Dave Pape · Public domain

A mathematician who solved a problem crystallographers had struggled with for decades: figuring out a molecule's three-dimensional structure directly from X-ray diffraction data, without the laborious indirect methods previously required. His "direct methods," developed with Jerome Karle, turned structure determination from a painstaking specialist's craft into a routine calculation, and the two shared the 1985 Nobel Prize in Chemistry for the breakthrough — a rare Nobel awarded for a mathematical technique rather than a chemical discovery itself.