William Thurston

Early Life and Education

William Paul Thurston was a notable American mathematician who made significant contributions to low-dimensional topology and geometry.

William Thurston was born on October 30, 1946, in Washington, D.C. He was raised in an academic environment, as his father, Paul Thurston, was an aeronautical engineer, and his mother, Margaret Thurston, was a seamstress. Thurston was born with congenital strabismus, a vision disorder in which the eyes do not align with each other.

He attended Phillips Exeter Academy in New Hampshire, where he excelled in mathematics. After completing high school, Thurston pursued his undergraduate studies at New College in Sarasota, Florida, earning his Bachelor of Arts degree in mathematics in 1967. He continued his studies at the University of California, Berkeley, where he completed his Ph.D. in 1972. Afterward, he spent a year as an assistant professor at the Massachusetts Institute of Technology.

Academic Career

In 1974, William Thurston was appointed as a professor at Princeton University. In 1991, he returned to Berkeley to serve as a professor and director of the Mathematical Sciences Research Institute.

Geometrization Conjecture and Hyperbolization Theorem

One of Thurston’s most renowned achievements was the formulation of the Geometrization Conjecture in 1982. He proposed a groundbreaking conjecture suggesting there are eight different ways to classify three-dimensional shapes, referred to as “manifolds.”

In 1982, Thurston also proved the Hyperbolization Theorem, which stated that certain three-dimensional manifolds with “tame” geometries can be hyperbolic, meaning they possess constant negative curvature. Furthermore, he demonstrated that many knots are hyperbolic, indicating that the knot complement admits a geometric structure.

Contributions to Orbifolds

In 1981, Thurston made significant contributions to the study of orbifolds and introduced the concept of orbifold notation. He described orbifolds as geometric objects that exist between spaces with continuous symmetry, known as manifolds. Thurston’s work on orbifolds has had a profound impact on various areas of mathematics, including geometry, topology, and complex analysis.

Awards and Honors

In 1982, Thurston was awarded the prestigious Fields Medal, one of the highest honors in mathematics, for his groundbreaking work in topology and geometry.

Legacy and Death

William Thurston passed away on August 21, 2012, in Rochester, New York, due to sinus mucosal melanoma, a type of cancer affecting the nasal passages and sinuses. His discoveries continue to influence the field of mathematics, inspiring researchers to this day.