrational, Random House
  • (1963) Diophantine Approximations, Interscience
  • (1965) Mathematics of Choice, MAA
  • (1981) Maxima and Minima Without Calculus , MAA

See also[edit]


  1. ^ Ivan M. Niven at the Mathematics Genealogy Project
  2. ^ MAA presidents: Ivan Niven
  3. ^ Rosenbaum, R. A. (1959). "Review: Irrational Numbers by Ivan Niven. Carus Monograph, no. 11: New York, Wiley, 1956" (PDF). Bull. Amer. math. Soc. 64 (2): 68–69. 
  4. ^ Niven, Ivan (1969). "Formal power series". Amer. Math. Monthly 76: 871–889. doi:10.2307/2317940. 
  5. ^ Erdős, P.; Niven, I. (1946), "Some properties of partial sums of the harmonic series", Bull. Amer. Math. Soc. 52: 248–251, doi:10.1090/s0002-9904-1946-08550-x 
  6. ^ Whiteman, Albert Leon (1961). "Review: An introduction to the theory of numbers, by Ivan Niven and Herbert S. Zuckerman". Bull. Amer. Math. Soc. 67 (4): 339–340. doi:10.1090/s0002-9904-1961-10603-4.