Monster Theorem, due to the length and difficulty of the proof. Complete proofs were not written up until almost 20 years later. The proof involves a number of deep and original insights which have linked many apparently disparate fields to 3-manifolds. Thurston was next led to formulate his geometrization conjecture. This gave a conjectural picture of 3-manifolds which indicated that all 3-manifolds admitted a certain kind of geometric decomposition involving eight geometries, now called Thurston model geometries. Hyperbolic geometry is the most prevalent geometry in this picture and also the most complicated. The conjecture was proved by Grigori Perelman in 2002–2003. Density conjecture Thurston and Dennis Sullivan generalized Lipman Bers' density conjecture from singly degenerate Kleinian surface groups to all finitely generated Kleinian groups in the late 1970s and early 1980s. The conjecture states that every finitely generated Kleinian group is an algebraic limit of geometrically finite Kleinian groups, and was independently proven by Ohshika and Namazi–Souto in 2011 and 2012 respectively. Orbifold theorem In his work on hyperbolic Dehn surgery, Thurston realized that orbifold structures naturally arose. Such structures had been studied prior to Thurston, but his work, particularly the next theorem, would bring them to prominence. In 1981, he announced the orbifold theorem, an extension of his geometrization theorem to the setting of 3-orbifolds. Two teams of mathematicians around 2000 finally finished their efforts to write down a complete proof, based mostly on Thurston's lectures given in the early 1980s in Princeton. His original proof relied partly on Richard S. Hamilton's work on the Ricci flow. Awards and honors In 1976, Thurston and James Harris Simons shared the Oswald Veblen Prize in Geometry. Thurston received the Fields Medal in 1982 for "revolutioniz[ing] [the] study of topology in 2 and 3 dimensions, showing interplay between analysis, topology, and geometry" and "contribut[ing] [the] idea that a very large class of closed 3-manifolds carry a hyperbolic structure." In 2005, Thurston won the first American Mathematical Society Book Prize, for Three-dimensional Geometry and Topology. The prize "recognizes an outstanding research book that makes a seminal contribution to the research literature". He was awarded the 2012 Leroy P. Steele Prize by the American Mathematical Society for seminal contribution to research. The citation described his work as having "revolutionized 3-manifold theory". Personal life Thurston and his first wife, Rachel Findley, had three children: Dylan, Nathaniel, and Emily. Dylan was a MOSP participant (1988–90) and