William P. Thurston, 1946–2012 David Gabai and Steve Kerckhoff, Coordinating Editors William P. Thurston, a geometric visionary and one of the greatest mathematicians of the twentieth century, died on August 21, 2012, at the age of sixty-five. This obituary for Thurston contains reminiscences by some of his many colleagues and friends. What follows is the first part of the obituary; the second part will appear in the January 2016 issue of the Notices. illiam Paul Thurston, known univer- sally as Bill, was an extraordinary mathematician whose work and ideas revolutionized many fields of mathematics, including foliations, TeichmüllerW theory, automorphisms of surfaces, 3-manifold topology, contact structures, hyper- bolic geometry, rational maps, circle packings, incompressible surfaces, and geometrization of 3-manifolds. Bill’s influence extended far beyond his in- credible insights, theorems, and conjectures; he transformed the way people think about and view things. He shared openly his playful, ever curious, near magical and sometimes messy approach to mathematics. Indeed, in his MathOverflow profile he states, “Mathematics is a process of staring hard enough with enough perseverance at the fog of muddle and confusion to eventually break through to improved clarity. I’m happy when I can admit, at Courtesy of K. Delp. least to myself, that my thinking is muddled, and I William Paul Thurston David Gabai is professor of mathematics at Princeton Uni- versity. His email address is [email protected] try to overcome the embarrassment that I might Steve Kerckhoff is professor of mathematics at Stanford Uni- versity. His email address is [email protected]. reveal ignorance or confusion. Over the years, this Unless otherwise noted, all photographs are courtesy of has helped me develop clarity in some things, but I Rachel Findley. remain muddled in many others. I enjoy questions For permission to reprint this article, please contact: that seem honest, even when they admit or reveal [email protected]. confusion, in preference to questions that appear DOI: http://dx.doi.org/10.1090/noti1300 designed to project sophistication.” 1318 Notices of the AMS Volume 62, Number 11 His work was not older brother, Bob, only densely packed and sister, Jean, and with wonderful ideas, a younger brother, it was immensely rich George, who married and deep. Studying an Sarah, mathematician aspect of his work is of- Hassler Whitney’s ten like opening a box daughter. He married to find two or more in- his college sweet- side. Opening each of heart, Rachel Findley, those reveals two or and they had children more boxes that often Nathaniel, Dylan, and have little tunnels con- Emily. He had chil- necting to various other dren Jade and Liam systems of boxes. With from his second mar- great effort one reaches riage with Julian an end, being simulta- Thurston. Bill Thurston, 1952, Margaret Thurston, neously rewarded with with some of her Wheaton, MD. both great illumination Childhood creations. and the realization that Bill had a congenital one knows but a minuscule fraction of the whole. case of strabismus and could not focus on an object After a sufficient lapse of time, upon retracing the with both eyes, eliminating his depth perception. original trail, one catches further insights on topics He had to work hard to reconstruct a three- that one once thought one completely understood. dimensional image from two two-dimensional In a similar manner, this article hardly does ones. Margaret worked with him for hours when justice to the deep and complicated person that he was two, looking at special books with colors. was Bill Thurston. It gives but a few facts and vignettes from various dimensions of his life and, His love for patterns dates at least to this time. As at various spots, points readers to other resources a first-grader he made the decision “to practice where they might explore further. visualization every day.” Asked how he saw in Following this introduction are thirteen re- four or five dimensions he said it is the same membrances from mathematicians connected with as in three dimensions: reconstruct things from different aspects of Thurston’s professional life. It two-dimensional projections. is difficult not to be overcome by how Bill affected To stop sibling squabbling Paul would ask the people and institutions in so many different and kids math questions. While driving, Paul asked Bill profound ways. (when he was five), “What is 1 + 2 + · · · + 100?” Bill said, “5,000.” Paul said, “Almost right.” Bill Family said, “Oh, I filled one square with 1, two squares Bill’s father, Paul Thurston, had a PhD in physics and for 2 and all the way up to 100, so that’s half of × = worked at Bell Labs doing physics and engineering. 100 100 10; 000, but I forgot that the middle He was an expert at building things and was bold, squares are cut in two, so that’s 5,050!” smart, imaginative, and energetic. Once he showed Paul was a scoutmaster, and Bill was very Bill how he could boil water with his bare hands. involved with the Scouts. They did all sorts of He took an ordinary basement vacuum pump and things with ropes, e.g., making bridges. Bill was started it above the water so that the boiling point expert at making fires in the pouring rain. The was just above the air temperature. Then he stuck family loved camping and took many long trips. his hands in the water and it started boiling! Music was a big part of their lives. Bill’s mother, Margaret (nee Martt), was an expert seamstress who could sew intricate patterns that New College, Florida would baffle Paul and Bill. In later years, Bill’s Bill was a member of the charter class starting in fascination with hyperbolic geometry inspired 1964. According to alumnus and mathematician her to sew a hyperbolic hat-skirt, a seven-color John Smillie, the founders of New College decided torus, and a Klein quartic (genus-3 surface with that it was much easier to maintain quality than to a symmetry group of order 168) made from 24 bring it up, so a tremendous effort was made to heptagons that was designed by Bill and his sons, recruit one hundred of the brightest young people Nathaniel and Dylan. While at Ohio Wesleyan she for the inaugural class. This included Bill’s future wanted to be a math major but was told that wife, Rachel Findley. women don’t major in mathematics. New College was a three-year program with Bill was named after his father, Paul, and classes eleven months of the year. There was his mother’s brother, William, who died in a tremendous freedom in how individual academic hospital ship in the battle of Iwo Jima. He had an programs were structured and how students were December 2015 Notices of the AMS 1319 allowed to live. At various times Bill lived in a tent as he gave answers that befuddled his examiners in adjacent woods or slept in academic buildings, but provided hints at the remarkable originality of playing hide and seek with his thinking. the janitor. The library was Thurston’s graduate career contained an extra- minimal, and the college would ordinary collection of mathematical results. He buy whatever math books Bill proved the striking theorem that the Godbillon-Vey wanted. Smillie said that nearly invariant takes on uncountably many values. This all the books he took out had invariant comes from a de Rham cohomology class Bill’s name in them. that he relates to the helical wobble of the leaves of In Bill’s words: “I guess I was a foliation. His results show, among other things, disenchanted with how high that there exist uncountably many noncobordant school was and I wanted to codimension-one foliations of the 3-sphere. go to a place where I’d have Bill’s (unpublished) thesis, written under the some more freedom to work direction of Moe Hirsch, provided a precise descrip- in my own way.” New College tion of a large class of C2 foliations on 3-manifolds gave him that and more. After that are circle bundles. It also gave a counterexam- the first year, half the faculty ple to a result of S. P. Novikov that a certain partial resigned and the library was order associated to a foliation has a maximum. But, Bill Thurston, New on the brink of disaster. But beyond any single theorem, this period provided College. Thurston says that he and many the foundation for a collection of ideas that would other students benefited from help answer many fundamental questions about the turmoil. “It certainly taught us independence foliations and would ultimately lead to Thurston’s and how to think for ourselves.”1 According to revolutionary work on surfaces and 3-manifolds. Rachel, Bill could have left after two years for grad- uate school, but he really liked the independence MIT and the Institute for Advanced Study the school offered and chose to stay. Bill was a member of the Institute for Advanced Study in 1972–73 and an assistant professor at MIT Berkeley in 1973–74. There he continued his extraordinary Bill started Berkeley in 1967 in the thick of the work on foliations, for which he won the 1976 5 Vietnam War. “Many of us were involved in student Veblen Prize (shared with James Simons). In demonstrations and student strikes. We were particular, it was during this period that he and sprayed with tear gas, whether or not we protested. Milnor began their work on the kneading invariant We had friends who were killed, others who refused of piecewise monotone maps of the interval.