Ivan Morton Niven (October 25, 1915 May 9, 1999) was a Canadian-American number theorist best remembered 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 num ...

. 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 university, public research university in Eugene, Oregon, United States. Founded in 1876, the university is organized into nine colleges and schools and offers 420 undergraduate and gra ...

, and was president of the

Mathematical Association of America The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university A university () is an educational institution, institution of tertiary edu ...

. He wrote 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 cit ...

. He did his undergraduate studies at the

University of British Columbia The University of British Columbia (UBC) is a Public university, public research university with campuses near University of British Columbia Vancouver, Vancouver and University of British Columbia Okanagan, Kelowna, in British Columbia, Canada ...

and was awarded his doctorate in 1938 from the

University of Chicago The University of Chicago (UChicago, Chicago, or UChi) is a Private university, private research university in Chicago, Illinois, United States. Its main campus is in the Hyde Park, Chicago, Hyde Park neighborhood on Chicago's South Side, Chic ...

. 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. He died in 1999 in

Eugene, Oregon Eugene ( ) is a city in and the county seat of Lane County, Oregon, United States. It is located at the southern end of the Willamette Valley, near the confluence of the McKenzie River (Oregon), McKenzie and Willamette River, Willamette rivers, ...

Research

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 David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician and philosopher of mathematics and one of the most influential mathematicians of his time. Hilbert discovered and developed a broad range of fundamental idea ...

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 gave an elementary proof that

\pi

( pi) is

irrational Irrationality is cognition, thinking, talking, or acting without rationality. Irrationality often has a negative connotation, as thinking and actions that are less useful or more illogical than other more rational alternatives. The concept of ...

in 1947. 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 in the interval for which the sine of ' degrees is also a rational number are: : \begin \sin 0^\circ & = 0, \\0pt\sin 30^\circ & = \frac 12, \ ...

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 Paul Erdős ( ; 26March 191320September 1996) was a Hungarian mathematician. He was one of the most prolific mathematicians and producers of mathematical conjectures of the 20th century. pursued and proposed problems in discrete mathematics, g ...

, on partial sums of the harmonic series.

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 ''The American Mathematical Monthly'' is a peer-reviewed scientific journal of mathematics. It was established by Benjamin Finkel in 1894 and is published by Taylor & Francis on behalf of the Mathematical Association of America. It is an expositor ...

in 1970. In 2000, the asteroid

12513 Niven 1 (one, unit, unity) is a number, numeral, and glyph. It is the first and smallest positive integer of the infinite sequence of natural numbers. This fundamental property has led to its unique uses in other fields, ranging from science to sp ...

, discovered in 1998, was named after him.

Books

* * * * * * *

External links

*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 American textbook writers Canadian textbook writers Scientists from Vancouver