Weeks received his B.A. from Dartmouth College in 1978, and his Ph.D. in mathematics from Princeton University in 1985, under the supervision of William Thurston. Since then he has taught at Stockton State College, Ithaca College, and Middlebury College, but has spent much of his time as a free-lance mathematician.   
The Weeks manifold, discovered in 1985 by Weeks, is the hyperbolic 3-manifold with the minimum possible volume. Weeks has written various computer programs to assist in mathematical research and mathematical visualization. His SnapPea program is used to study hyperbolic 3-manifolds, while he has also developed interactive software to introduce these ideas to middle-school, high-school, and college students.
Weeks is particularly interested in using topology to understand the spatial universe.  His book The Shape of Space: How to Visualize Surfaces and Three-dimensional Manifolds (Marcel Dekker, 1985, ISBN 0-8247-7437-X) explores the geometry and topology of low-dimensional manifolds.   The second edition (2002, ISBN 0-8247-0709-5) explains some of his work in applying the material to cosmology. 
Weeks became a MacArthur Fellow in 1999.  In 2007, he won the Levi L. Conant Prize for his expository paper, "The Poincaré Dodecahedral Space and the Mystery of the Missing Fluctuations" (Notices of the AMS 2004), and in 2008 he gave the first Levi Conant Lecture at Conant's former employer, the Worcester Polytechnic Institute.  
- Biography for Bay Area Mathematical Adventures talk announcement, San Jose State University, March 2009, retrieved 2011-05-19.
- "2007 Conant Prize" (PDF), Notices of the AMS, 54 (4): 519–520, 2007.
- Mathematician Jeffrey Weeks to Deliver Inaugural Levi Conant Lecture at Worcester Polytechnic Institute: Winner of the 2007 Conant Prize from the American Mathematical Society, Weeks Will Explore the Possible Shapes of the Universe, Worcester Polytechnic Institute, March 21, 2008.
- Overbye, Dennis (October 8, 2003), "New Model of the Universe: It's Shaped Like a Soccerball", New York Times.
- Review by Thomas Banchoff (1987), Mathematical Reviews, MR 0806764.
- Review by Alan H. Durfee (1989), American Mathematical Monthly 96 (7): 660–662, doi: 10.2307/2325200.
- Review (2002), Mathematical Reviews, MR 1875835.
- "The call of genius surprises winners of MacArthur grants", USA Today, June 23, 1999.