Biography:Ivan M. Niven

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Short description: Canadian-American number theorist (1915–1999)
Ivan M. Niven
Ivan Niven.jpg
BornOctober 25, 1915
Vancouver , Canada
DiedMay 9, 1999(1999-05-09) (aged 83)
Known forNiven number
Niven's constant
Niven's proof
Niven's theorem
Eilenberg–Niven theorem
AwardsLester R. Ford Award (1970)
Academic background
Alma mater
Doctoral advisorLeonard Eugene Dickson[1]
Academic work
InstitutionsUniversity of Oregon
Doctoral studentsMargaret Maxfield

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 gave a proof that [math]\displaystyle{ \pi }[/math] is irrational in 1947.[3] 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 [math]\displaystyle{ g(n) }[/math] such that every positive integer is the sum of at most [math]\displaystyle{ g(n) }[/math] [math]\displaystyle{ n }[/math]-th powers of positive integers. David Hilbert had proved the existence of such a [math]\displaystyle{ g(n) }[/math] in 1909; Niven's work established the value of [math]\displaystyle{ g(n) }[/math] for all but finitely many values of [math]\displaystyle{ n }[/math].

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.[4]

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.[5] In 2000, the asteroid 12513 Niven, discovered in 1998, was named after him.[6][7]

Books

  • (1956) Irrational Numbers (Carus Mathematical Monographs, Number 11), Mathematical Association of America[8]
  • (1960) (with Herbert S. Zuckerman) An Introduction to the Theory of Numbers, Wiley[9]
  • (1961) Calculus: An Introductory Approach, Van Nostrand[10][11][12][13]
  • (1961) Numbers: Rational and Irrational, Random House
  • (1963) Diophantine Approximations, Interscience
  • (1965) Mathematics of Choice: How to Count Without Counting, Mathematical Association of America
  • (1981) Maxima and Minima Without Calculus , Mathematical Association of America

External links

See also

References

  1. ↑ 1.0 1.1 Ivan M. Niven at the Mathematics Genealogy Project
  2. ↑ MAA presidents: Ivan Niven
  3. ↑ Niven, Ivan (1947), "A simple proof that π is irrational", Bulletin of the American Mathematical Society 53 (6): 509, doi:10.1090/s0002-9904-1947-08821-2, https://www.ams.org/bull/1947-53-06/S0002-9904-1947-08821-2/S0002-9904-1947-08821-2.pdf 
  4. ↑ 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 
  5. ↑ Niven, Ivan (1969). "Formal power series". Amer. Math. Monthly 76 (8): 871–889. doi:10.2307/2317940. http://www.maa.org/programs/maa-awards/writing-awards/formal-power-series. 
  6. ↑ "AstDyS-2 Asteroids – Dynamic Site – (12513) Niven". https://newton.spacedys.com/astdys/index.php?pc=1.1.0&n=12513. 
  7. ↑ "Asteroids with Canadian connections", Journal of the Royal Astronomical Society of Canada 94 (2): 47, April 2000, http://www.rasc.ca/journal/pdfs/2000-Apr.pdf 
  8. ↑ Rosenbaum, R. A. (1959). "Review: Irrational Numbers by Ivan Niven. Carus Monograph, no. 11: New York, Wiley, 1956". Bull. Amer. Math. Soc. 64 (2): 68–69. doi:10.1090/S0002-9904-1958-10170-6. https://www.ams.org/journals/bull/1958-64-02/S0002-9904-1958-10170-6/S0002-9904-1958-10170-6.pdf. 
  9. ↑ 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. https://www.ams.org/journals/bull/1961-67-04/S0002-9904-1961-10603-4/. 
  10. ↑ 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.
  11. ↑ 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.
  12. ↑ 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
  13. ↑ 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



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