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Computer experiment played an important motivational role in Thurston's work, including the formulation of his (now proved) Geometrization Conjecture.
Nathan Dunfield of the University of Illinois at Urbana-Champaign demonstrates the computer program SnapPy for studying hyperbolic structures on 3-manifolds, which is based on ideas introduced by Thurston in his revolutionary lecture notes, June 27, 2014 at the Bill Thurston Legacy Conference.
The conference, "What's Next? The mathematical legacy of Bill Thurston," held at Cornell June 23-27, 2014, brought together mathematicians from a broad spectrum of areas to describe recent advances and explore future directions motivated by Thurston's transformative ideas.