Bill passed away peacefully at 8PM on Tuesday, August 21, in the Strong Memorial Hospital in Rochester, NY, surrounded by family. His son Dylan wrote this about his contributions to mathematics:

*The achievements on Bill's own CV are numerous, well-documented, and well-celebrated. But as mathematicians will tell you over and over again, far more significant is how he revolutionized the way mathematicians work and communicate.*

Bill emphasized constantly that the goal of mathematics, and the source of its beauty and utility, is *human understanding*. He aimed to gain and share an intuitive understanding of mathematics, recruiting all human senses -- vision, motion, even touch. As Benson Farb (U. Chicago) says, "He changed our idea of what it means to 'encounter' and 'interact with' a cgeometric object. The geometry that came before almost looks like pure symbol pushing in comparison."

He had a passion for making mathematics accessible and appealing to children and researchers alike. In his course "Geometry and the Imagination", he guided high-school teachers to study the same bicycle tracks that Sherlock Holmes investigated. In 2010, he worked with the fashion designer Issey Miyake on a show inspired by the geometries whose study he pioneered.

Bill emphasized constantly that the goal of mathematics, and the source of its beauty and utility, is *human understanding*. He aimed to gain and share an intuitive understanding of mathematics, recruiting all human senses -- vision, motion, even touch. As Benson Farb (U. Chicago) says, "He changed our idea of what it means to 'encounter' and 'interact with' a cgeometric object. The geometry that came before almost looks like pure symbol pushing in comparison."

He had a passion for making mathematics accessible and appealing to children and researchers alike. In his course "Geometry and the Imagination", he guided high-school teachers to study the same bicycle tracks that Sherlock Holmes investigated. In 2010, he worked with the fashion designer Issey Miyake on a show inspired by the geometries whose study he pioneered.

The comments section, which is now closed, is a collection of thoughts, stories, and reminiscences about Bill's life.

Some remembrances around the web:

Harry Baik

Richard Brown

Danny Calegari

Nathan Dunfield

Jordan Ellenberg

Jesse Johnson

Justin Lanier

Christian Perfect

David Speyer

Daina Taimina

Terry Tao

Peter Woit

A page of remembrances has also been set up by Bill's family: follow this link.

## Comments

I've known Bill for around 18 years. My first encounter with him was at a graduate workshop at MSRI that he organized with Jane Gilman and David Epstein. There was a picnic in Tilden Park that we walked to, and after the hike over there, Bill told us how many steps he had taken. He then demonstrated how he counted in binary on his fingers, and he had trained himself to carry out this counting automatically while walking. Not only was this clever, but it actually requires some tricky coordination! I told him I was working on an algorithm to recognize the unknot, and he immediately showed me his methods to recognize the unknot using Jeff Weeks' program Snappea. It was clear to me that his methods were powerful and suited to my abilities, so I ended up eventually working on the geometry of 3-manifolds.After obtaining my PhD at UCSD, I was a postdoctoral fellow at UC Davis, where I went principally to work with Bill and Joel Hass. The first time I met Bill there, I explained one of the results from my thesis about how volume combines under gluing hyperbolic manifolds, which took only a few minutes since he immediately understood the ideas. He then went to the board to suggest a different approach, based on the recent ideas of Besson-Courtois-Gallot which might give a sharp estimate. He wanted to base a proof on a generalization of his "skateboard park" proof of the Jordan Curve Theorem, where one adds little flanges to the concave parts of the boundary of a curve in the plane, in order to convexify its interior while keeping the metric non-positively curved. We spent some time learning the work of B.C.G., and eventually this approach turned into a joint paper (together with Pete Storm) when Perelman's more powerful results became available.

We had many other valuable conversations on surface and foliations and other things. I also cotaught Geometry and the Imagination class with him one quarter, and a differential geometry class. These experiences were quite valuable to me to learn his approach to instruction. He really did not want to ruin the students' process of self-discovery, and chastised me once for giving too big of a hint. Attending his seminar a few quarters, I learned about his approach to mathematical discovery, especially using computers. He was fond of iterating some geometric construction, observing the patterns, and then trying to find explanations for them. Although his intuition and grasp of math seemed quick and intuitive during classes and discussion, I think it was based on years of deep thinking and construction mental models which he could then draw upon when needed.

Bill Thurston has influenced my work since the 1970's. He embodied a vision of mathematical understanding that enlivens and humanizes mathematics and mathematics education. I was especially encouraged by the vision he described in his [i]On Proof and Progress[/i] paper where he wrote about mathematics: "The measure of our success is whether what we do enables [i]people[/i] to understand and think more clearly and effectively about mathematics."

He will be greatly missed; but those of us who were influenced by him will be forever changed.

I knew cousin Bill before he made a name for himself. I remember a trip to California in 1968 while Bill was at Berkley. I was just 8 years old and the San Francisco/Berkley area was at the center of a cultural revolution that hadn't reached central Ohio yet. We thought he had a exciting life then. We new he had a great future but he clearly exceeded all expectations.

I knew Bill's name and his legend when I was in China. In 2001 I was very excited since I was accepted by UC Davis as a graduate student, and I knew that I could work with Bill. Around the winter of 2003, I went to his office nervously and asked him if he would be my thesis advisor, he agreed immediately. But he also told me that he would move to Cornell in Fall of 2003. Sunny Fawcett and I decided to transfer to Cornell with Bill. For some personal reason Sunny quitted math soon,

so I was his only PHD student at Cornell for several years. In those years, he provided me financial support one semester in every academic year, so I could focus on my research without any teaching task. But my research progress is very slow, actually I made no progress in a very long time. He had to endure my nonsense in our every Friday's meeting for a very long time, but he never lost his patience.

I didn't have any personal contact with Bill except mathematics, but we still had some chance to talk about Apple, iPhone and digital SLR's lens. Once he told me the advantages of the fixed focal length lens

for digital SLR, and he also showed me some photos that he took for his little kids. To his Kids, Bill must be a very good father. I still remember that he brought sleeping Liam to our Friday's meeting several times, his arm pillowed the sleeping baby, and the baby was very nice since he seldom woke up during the meetings.

Bill is the same age as my father, I'm very sad that Bill left us so early. Bill should be happy about one thing, i.e. he was proved that he was always right. Wish him rest in peace.

My main contact with Bill was the courses he taught at Cornell over the last few years. Their titles alternated between [i]Topics in Geometry[/i] and [i]Topics in Topology[/i] but I couldn't tell you which was which, those two fields being so intertwined in Bill's mathematics.

They were distinctly free-form courses. Sometimes in the first meeting he would ask everyone to suggest what the course might be about. It became clear that he was not looking for topics requiring weighty background knowledge. Instead, he liked seemingly elementary questions, usually in topology, combinatorics, graph theory, dynamics, or geometry. Week-by-week he would develop one or more of the suggestions, drawing connections with all sorts of areas of mathematics and probing from different directions, often using computer experiments and graphics. As the semester went on a mathematical landscape would miraculously be revealed and open problems would fall. Perhaps the most striking example, from the semesters I attended, was what began as an exploration of what Bill called "sweep outs" and grew over the semester to the ideas for solving a major open question about stabilization of Heegaard splittings of 3-manifolds. (It eventually became a paper with Joel Hass and Abby Thomson.) Another example was a question about planar graphs and duality which Bill cracked by translating it to the language of manifolds, where geometric intuition could more easily be brought to bear. (This developed into the one paper I coauthored with Bill.) As his illness set in, the classes' topics shifted towards mathematical reminiscences.

Another memory I have of those classes was how Bill tried to involve everyone. (Once he asked us to draw the entity that is "mathematics" on the board -- a tree, a blob,...?) He longed to provoke a dialogue. The nature of the classes intimidated some, I think, despite Bill's best efforts. I often regretted not having more time or mental energy to devote to them in a busy semester, so as to be able to engage more fully -- Bill's ideas were hard to keep up with!

Bill delighted in children. I remember him at the 2004 Topology Festival devotedly carrying his son Liam around in a sling. After my son Benjamin was born, Bill wrote to Tara and me "Babies are all-consuming, [...]. But they don't stay babies very long in real-world time (as distinguished from new-parent time). Their needs taper off at an exponential rate, even though the exponent is small. Enjoy being consumed, while it lasts." Later he visited us and I remember him contentedly cradling and soothing Benjamin. He was fascinated by child learning. In his talk at that same Topology Festival he said "Children are much smarter than us; they just don't know as much."

Other memories I have of Bill are more eclectic. I remember him playing Wii computer games with great gusto. I remember being asked by one of his former students to watch out for Bill and call her the moment he arrived at his office, so she could then call him to badger him to complete her letter of recommendation. I remember seeing a draft of a letter Bill was preparing when our postdoc program was being cut back in a budget crisis: "Dear Dean [...] and other Muckety-Mucks," it began (just in its draft from, I think!); what followed was a powerful explanation of the important role postdocs play in a mathematics department and how being a postdoc is an essential

stage in the development of a research mathematician. I remember the thrill he took from his collaboration with Dai Fujiwara and participating in Paris fashion week. I remember the excitement at Cornell's undergraduate mathematics club when Bill gave a presentation in which he demonstrated the modular surfaces he had been developing with Kelly Delp. I remember a beautiful loaf of bread he baked. I remember him introducing himself to often star-struck visitors in the Cornell Mathematics Department. And I remember him facing his illness with great courage, hoping to beat it or delay it not for his sake, but for that of his younger children.

Bill was extraordinarily insightful: in his mathematics, of course, but also in many areas of life. His ideas and his approach to the subject should live on, thanks to the enormous influence he has had. But Bill himself will be desperately missed.

I was fortunate enough to enter mathematics just as Bill was revolutionizing geometry and topology and in fact the way we think about things. I remember well going to hear him talk for the first time in 1975. He drew this example of a pseudo-Anosov map and the effect of a simple closed curve under iteration limiting on this object he called a measured foliation. He also talked about the boundary of Teichmuller space. It literally blew my mind and changed everything for me and of course many others. Up to that point I think it was fair to say that people working in these fields did not think one should study what happens to longer and longer curves on a surface.

Over the next several years whenever I saw Bill and I had a few minutes of his time or I heard a lecture of his, I would go home and just ponder some of his ideas. Sometimes a sentence or two of his would lead me to think about something for a year or more.

I have never met another mathematician whose mind worked in as deep or profound a fashion as Bill's.

It is hard to believe he is gone.

This is a great loss for mathematics.

Hi everybody,

I wanted to share with you the high resolution version of the video:

William Thurston " The mystery of 3-manifolds'' recorded in June 2010.

This version has just been put by Francois Tisseyre on :

https://vimeo.com/48631569

I just viewed it on full screen mode (it can even be projected on a big cinema type screen).

I was one of the 500 lucky people sitting in that room. I also recommend

another video

http://vimeo.com/22475977 (also to be viewed to full screen mode)

including some touching comments of Bill on Poincare conjecture.

I was so lucky to have taken two classes with Professor Thurston at UC Davis. When he learned that some of us were interested in teaching math in high school and community college, he started adding connections between the course topics and the mathematics we would be teaching. One day he mentioned how mathematics caught his attention: fractions. What would he say that was so interesting about fractions that drew a genius to math? In his mind, they were unfinished. He saw that by formalizing incomplete division, fractions are more useful than if we went to the effort of performing the division.

I have often thought, as I teach and answer questions, that so much of mathematics, and life, is in a sense unfinished and more powerful as a result.

He wanted to base a proof on a generalization of his "skateboard park" proof of the Jordan Curve Theorem, where one adds little flanges to the concave parts of the boundary of a curve in the plane,

Add Comment

We are sorry. New comments are not allowed after 1 days.