For most of his professional life, Mr. Thurston was among a very rarefied group in his field that thinks deep theoretical thoughts with no particular practical application, a luxury he reveled in. "I don't do it for the bottom line," he told the Wall Street Journal in 1983. "The inner force that drives mathematicians isn't to look for applications; it is to understand the structure and inner beauty of mathematics."
Cosmologists have drawn on Mr. Thurston's discoveries in their search for the shape of the universe.
On a more unlikely note, his musings about the possible shapes of the universe inspired designer Issey Miyake's 2010 ready-to-wear collection, a colorful series of draped and asymmetrical forms.
Mr. Thurston received an undergraduate degree at New College in Florida and a Ph.D. in mathematics at the University of California, Berkeley, in 1972. He quickly earned a reputation as an original thinker and caught the attention of Princeton's mathematics department, which recruited him to be a professor at the age of 27.
He was in his mid-30s when he received the Fields Medal in 1982 for his work in deepening the connection between geometry and topology. The medal is awarded every four years by the International Mathematical Union. He worked longest at Princeton but also held posts at Berkeley and the University of California at Davis. He was most recently at Cornell.
Mr. Thurston's first marriage, to Rachel Findley, ended in divorce. In addition to his son Dylan and his brother Robert, he is survived by his wife, Julian Muriel Thurston; their children Hannah Jade and Liam; two children from his first marriage, Nathaniel and Emily; his mother, Margaret; a sister and brother; and two grandchildren. - N.Y. Times News Service