Even as he contributed to theoretical physics, Bill's work was proof that the most abstract math can have gorgeous practical applications.
Mathematicians and math enthusiasts are mourning the loss of William P. Thurston, who had a special place in the profession. Bill was one of our star authors when I worked at Princeton University Press, and a delightful person to edit and publish, paradoxically because he was a perfectionist who would not rush into print. Our anticipation only grew as we worked with him, and was more than justified. His long-awaited Three-Dimensional Geometry and Topology is one of the most acclaimed books in its field.
Topology studies possible geometric deformations without tearing or cutting, regardless of measurements. (An old joke defines a topologist as somebody who can't tell the difference between a doughnut and a coffee cup.) The New York Times' obituary reminded me of how practical his work could be despite its apparent abstraction:
[C]osmologists 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 Style.com 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.'"
Mathematicians can cite many other examples of surprising applications. Could the 19th-century founders of mathematical logic have imagined where Alan Turing would take their new field a hundred years later? With the computer science that Turing founded, the once-abstract field of number theory became a foundation of cryptography. The mathematics of origami have contributed to designing solar sails and automotive airbags. In the 1980s, the topological subfield of knot theory became a powerful tool in particle physics. Symposia have already been held on applications of topology to the design of industrial robots. I've even read the statement -- but haven't been able to find the reference again -- that every significant pure math idea has an application. We just haven't discovered some yet.
All this is timely, because in some quarters of neo-mercantilist, managerial academia, some mathematics is considered too pure for the national economy, especially in the UK.
In a famous paper on the uncanny way that math describes reality, the physicist Eugene Wigner concluded:
The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.
Bill Thurston was one of the great bestowers of that gift.
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