# Andrew Granville

Andrew James Granville (born September 7, 1962 in London ) is a British-Canadian mathematician who works in the field of number theory . Granville has been Professor at the University of Montreal since 2002 .

## Life

Granville studied mathematics from 1980 to 1983 at Trinity College, Cambridge , where he graduated in 1984 with a diploma with honors. From 1984 to 1987 he did his doctorate with the thesis Diophantine Equations with Varying Exponents at Queen's University in Kingston, Canada . His doctoral supervisor was the Brazilian number theorist Paulo Ribenboim . From 1987 to 1989 he was a post-doctoral student at the University of Toronto and from 1989 to 1991 at the Institute for Advanced Study in Princeton . From 1991 to 2002 he held various positions at the University of Georgia , from 1995 onwards as a full professor.

## Scientific work

Granville works primarily in the field of analytical number theory . In 1994, together with Carl Pomerance and WR (Red) Alford, he proved that there are infinitely many Carmichael numbers . The proof is based on an idea by Paul Erdős . Because of this significant evidence, he and Pomerance were invited as a guest speaker at the International Congress of Mathematicians in Zurich in 1994 (lecture by Granville: Unexpected irregularities in the distribution of prime numbers ). Since Granville also published together with Erdős, he has the Erdős number 1.

In 1995, wrote Granville and Nigel Boston an argument with Marilyn vos Savant's book The world's most famous math problem- in which they recklessly the announced proof of Fermat's great theorem by Andrew Wiles questioned.

In 1998, Granville formulated a weaker conjecture related to the abc conjecture. The prime numbers are also part of Granville's research area . In 2003 he found an error in the later corrected proof by Goldston and Yildirim .

In 2007 he found connections between the Goldbach Hypothesis and the Generalized Riemann Hypothesis .

In 1988 he showed that the first part of the Fermat conjecture holds for all prime exponents . ${\ displaystyle p <6 {,} 93 \ cdot 10 ^ {17}}$

With K. Soundararajan he introduced a new approach to analytical number theory ( pretentious approach ) in the 2010s , based on older work by Gábor Halász . The results of multiplicative number theory are derived without having to study the zeros of the Riemann zeta function and related L functions.

## Honors and prizes

Granville has received a number of awards and honors. In 2006 he was named a Fellow of the Royal Society of Canada . In 2008, the Mathematical Association of America awarded Andrew Granville the Chauvenet Prize for his work It is easy to determine whether a given integer is prime .

## Individual evidence

1. ^ Mathematics Genealogy Project: Andrew James Granville
2. Andrew Granville's short resumé , Department of Mathematics and Statistics, Université de Montréal (short résumé of Andrew Granville)
3. ^ WR Alford, Andrew Granville, Carl Pomerance: There are infinitely many Carmichael numbers ( PostScript file), Annals of Mathematics 139, 1994, pp. 703-722.
4. researchmagazine.uga.edu: Divide and Conquer ( Memento of the original from June 10, 2010 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.
5. List of mathematicians with Erdős number 1 ( Memento from November 17, 2008 in the Internet Archive )
6. ^ Nigel Boston, Andrew Granville: Review of The world's most famous math problem , Amer. Math. Monthly 102 (1995) pp. 470-473
7. Andrew Granville: ABC Allows Us to Count Squarefrees (PDF; 970 kB)
8. heise.de: Gap in the prime number proof
9. Granville, Monagan, Trans. AMS, Vol. 306, 1988, pp. 329-359
10. http://www.maa.org/Awards/chauvent.html ( Memento from April 30, 2010 in the Internet Archive )
11. The Mathematical Association of America's explanatory note on the award to Andrew Granville (PDF; 49 kB)