PDF version. berkeleygenomics.org.

William Thurston was a world-renowned mathematician. His ideas revolutionized many areas of geometry and topology[1]; the proof of his geometrization conjecture was eventually completed by Grigori Perelman, thus settling the Poincaré conjecture (making it the only solved Millennium Prize problem). After his death, his students wrote reminiscences, describing among other things his exceptional vision.[2] Here's Jeff Weeks:

Bill's gift, of course, was his vision, both in the direct sense of seeing geometrical structures that nobody had seen before and in the extended sense of seeing new ways to understand things. While many excellent mathematicians might understand a complicated situation, Bill could look at the same complicated situation and find simplicity.

Thurston emphasized clear vision over algebra, even to a fault. Yair Minksy:

Most inspiring was his insistence on understanding everything in as intuitive and immediate a way as possible. A clear mental [...]

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