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Topic: William P. Thurston, Theoretical Mathematician, Dies at 65
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Jerry P. Becker

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Registered: 12/3/04
William P. Thurston, Theoretical Mathematician, Dies at 65
Posted: Aug 23, 2012 1:31 PM
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From The New York Times, Wednesday, August 22,
2012. See

William P. Thurston, Theoretical Mathematician, Dies at 65

By Leslie Kaufman

PHOTO SIDEBAR: William P. Thurston, a Cornell
mathematics professor who won the Fields Medal,
in 2006 at his home by Cayuga Lake. Bill Wingell
for The New York Times

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

The cause was cancer, his son Dylan said.

Dr. 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
three-dimensional spaces are made up of eight
types of geometric pieces, a discovery he likened
to finding eight outfits that could fit anybody
in the world.

For most of his professional life, Dr. 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," Dr. 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 Dr. Thurston
delighted in working in a very esoteric realm.
But he added that Dr. Thurston's work had made "a
tremendous difference in the way we look at many

Without that work, a Russian mathematician,
Grisha Perelman, would not have been able in 2003
to solve the Poincaré conjecture, which asserts
that the sphere is the only three-dimensional
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 Dr.
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 the
designer Issey Miyake's 2010 ready-to-wear
collection, a colorful series of draped and
asymmetrical forms. The fashion Web site reported that after the show, the
house's designer and Dr. Thurston "wrapped
themselves for the press in a long stretch of red
tubing to make the point that something that
looks random is actually (according to Thurston)
'beautiful geometry.' "

To his colleagues, Dr. Thurston's most unusual
gift was his ability to visualize complex shapes
and problems. They said he loved nothing more
than to sit in a common room and help colleagues
or students brainstorm on solutions to vexing
issues. "He could look at a problem and see
simplicity where nobody else could find it," said
Jeff Weeks, a mathematician who studied with Dr.
Thurston at Princeton.

For example, he could think in multiple
dimensions. "People don't understand how I can
visualize four or five dimensions," Dr. Thurston
told The Journal. "Five-dimensional shapes are
hard to visualize - but it doesn't mean you can't
think about them. Thinking is really the same as

William Paul Thurston was born on Oct. 30, 1946,
in Washington, to Paul and Margaret Thurston. His
father was a Naval engineer. William showed
aptitude in math early on, amazing preschool
teachers with his ability to add two- and
three-digit numbers in his head, his older
brother, Robert, recalled. Asked how he did it,
he replied that he "counted on his fingers in his
mind," Robert Thurston said.

Dr. 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 renowned 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, Davis.
He was most recently at Cornell.

Dr. 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, Jean Baker; a brother,
George; and two grandchildren.

Dylan Thurston, also a mathematician, said that
despite working in a realm of rather cold
abstractions, his father was personally very warm.

"Growing up there were many beautiful
mathematical pictures in the house," he said. "He
was a very visual thinker; he had powers to see
spaces that no one before him could, and he was
always drawing pictures of what he could see and
doodles in notebooks, and we would talk about it.

"Math was always very fun for him."

Jerry P. Becker
Dept. of Curriculum & Instruction
Southern Illinois University
625 Wham Drive
Mail Code 4610
Carbondale, IL 62901-4610
Phone: (618) 453-4241 [O]
(618) 457-8903 [H]
Fax: (618) 453-4244

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