GoKawiilErdős was right. By the time Tao was 24, he had made enough new discoveries to have his choice of permanent faculty positions; he ultimately decided to settle at the University of California, Los Angeles. Around that time, he met a young English number theorist named Ben Green. The two began collaborating on a proof that certain kinds of patterns called arithmetic progressions — in which the numbers in a set increase by a fixed interval, like 7, 10, 13, 16 — inevitably appear in large collections of prime numbers, despite the fact that primes appear to be scattered randomly along the number line. Their proof would become the signature result of Tao’s early career, contributing to his winning the Fields Medal in 2006, and propelling him to the upper echelons of mathematics.
Tao could have built a successful career without collaborating with anyone, but that’s not the way he liked to work. He viewed working with other researchers as a primary way to discover new ideas — take what you know, pair it with what I know, and see what happens.
This approach led Tao’s mathematical research to range over an unusually broad set of topics, from analytic number theory, including the Green-Tao theorem about prime numbers, to analysis, where he studied properties of the Navier-Stokes equations that describe the behavior of fluids, to algorithms for constructing MRI images from digital data. (The MRI collaboration developed during conversations Tao had with Emmanuel Candès, a statistician then at the California Institute of Technology, while they were both dropping off their kids at preschool.) This thirst for collaborative discovery also led Tao to do a lot of his work in public. In 2007, he started a blog, where he began publishing regular updates about his research. By that point, Tao was one of the most famous mathematicians not only in his field but in the world. His posts received a lot of attention and sometimes led to long exchanges in the comments section, where Tao enthusiastically participated. He did it because he found it fun, and because he hoped the conversation might generate new ideas.
Around that time, another early math blogger had a similar thought. Like Tao, Timothy Gowers was a prominent research mathematician with a taste for public exchange. But rather than trusting serendipity to strike in his blog’s comment section, Gowers wanted to channel public energy in a focused way. In January 2009, he published a blog post announcing his desire to facilitate a new kind of “massively collaborative mathematics.” He would propose a problem in an open online forum, and “anybody who had anything whatsoever to say about the problem could chip in.” He named it the Polymath Project.
Tao viewed working with other researchers as a primary way to discover new ideas — take what you know, pair it with what I know, and see what happens.
Tao jumped in. Like Gowers, he understood that some math problems were more amenable than others to being solved through large-scale collaboration. The key, as Tao wrote in a comment on Gowers’ initial post, was to find problems that could “generate a number of simpler sub-problems … which can largely be worked on in parallel.” By breaking big problems into individual cases, different teams or individuals could work on their own and then assemble their results as pieces of a bigger whole. At the same time, Tao knew that perhaps the biggest challenge with the Polymath model would be organizing: moderating contributions and checking to make sure that all the contributions were correct.
For the first Polymath project, Gowers proposed improving a result called the Hales-Jewett theorem, which was about patterns that appear when you shade cells in a grid with one of two different colors. After a few months of work, coordinated through thousands of comments by dozens of mathematicians, the group had proved a more exact statement about how those coloring patterns emerge. That fall, they released the work as a first-of-its-kind math paper with the pseudonymous byline “D.H.J. Polymath.” Gowers’ experiment had been a success. It allowed many mathematicians — professional and amateur alike — to work together and yielded a proof in the end.
Over the next decade, there were 15 more Polymath projects, some of which Tao led, and the initiative attracted mainstream attention. On October 29, 2011, The Wall Street Journal ran an article called “The New Einsteins Will Be Scientists Who Share” and reported that the Polymath Project had “pioneered a new approach to problem-solving.”
Samuel Velasco/Quanta Magazine
Yet in other ways, the Polymath Project was an idea before its time. Tao found it exhilarating to be at the center of a frenzy of mathematical activity, but he recognized that the comments section of a blog was a limited platform for collaboration. Massive open collaboration increased the likelihood of a certain kind of serendipitous discovery, but at the same time it heightened the odds that any one of the many participants would contribute a mistake. The only way to guard against error was for a moderator to carefully check all the work. But that kind of moderation bottleneck undermined the Polymath vision.
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