Ian Agol[needs IPA] (born May 13, 1970) is an American mathematician who deals primarily with the topology of three-dimensional manifolds.

[6] It states that a hyperbolic 3-manifold with finitely generated fundamental group is homeomorphic to the interior of a compact 3-manifold.

[8][9] Agol, Calegari, and Gabai received the 2009 Clay Research Award for their proof of the Marden tameness conjecture.

[12] In 2015, he was awarded the 2016 Breakthrough Prize in Mathematics, "for spectacular contributions to low dimensional topology and geometric group theory, including work on the solutions of the tameness, virtually Haken and virtual fibering conjectures.

[14] His identical twin brother, Eric Agol,[15][16][17] is an astronomy professor at the University of Washington in Seattle.