Every once in a while scientific fields become so saturated and mature that progress seems impossible. What is needed is a new science. But inventing a science from scratch would take more than a lifetime and acceptance is unlikely. Fortunately, there is a solution. Areas of science that overlap are often under developed. They are also complex. With the science of heuristics, and isomorphic studies (universalization of patterns and rules, which are applicable to more than one area), and lots of mathematical and concept based research new sciences are possible.
There is a caveat, however. Young sciences, like startup businesses, must behave differently than mature sciences. What is unproven must be tested, whether it's been done, or is thought to be practical. In other words, rather than the unproven being considered false, it is considered possible, if there is any way of approaching it experimentally left at all. This is one of the only ways to produce scientific progress. Scientific method is good for textbooks, but not an effective way of producing progress. The old empirical method of trial and error is best for producing progress in a young scientific field. This is equally true of the areas of overlap between seemingly mature sciences.
Another point to consider is, for a science to be considered and developed further in society, it must be useful in producing something new. With overlap, a lot of old things can be made more efficiently, but new possibilities produce interest. The science must also be relatively open... with no secrets or expensive textbooks. Amateurs often produce more results (with varying levels of success) than experts because they don't "know" that certain things aren't supposed to work. Whatever works, will work... let's just leave the testing to the experts.
Some work in developing these sciences can be done by putting the applicable math and physics in computer code or scripts. Making computer models is sometimes more possible than multibillion dollar projects for amateurs. If you don't know programming, there are many free resources online that teach it. Even free programming tools. Blender (the 3d modeling tool) is relatively open to being coded.. it seems to use python scripting. http://wiki.blender.org/index.php/Doc:2.6/Manual
So to sum it up. Invent a new science by doing the following.
1. Pick two or more sciences with interesting areas of overlap.
2. Define the rules or criteria that enable the sciences to work together well.
3. Test new ideas and experiments to try. Or model them.
4. Viable sciences will create new things, and be able to be learned by an amateur community.
Last of all... if the science doesn't seem to be currently viable. Don't waste the effort that you've already put into it. It may make interesting stories, games or short youtube videos. The inspiration from amateur science may just be what we need to pull our little world from its current stagnation.