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 | |
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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 |
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.[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]
Recognition
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]
Books
- 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.
External links
- Donald Albers and G. L. Alexanderson. "A conversation with Ivan Niven", College Mathematics Journal, 22, 1991, pp. 371–402.