Question

1. I have no proposal, but only want to mention a historical example of what can be called "Citizen science" in mathematics. http://www.computer.org/portal/web/csdl/doi/10.1109/85.707573. This is how the book of Abramowitz and Stegun, Handbook of Mathematical Functions was created. During the Great Depression, the National Bureau of Standards hired jobless people (not professional mathematicians) to compute tables of special functions. The result was a good and useful book. Perhaps nobody is using tables nowadays but the book is still useful.

2. Suppose that the 4-color was checked by 1000 amators amateurs instead of a computer. Would the proof be more reliable, or more convincing?

3. In astronomy, there is a whole area which is mostly done as "Citizen's Science". It is the discovery of new comets. Only amateurs can afford just to look at random places in the sky. However, with improvement of computers speed and software, I predict that even this will be soon "automatized".

4. And one more question: it is somehow taken for granted that "citizen's science" is something desirable, so this part of the question is not even discussed. (I am not so sure).