Via Spontaneous Symmetry, a fascinating story about parallel processing and the power of blogging:
Normally, when [a mathematician] seeks a proof, he locks himself in a room with a chalkboard for long periods of time. He may consult his peers at his university, he may read books, he may look through papers, but the majority of thinking takes place within one brain. It’s serial. Gowers had a better idea. Instead of retreating to a dark room, he posted a section on his blog asking for help with the proof. Anyone from around the world could contribute to the idea by posting a comment. He hoped, in this fashion, to link together the brains of people from all around the world. Gowers eventually received hundreds of comments and, over the course of a few weeks, using the ideas in these comments, he was able to piece together a simple proof.
Though SS aptly notes:
I’m afraid to ask how many inane “comments” the poor mathematician had to wade through between each substantive remark.
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Very powerful. Using the wisdom of the crowds, you can solve complex problems much quicker though I’m sure it was not fun sifting through each comment and checking everyone’s mathematics in this case. Very good illustration on how crowdsourcing is effective.
I’m constantly impressed by the power of crowdsourcing. What struck me about this particular example is that unlike most crowdsourced projects, the scale of the project wasn’t obviously beyond the grasp of one person. With map data, for example, there’s no way a single person can supply it all. But each person’s contribution can be used as-is, without further manipulation down the line (a street is a street!). A proof, on the other hand, typically requires knowledge that is acted upon in each successive step – it is self-referential – which means that later information must account for data received earlier. Therefore, it’s very difficult to work on a proof without intimate knowledge of the entire project, which is contrary to the philosophy of crowdsourced work – and makes it all the more impressive that it was successful.