Here is a report about such public participation from the Guardian. I reprint some passages that merit our attention:
Mathematicians are not known as a social bunch, but a new "WikiMaths" project is allowing anyone to join in their cutting-edge research. A study into the effectiveness of the world's first virtual mathematics project will be released this week.
It all started in 2009, when Cambridge mathematician Tim Gowers wrote about the possibility of an open online group allowing unprecedented numbers of people to work on the same problem, hopefully solving conundrums much more quickly. He suggested the "Hales–Jewett theorem" as a good first target.
Contributions poured in – a staggering 1,228 significant comments across 14 blog posts with 39 people providing meaningful contributions. Within six weeks the answer had been found. It was published under the collective pseudonym "DHJ Polymath".
But was the process truly collaborative? Researchers at Carnegie Mellon University in Pittsburgh, think so. Much of the work was done by professional mathematicians, but a number of smaller, vital contributions came from those without serious credentials.
The 39 contributors to the Hales–Jewett theorem solution ranged from the world's top mathematicians to secondary school maths teachers. Several seminal ideas came from inexperienced mathematicians. Which all means that the exercise could redefine who is considered a mathematician – and offer new insight into unsolved problems.
Several interesting questions follow from this. One is whether this remains an episode or whether the spreading of web2.0 will lead to many more such episodes so that the institution of science changes. If the most abstract and arcane branch of knowledge benefits from vital contributions from people without serious credentials the less technical sciences would benefit even more.