William Thurston, a mathematician who revolutionized understanding of the structure of 3-D spaces and won the Fields Medal, often described as the equivalent of the Nobel Prize for mathematics, died Tuesday in Rochester, N.Y. He was 65.

Thurston’s fields of expertise were geometry and topology, the study of different possible shapes for multidimensional space. Perhaps his greatest accomplishment in a lifetime of breakthroughs was his Geometrization conjecture, which postulated that all possible 3-D spaces are made up of eight types of geometrical pieces, a discovery he likened to finding eight outfits that could fit anybody in the world.

For most of his professional life, 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,” Thurston 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.”

John Milnor, co-director of the Institute for Mathematical Sciences at Stony Brook University on Long Island, acknowledged that Thurston delighted in working in a very esoteric realm. But he added that Thurston’s work had made “a tremendous difference in the way we look at many problems.”

Without that work, a Russian mathematician, Grisha Perelman, would not have been able in 2003 to solve the Poincare conjecture, which asserts that the sphere is the only 3-D shape in which every loop in its structure can be shrunk to a single point, without ripping or tearing either the loop or the space. The problem had challenged mathematicians for 100 years.

In addition, cosmologists have drawn on 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.