Crowd-sourcing has reached mathematics, and at first glance it might seem as if this stereotypically solitary discipline is finally catching up with what other sciences have been doing for years. But, as we explore on page 422, the maths project Polymath, which invites participants to pitch in with ideas and results that might help to solve whatever problem the coordinator has set, is in some ways ahead of the curve. Not all of Polymath’s challenges — nine so far — have produced a successful solution. But even ‘failures’ can be productive, and all of these efforts represent genuine collaborations at the highest technical level.

It is in these respects that Polymath differs from the many other crowd-sourcing enterprises. Most commercial ventures are competitive: entrants vie to ‘win’ the challenge, and often to receive a financial prize as a result. As one researcher who has used these resources comments, this isn’t necessarily the way to secure a truly useful solution: an extended period of post-competition development is often needed to turn a winning entry into a practical approach. Entrants may not have the motivation or the time for that.

Other established crowd-sourcing efforts, such as Galaxy Zoo and Foldit, are all about weight of numbers, not expertise: they enlist lay volunteers to conduct repetitive tasks — such as classifying galaxy morphologies or predicting protein structures — for which human judgement still out-performs automated solutions. This is useful, but is not going to lead to the kind of conceptual novelty that drives science forwards.

So although all the various approaches to harnessing the ‘wisdom’ (or perhaps just the labour) of the crowd have a part to play, there are surely lessons that other disciplines could learn from Polymath. One is the value of openness. The system is fully democratic: anyone can propose and coordinate a project, and if it is deemed to be worth the effort, anyone can pitch in with answers or suggestions, however small, which are judged purely on merit. “Anybody who had anything whatsoever to say about the problem could chip in,” Polymath’s creator Timothy Gowers explains. “You would contribute ideas even if they were undeveloped and/or likely to be wrong.” Although it is perhaps not surprising that the challenges so far have been instigated by senior researchers, an ethos of this sort means that, in principle, the barrier to participation of younger, less experienced people is low.

And the process is a conversation, not a competition. It’s not just, or even primarily, about cracking a problem, but about sharing ideas. “One strength is in gathering literature and connections with other fields that a traditional small collaboration might not be aware of without a fortuitous conversation with the right colleague,” says Terence Tao, another of Polymath’s coordinators. And participants are learning the effort’s limits. “Projects that seem to require a genuinely new idea have so far not been terribly successful,” says Gil Kalai of the Hebrew University of Jerusalem in Israel. That’s one reason why he feels “it will be nice to have a Polymath devoted to theory-building rather than to specific problem-solving”.

Sometimes it is not market forces that achieve efficiencies, but cooperatives.

Preconceptions aside, it is perhaps not surprising that mathematicians are the first to approach crowd-sourcing in this way. Their field is relatively small and well connected, and not nearly as competitive as some might think. It has an active blogging community. And it faces problems that can be tackled online with digital pen and paper. It is less obvious how, say, a chemistry challenge that demands lab work could be solved in this manner.

But is that really the case? Some of the successful Polymath problems have been those that could be broken down into smaller parts that individuals could work on independently. An organic chemical synthesis is rather like that: a series of distinct steps between intermediates. The total synthesis of quinine was famously — and controversially — claimed in 1944 on that basis, when, rather than making the compound itself, Robert Woodward and William Doering bridged the last gap in a multi-stage process that had been largely completed by others. Might not these feats of synthesis be more systematically apportioned between several groups, swapping ideas, tips and techniques along the way? That could be much more efficient than the herculean efforts often doggedly pursued in single labs today, not least because there is less chance of going down blind alleys when many minds are involved. But it would require a change in the prevailing mentality of competition and victory that was evident, for example, in the total synthesis of taxol that was reported in 1994.

This is just one way in which crowd-sourcing need not be about letting a thousand flowers bloom and then throwing away all but the most fragrant, nor putting all hands to the pump. Sometimes it is not market forces that achieve efficiencies, but cooperatives.