Tim Gowers gives a lengthy report here on the development of the Mathematical Tricks Wiki, which he is now calling the Tricki. The Tricki will be a wiki/database of mathematical problem solving techniques that will, if development proceeds, eventually be something like an expert system that mimics how a human mathematician’s brain works when solving problems. In Gowers’ words:
The main content of the Tricki will be a (large, if all goes according to plan) body of articles about methods for solving mathematical problems. Associated with these articles will be many qualities that will vary substantially from article to article. For example, some will be about very general problem-solving tips such as, “If you can’t solve the problem, then try to invent an easier problem that sheds light on it,” whereas others will be much more specific tips such as, “If you want to solve a linear differential equation, you can convert it into a polynomial equation by taking the Fourier transform.” Some articles will be written at a very elementary level, and some will be quite advanced… Some will concern particular areas of mathematics, such as algebraic geometry or probability, whereas others will concern techniques that are relevant to many different areas. And so on.
Gowers thinks that the Tricki could revolutionize the way mathematics is done in much the same way that or ArXiV have done, and I think he’s right. Read the whole thing for some fascinating ideas on how he envisions the navigation and human-computer interaction of this system.