KNOWPIA
WELCOME TO KNOWPIA

**Ivan Morton Niven** (October 25, 1915 – May 9, 1999) was a Canadian-American number theorist best remembered 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 wrote several books on mathematics.

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

Born | October 25, 1915 Vancouver, Canada |

Died | May 9, 1999 | (aged 83)

Known for | Niven number Niven's constant Niven's proof Niven's theorem Eilenberg–Niven theorem |

Awards | Lester R. Ford Award (1970) |

Academic background | |

Alma mater | |

Doctoral advisor | Leonard Eugene Dickson^{[1]} |

Academic work | |

Institutions | University of Oregon |

Doctoral students | Margaret Maxfield |

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.

Niven completed the solution of most of Waring's problem in 1944.^{[3]} 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 gave an elementary proof that is irrational in 1947.^{[4]}

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.^{[5]}

Niven received the University of Oregon's Charles E. Johnson Award in 1981. He received the MAA Distinguished Service Award^{[6]} in 1989.

He won a Lester R. Ford Award in 1970.^{[7]} In 2000, the asteroid 12513 Niven, discovered in 1998, was named after him.^{[8]}^{[9]}

*Irrational Numbers*. [Carus Mathematical Monographs]. The Mathematical Association of America. 1956. ISBN 0-88385-011-7.^{[10]}- Niven, Ivan; Zuckerman, Herbert S.; Montgomery, Hugh L. (1991) [First published 1960].
*An Introduction to the Theory of Numbers*. New York: John Wiley & Sons. ISBN 978-81-265-1811-1.^{[11]} *Calculus*. Van Nostrand Reinhold Company. 1966. ISBN 978-0-442-06032-9.^{[12]}^{[13]}^{[14]}^{[15]}*Numbers: Rational and Irrational*. Washington DC: The Mathematical Association of America. 2011 [First published 1961]. doi:10.5948/upo9780883859193. ISBN 978-0-88385-919-3.*Diophantine Approximations*. Mineola, N.Y: Dover Publications. 1 January 2008 [First published 1963]. ISBN 978-0-486-46267-7.^{[16]}*Mathematics of Choice: How to Count without Counting*. Washington, DC: Mathematical Association of America. 1965. ISBN 978-0-88385-615-4.*Maxima and Minima Without Calculus*. Washington, D.C.: Cambridge University Press. 1981. ISBN 978-0-88385-306-1.

- Donald Albers and G. L. Alexanderson. "A conversation with Ivan Niven",
*College Mathematics Journal*, 22, 1991, pp. 371–402.

- ^
^{a}^{b}Ivan M. Niven at the Mathematics Genealogy Project **^**MAA presidents: Ivan Niven**^**Niven, Ivan M. (1944). "An unsolved case of the Waring problem".*American Journal of Mathematics*.**66**(1). The Johns Hopkins University Press: 137–143. doi:10.2307/2371901. JSTOR 2371901. MR 0009386.**^**Niven, Ivan (1947), "A simple proof that π is irrational" (PDF),*Bulletin of the American Mathematical Society*, vol. 53, no. 6, p. 509, doi:10.1090/s0002-9904-1947-08821-2**^**Erdős, P.; Niven, I. (1946), "Some properties of partial sums of the harmonic series",*Bull. Amer. Math. Soc.*,**52**(4): 248–251, doi:10.1090/s0002-9904-1946-08550-x**^**"Yueh-Gin Gung and Dr. Charles Y. Hu Award for Distinguished Service".*Mathematical Association of America*. Retrieved 28 April 2024.**^**Niven, Ivan (1969). "Formal power series".*Amer. Math. Monthly*.**76**(8): 871–889. doi:10.2307/2317940. hdl:10338.dmlcz/120493. JSTOR 2317940.**^**"AstDyS-2 Asteroids – Dynamic Site – (12513) Niven".*newton.spacedys.com*. Retrieved 3 April 2020.**^**"Asteroids with Canadian connections" (PDF),*Journal of the Royal Astronomical Society of Canada*,**94**(2): 47, April 2000, archived from the original (PDF) on 2005-02-16**^**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 [www.jstor.org/stable/24338116 JSTOR]**^**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**^**D.S. (1959). "Review:*Diophantine Approximations*Interscience Publishers, New York, 1963" (PDF).*Bull. Amer. Math. Soc*.**64**(2): 68–69. doi:10.1090/S0002-9904-1958-10170-6.