Recall from a few weeks ago that Timothy Gowers started an “open source” experiment in doing math research on his blog. It sounds like it was a resounding success! Timothy Gowers announced on his blog that he is pretty convinced that the crowd on his blog has come up with a new proof of the density Hales-Jewett theorem. Given how well this went, you can bet that other such projects will soon start up.
We’d also like to point out a couple of morals to the story. Math research is a social affair; most people think of mathematicians working alone at their desks for years and years, but actually much of mathematics is done in collaboration (not usually in groups as big as this one!). There is lots of math research going on right now; in fact, this is probably one of the most exciting times in the history of math! The path followed by the researchers on Gowers blog is typical of math research: trying small cases, using computers to do other cases, proving lemmas which may or may not end up being helpful to the final solution, lots of mistakes and false solutions and, hopefully, finally a correct solution!
Many people think of math as a dusty old subject which was all settled a couple of hundred years ago and now it’s just a matter of knowing the right trick to get the already known answer. In fact, it’s the exact opposite! It’s a dynamic field with many more questions than answers!
Mathematical study and research are very suggestive of mountaineering. Whymper made several efforts before he climbed the Matterhorn in the 1860’s and even then it cost the life of four of his party. Now, however, any tourist can be hauled up for a small cost, and perhaps does not appreciate the difficulty of the original ascent. So in mathematics, it may be found hard to realise the great initial difficulty of making a little step which now seems so natural and obvious, and it may not be suprising if such a step has been found and lost again.
–L.J. Mordell, Three Lectures on Fermat’s Last Theorem, p.4