Ivan Morton Niven (October 25, 1915 May 9, 1999) was a Canadian-American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

, specializing in

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mat ...

and known for his work on

Waring's problem In number theory, Waring's problem asks whether each natural number ''k'' has an associated positive integer ''s'' such that every natural number is the sum of at most ''s'' natural numbers raised to the power ''k''. For example, every natural numb ...

. He worked for many years as a professor at the

University of Oregon The University of Oregon (UO, U of O or Oregon) is a public research university in Eugene, Oregon. Founded in 1876, the institution is well known for its strong ties to the sports apparel and marketing firm Nike, Inc, and its co-founder, billion ...

, and was president of the Mathematical Association of America. He was the author of several books on mathematics.

Life

Niven was born in

Vancouver Vancouver ( ) is a major city in western Canada, located in the Lower Mainland region of British Columbia. As the List of cities in British Columbia, most populous city in the province, the 2021 Canadian census recorded 662,248 people in the ...

. He did his undergraduate studies at the

University of British Columbia The University of British Columbia (UBC) is a public research university with campuses near Vancouver and in Kelowna, British Columbia. Established in 1908, it is British Columbia's oldest university. The university ranks among the top thre ...

and was awarded his doctorate in 1938 from the

University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private university, private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park, Chicago, Hyde Park neighborhood. The University of Chic ...

. He was a member of the

faculty from 1947 to his retirement in 1981. He was president of the Mathematical Association of America (MAA) from 1983 to 1984. He died in 1999 in Eugene, Oregon.

Research

Niven gave a proof that

\pi

is irrational in 1947. Niven completed the solution of most of

in 1944. This problem, based on a 1770 conjecture by

Edward Waring Edward Waring (15 August 1798) was a British mathematician. He entered Magdalene College, Cambridge as a sizar and became Senior wrangler in 1757. He was elected a Fellow of Magdalene and in 1760 Lucasian Professor of Mathematics, holding the ...

, consists of finding the smallest number

g(n)

such that every positive integer is the sum of at most

g(n)

n

-th powers of positive integers. David Hilbert had proved the existence of such a

g(n)

in 1909; Niven's work established the value of

g(n)

for all but finitely many values of

n

. Niven numbers, Niven's constant, and

Niven's theorem In mathematics, Niven's theorem, named after Ivan Niven, states that the only rational values of ''θ'' in the interval 0° ≤ ''θ'' ≤ 90° for which the sine of ''θ'' degrees is also a rational number ...

are named for Niven. He has an

Erdős number The Erdős number () describes the "collaborative distance" between mathematician Paul Erdős and another person, as measured by authorship of mathematical papers. The same principle has been applied in other fields where a particular individual ...

of 1 because he coauthored a paper with Paul Erdős.

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 Lester is an ancient Anglo-Saxon surname and given name. Notable people and characters with the name include: People Given name * Lester Bangs (1948–1982), American music critic * Lester W. Bentley (1908–1972), American artist from Wisc ...

in 1970. In 2000, the asteroid 12513 Niven, discovered in 1998, was named after him.

Books

*(1956) ''Irrational Numbers'' (

Carus Mathematical Monograph The ''Carus Mathematical Monographs'' is a monograph series published by the Mathematical Association of America.Drake, Miriam A. (2003). ''Encyclopedia of Library and Information Science: Lib-Pub.'' CRC Press, Books in this series are intended to ...

s, Number 11) *(1960) (with Herbert S. Zuckerman) ''An Introduction to the Theory of Numbers'', Wiley *(1961) ''Calculus: An Introductory Approach'', Van NostrandCobb, 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 *(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

External link

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

References

{{DEFAULTSORT:Niven, Ivan Morton 1915 births 1999 deaths Canadian mathematicians 20th-century American mathematicians University of Oregon faculty Canadian emigrants to the United States Number theorists University of British Columbia alumni University of Chicago alumni Presidents of the Mathematical Association of America Place of birth missing Textbook writers