Friday, October 02, 2009

Open-Source Mathematics

Today I saw the 2009 Charles Simonyi Annual Lecture in the communication of science in the Oxford Playhouse. It was given by Cambridge mathematician Timothy Gowers (apparently the first mathematician to ever give this lecture in its short history). The title of his talk was "Open Source Mathematics", and we were greeted by a friendly Beamer presentation. (I don't actually use Beamer for my talks, but I was pretty amused to see that format in the Oxford Playhouse as opposed to the types of venues where one would more typically see that format used.)

Gowers was discussing his Polymath1 open-source mathematics project, which was an attempt to bring theorem-proving outside of the realm of the single mathematician and into a more public domain. Although most of the active participants in this project (they were quite successful, though how widespread such success can be remains to be seen) ended up being professional mathematicians with highly-developed expertise in relevant areas, the whole thing was done in a public arena---namely, Gowers' blog---there were lots of people who were not mathematicians who were following the whole thing and making comments (and occasionally giving suggestions, though apparently not ones that actually helped solve the problem). Interestingly, this project also provides a public record of this type of problem-solving process, which could prove to be a great teaching resource.

In closing, I have two basic comments:

(1) I am very interested in seeing how such efforts develop in the future. (For example, take a look at the polymath blog that has now developed.)

(2) I enthusiastically applaud Gowers and company for this very successful effort!


Ravi said...

I heard one of the other main collaborators, Ryan O'Donnell, give a talk on this at Microsoft Research New England and came away feeling like it's a great idea but that in the end 95% of the work was done by maybe 4 or so people. Maybe O'Donnell, Gowers, Tao, and a few others. I guess most open-source software projects end up the same. In the polymath case it seemed the number of posts grew so quickly that if one ever fell behind then it would impossible to catch up.

At the end the consensus among the audience and speaker seemed to be that future projects need to be better organized so that people who wander in and out can still contribute. One possibility mentioned was a Wiki summarizing hypotheses and conclusions, where one can look at the history and/or discussion to see the development of each aspect, without having to sort through a huge jumble of posts. I haven't looked at the new Polymath site, but hopefully they've structured things in such a way that it'll be easier for people to make small contributions without spending days trying to read a horde of posts just to get up to speed.

Mason said...

Gowers said that that number was 6-8, but it's certainly far from a true grassroots effort. In many ways, what has been accomplished is similar to the discussions I have with my collaborators and students on the private part of netwiki (the networks wiki I help Peter Mucha maintain). Nevertheless, this is a step in the right direction.

Ernie Croot seems to be an active participant on the current polymath blog, and he and Terry Tao seem like people who could really help in such directions.

Lemming said...

With any luck, Google Wave is going to be an ideal place to hold this sort of collaboration in the future. The preview is clunky but promising so far, and there's lots of work being done to integrate LaTeX, symbolic manipulation packages, bibliographic helpers, etc.