Shigefumi Mori completes in 1988, in the Journal of the American Mathematical Society, the minimal model program for 3-dimensional algebraic varieties, proving the so-called "flip theorem" that closes a line of work developed over nearly a decade (from around 1980). The minimal model program, begun in dimension 2 by Italian mathematicians of the early 20th century and extended to higher dimensions as one of the great projects of 20th-century algebraic geometry, seeks to find the "simplest possible" representative within each birational equivalence class of varieties; Mori solves the three-dimensional case, paving the way for later generalizations to higher dimensions. Mori received the Fields Medal in 1990.