Ivan M. Niven

Template:Short description Template:Infobox academic Ivan Morton Niven (October 25, 1915Template:Snd 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.<ref>https://www.ams.org/about-us/governance/council/council-minutes0883</ref> He wrote 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.<ref name=mgp>Template:MathGenealogy</ref> 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.<ref>MAA presidents: Ivan Niven Template:Dead link</ref>

He died in 1999 in Eugene, Oregon.

Research

Niven completed the solution of most of Waring's problem in 1944.<ref name="Niven Waring">Template:Cite journal</ref> This problem, based on a 1770 conjecture by Edward Waring, consists of finding the smallest number <math>g(n)</math> such that every positive integer is the sum of at most <math>g(n)</math> <math>n</math>-th powers of positive integers. David Hilbert had proved the existence of such a <math>g(n)</math> in 1909; Niven's work established the value of <math>g(n)</math> for all but finitely many values of <math>n</math>.

Niven gave an elementary proof that <math>\pi</math> (pi) is irrational in 1947.<ref>Template:Citation</ref>

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.<ref>Template:Citation</ref>

Recognition

Niven received the University of Oregon's Charles E. Johnson Award in 1981. He received the MAA Distinguished Service Award<ref name="MAA Distinguished Service Award">Template:Cite web</ref> in 1989.

He won a Lester R. Ford Award in 1970.<ref>Template:Cite journal</ref> In 2000, the asteroid 12513 Niven, discovered in 1998, was named after him.<ref name="AstDys-12513">Template:Cite web</ref><ref>Template:Citation</ref>

Books

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• Template:Cite book<ref>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.</ref><ref>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]</ref><ref>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</ref><ref>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</ref>
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External links

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

See also

• [[Proof that π is irrational|Proof that Template:Pi is irrational]]