## Polymath = user innovation

In February 2007, Mike Adams, who had recently joined Automattic, the company that makes WordPress, decided on a lark to endow all blogs running on WordPress.com with the ability to use LaTeX, the venerable mathematical typesetting language. So I can write this:

$latex \pi r^2$

And produce this:

$\pi r^2$

When he introduced the feature, Mike wrote:

Odd as it may sound, I miss all the equations from my days in grad school, so I decided that what WordPress.com needed most was a hot, niche feature that maybe 17 people would use regularly.

A whole lot more than 17 people cared. And some of them, it turns out, are Fields medalists. Back in January, one member of that elite group — Tim Gowers — asked: Is massively collaborative mathematics possible? Since then, as reported by observer/participant Michael Nielsen (1, 2), Tim Gowers, Terence Tao, and a bunch of their peers have been pioneering a massively collaborative approach to solving hard mathematical problems.

Reflecting on the outcome of the first polymath experiment, Michael Nielsen wrote:

The scope of participation in the project is remarkable. More than 1000 mathematical comments have been written on Gowers’ blog, and the blog of Terry Tao, another mathematician who has taken a leading role in the project. The Polymath wiki has approximately 59 content pages, with 11 registered contributors, and more anonymous contributors. It’s already a remarkable resource on the density Hales-Jewett theorem and related topics. The project timeline shows notable mathematical contributions being made by 23 contributors to date. This was accomplished in seven weeks.

Just this week, a polymath blog has emerged to serve as an online home for the further evolution of this approach.

I am completely unqualified to evaluate the nature of mathematical discourse that’s going in on these polymath collaborations, or the claims being made regarding outcomes. But it sure makes my spidey-sense tingle.

I am, however, qualified to evaluate the nature of the collaborative methods being employed. And on that front, I’m amused (and chagrined) to recall something I wrote back in 2000, in a report called Internet groupware for scientific collaboration. The report was commissioned by Greg Wilson, who organized this week’s Science 2.0 event in Toronto. At that event, my report served as a historical frame for the polymath experimentation that’s going on right now, and that Michael Nielsen discussed at the Toronto event in an updated version of this talk.

In my 2000 report I said:

TeX and LaTeX define scientific publishing for a generation of scientists. But these formats don’t integrate directly into the shared spaces of the Web. The rise of XML as a universal markup language, along with vocabularies such as MathML (for mathematical notation) and SVG (for scalable vector graphics), suggests that the Web may yet reach its original collaborative goal.

Why didn’t I see, then, that the crux of the issue wasn’t XML and MathML and SVG, but rather the ability to “integrate directly into the shared spaces of the Web”? And that what ought to be integrated directly was the typesetting language already familiar to mathematicians, namely LaTeX?

The answer is that I needed (and still need) to be reminded that good-enough solutions here now, and familiar to people, often trump great solutions that aren’t here and wouldn’t be familiar if they were.

From that perspective, I’m wondering what will and won’t turn out be good enough for the polymathematicians. The current setup is admittedly imperfect, and they’re now begining to explore WordPress plugins that enable, for example, more powerful ways to organize, reply to, and refer to one anothers’ comments.

I don’t think anybody yet knows what the right tooling will be for polymathematical collaboration. The ones who are best qualified to figure it out are the polymathematical collaborators themselves, but they are not WordPress plugin developers.

What’s needed is what Eric von Hippel calls a user innovation toolkit. The idea is this: Leading users, as they employ a tool, also modify it, and in so doing they express intentions that tool developers can then capture and formalize.

If you look at the systems of notation that the polymathematicians are creating in order to organize and refer to their contributions in these long and complex threads of mathematical discourse, you can see intentions being expressed. So arguably, WordPress is a user innovation toolkit, and we’ll see these innovations codified in future plugins. I’ll be watching with great interest.

Update: As per Jonathan Fine’s comment below, it appears that MathTran.org has offered the same kind of service for quite a while now: