# Ivan M. Niven

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Ivan M. Niven
BornOctober 25, 1915
DiedMay 9, 1999 (aged 83)
Academic background
Alma materUniversity of British Columbia (BA)
University of Chicago (PhD)
Doctoral advisorLeonard Eugene Dickson[1]
Academic work
InstitutionsUniversity of Oregon

Ivan Morton Niven (October 25, 1915 – May 9, 1999) was a Canadian-American mathematician, specializing in number theory and known for his work on Waring's problem. He worked for many years as a professor at the University of Oregon, and was president of the Mathematical Association of America. He was the author of several books on mathematics.

## Life

Niven 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 was president of the Mathematical Association of America (MAA) from 1983 to 1984.[2]

He died in 1999 in Eugene, Oregon.

## Research

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 ${\displaystyle g(n)}$ such that every positive integer is the sum of at most ${\displaystyle g(n)}$ ${\displaystyle n}$th powers of positive integers. David Hilbert had proved the existence of such a ${\displaystyle g(n)}$ in 1909; Niven's work established the value of ${\displaystyle g(n)}$ for all but finitely many values of ${\displaystyle n}$.

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.[3]

## Recognition

Niven received the University of Oregon's Charles E. Johnson Award in 1981. He received the MAA Distinguished Service Award in 1989.

He won a Lester R. Ford Award in 1970.[4] In 2000, the asteroid 12513 Niven, discovered in 1998, was named after him.[5][6]

## Books

• (1956) Irrational Numbers (Carus Mathematical Monographs, Number 11)[7]
• (1960) (with Herbert S. Zuckerman) An Introduction to the Theory of Numbers, Wiley[8]
• (1961) Calculus: An Introductory Approach, Van Nostrand[9][10][11][12]
• (1961) Numbers: Rational and Irrational, Random House
• (1963) Diophantine Approximations, Interscience
• (1965) Mathematics of Choice: How to Count Without Counting, MAA
• (1981) Maxima and Minima Without Calculus , MAA

## References

1. ^ a b
2. ^ MAA presidents: Ivan Niven
3. ^ 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
4. ^ Niven, Ivan (1969). "Formal power series". Amer. Math. Monthly. 76: 871–889. doi:10.2307/2317940.
5. ^ [1] Entry on (12513) Niven in AstDyS
6. ^ "Asteroids with Canadian connections" (PDF), Journal of the Royal Astronomical Society of Canada, 94 (2): 47, April 2000
7. ^ 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. doi:10.1090/S0002-9904-1958-10170-6.
8. ^ 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.
9. ^ Kaltenborn, H. S., Reviewed Work: Calculus: An Introductory Approach. by Ivan Niven The American Mathematical Monthly, vol. 69, no. 1, 1962, pp. 69–69. JSTOR, www.jstor.org/stable/2312762.
10. ^ Bishop, R. L., Reviewed Work: Calculus, An Introductory Approach by Ivan Niven Pi Mu Epsilon Journal, vol. 3, no. 5, 1961, pp. 236–236. JSTOR, www.jstor.org/stable/24338116.
11. ^ Goodstein, R. (1962). Calculus. An introductory approach. By I. Niven. Pp. 169. 36s. 1961. (D. van Nostrand, London). The Mathematical Gazette, 46(358), 333–333. doi:10.2307/3611795
12. ^ Cobb, R. (1967). Calculus: An Introductory Approach. 2nd Edition. (University Series in Undergraduate Mathematics.) By Ivan Niven. Pp. viii, 202. 46s. 6d. 1967. (D. Van Nostrand Co. Ltd.). The Mathematical Gazette, 51(378), 330–330. doi:10.2307/3612954