Ivan M. Niven

Ivan Morton Niven (born October 25, 1915 in Vancouver , † May 9, 1999 in Eugene ) was an American - Canadian mathematician who dealt in particular with number theory ( Diophantine approximation , additive number theory , irrationality and transcendence questions ) and combinatorics .

biography

Niven studied at the University of British Columbia (Master's degree in 1936) and received his doctorate in 1938 from the University of Chicago under Leonard Dickson (A Waring Problem). In 1938/39 he was with Hans Rademacher at the University of Pennsylvania . He then spent three years at the University of Illinois and five years at Purdue University before going to the University of Oregon in 1947 , where he stayed until his retirement in 1982. 1957/58 he was visiting professor at Stanford University and 1964/65 at the University of California, Berkeley .

In 1947 he gave a simple proof of the irrationality of ${\ displaystyle \ pi}$ (already proven by Johann Heinrich Lambert in 1760). He was also known for a work on the Waring problem (on which he was already doing his doctorate). This problem, which goes back to a conjecture made by Edward Waring in 1770, asks for the smallest natural number , so that every natural number is the sum of at most -th powers of natural numbers. David Hilbert had already proven the existence of one in 1909 . Niven completed a series of papers by his teacher Dickson, Pillai, and RK Rubugunday in his 1944 paper . As a result of their work, a formula could be given for exponents for : ${\ displaystyle g (k)}$ ${\ displaystyle g (k)}$ ${\ displaystyle k}$ ${\ displaystyle g (k)}$ ${\ displaystyle k \ geq 6}$ ${\ displaystyle g (k)}$

{\ displaystyle g (k) = \ left \ lfloor \ left ({\ frac {3} {2}} \ right) ^ {k} \ right \ rfloor + 2 ^ {k} -2}

.

He wrote a number of mathematics books (including a well-known introduction to elementary number theory) and also traveled regularly in the 1960s on behalf of the Mathematical Association of America (MAA) to give popular lectures on mathematics. 1974/75 he was Vice President of the MAA and 1983/84 its President. In 1989 he received the MAA's highest honor, the Award for Distinguished Service in Mathematics. In 1970 he received the MAA's Lester R. Ford Award for his article on formal power series in the American Mathematical Monthly 1969.

In 1981 he received the Charles E. Johnson Award from the University of Oregon. In 1962 he gave a lecture at the International Congress of Mathematicians in Stockholm ( On the covering of lattice points in 3-space ).

Niven worked several times with Paul Erdős .

Niven numbers and the Niven constant are named after him; in addition, the asteroid (12513) Niven, discovered in 1998, was named after him in 2000 . The set of Niven addresses the issue of rational values of trigonometric functions at rational values of the argument in degrees.

Fonts

with Herbert Samuel Zuckerman, Hugh Montgomery : Introduction to the theory of numbers, 5th edition, Wiley 1991 (English first Wiley 1960, German Niven, Zuckerman: Introduction to number theory, BI Verlag 1976, 2nd volumes)
Maxima and Minima without Calculus, MAA, Dolciani Mathematical Expositions, 1981
Diophantine Approximations, Interscience 1963
Irrational Numbers, Carus Mathematical Monograph 1956
Numbers: Rational and Irrational, Random House 1961
Mathematics of Choice- how to count without counting, MAA 1965
Calculus - an introductory approach, Princeton, Van Nostrand 1961, 1965

literature

Donald Albert, G. Alexanderson: A conversation with Ivan Niven, College Mathematics Journal, Vol. 22, 1991, pp. 371-402.

Web links

References

↑ Bulletin AMS, Vol. 53, 1947, p. 509

↑ Ivan Niven: An unsolved case of the waring problem. In: American Journal of Mathematics. Volume 66, 1944, pages 137-143.

↑ for the values the values are also known exactly, Lagrange had already done ${\ displaystyle k = 3,4,5}$ ${\ displaystyle k = 2}$

^ Niven: Formal power series, American Math. Monthly, Vol. 76, 1969, pp. 871-889

personal data
SURNAME	Niven, Ivan M.
ALTERNATIVE NAMES	Niven, Ivan Morton (full name)
BRIEF DESCRIPTION	American-Canadian mathematician
DATE OF BIRTH	October 25, 1915
PLACE OF BIRTH	Vancouver
DATE OF DEATH	May 9, 1999
Place of death	Eugene , Oregon

[1] Bulletin AMS, Vol. 53, 1947, p. 509

[2] Ivan Niven: An unsolved case of the waring problem. In: American Journal of Mathematics. Volume 66, 1944, pages 137-143.