| 2015 | Member | Academia Europaea |
| 2015 | Royal Society Wolfson Research Merit Award | Royal Society of London |
| 2012 | Fellow | American Mathematical Society |
| 2009 | Lester R. Ford Prize | Mathematical Association of America |
| 2008 | Chauvenet Prize | Mathematical Association of America |
| 2007 | Lester R. Ford Prize | Mathematical Association of America |
| 2006 | Fellow | Royal Society of Canada |
| 2006 | Jeffrey-Williams Prize | Canadian Mathematical Society |
| 2002 | Canadian Research Chair | (from Prime Minister Chretien) |
| 1999 | Ribenboim Prize | Canadian Number Theory Association |
| 1995 | Hasse Prize | Mathematical Association of America |
| 1994 | Invited Speaker, ICM | Zurich |
| 1994-99 | Presidential Faculty Fellowship | (from President Clinton) |
| 1992-95 | Alfred P. Sloan Research Fellowship | |
| 1989 | Teaching Commendation | Erindale College, U. Toronto |
| 1985-87 | J.S. McLaughlin Fellowship | Queen's University |
| 1983-84 | Senior Scholarship | Cambridge University |
| 1980-82 | Exhibition | Cambridge University |
I have a Bacon number of three:
Kevin Bacon appeared in the movie ``JFK'' with Martin Sheen in 1991.
Martin Sheen appeared in ``Loophole'' with my sister, Jennifer Granville, in 1981.Jennifer Granville and I will appear together in "MSI'' (2019), a trailer for which can be found at https://vimeo.com/66218204. Since this has not yet happened, in the meantime we have co-authored, ``Writing and performing mathematics as metaphor'' together with Michael Spencer), which appeared in Art in the Life of Mathematicians, American Mathematical Society (2015), 112-137.