# Ivan M. Niven

**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.

Ivan M. Niven | |
---|---|

Born | October 25, 1915 |

Died | May 9, 1999 83) | (aged

Academic background | |

Alma mater | University of British Columbia (BA) University of Chicago (PhD) |

Doctoral advisor | Leonard Eugene Dickson[1] |

Academic work | |

Institutions | University of Oregon |

## 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 such that every positive integer is the sum of at most th powers of positive integers. David Hilbert had proved the existence of such a in 1909; Niven's work established the value of for all but finitely many values of .

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

## See also

## References

- Ivan M. Niven at the Mathematics Genealogy Project
- MAA presidents: Ivan Niven
- 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 - Niven, Ivan (1969). "Formal power series".
*Amer. Math. Monthly*.**76**: 871–889. doi:10.2307/2317940. - Entry on (12513) Niven in AstDyS
- "Asteroids with Canadian connections" (PDF),
*Journal of the Royal Astronomical Society of Canada*,**94**(2): 47, April 2000 - 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. - 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. - 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.
- 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.
- 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
- 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