I hope this question is appropriate for MO – I cannot decidedly tell with soft questions. I was wondering what are the strategies people use when searching for literature on a subject. I shall clarify my question with an example. Suppose, for instance, I want to learn more about $\star$-independence or $\star$-spread and assuming I already do not have a reference for it, how do I go about searching for literature on it. If the latter assumption is relaxed (that is I already have a couple of references on the concept), presumably I can keep looking for cross references and that might, in a small number of steps, exhaust all the literature on the subject. However, I find frequently this is not the case. The problem here is two fold:
1) If I am looking at exploring about a mathematical object/theorem which does not have a name and does not involve any objects which have exotic names, for instance, "A finite union of subspaces of a vector space is a proper subset of the space if the ambient field is infinite" (I hope this is not a bad example and even if it is, that it conveys the underlying issue). Google searching any keywords for an example like this only yields tons of irrelevant entries. This is especially true in cases where the mathematical objects involved have other meanings in english (which can be said about almost every other thing in math e.g. ring, field, ideal, module, etc) and even when this is not the case, it could be a ubiquitous word in mathematics (e.g. vector, space, manifold, etc). So if the concept or theorem does not contain a distinguished word, searching about it is difficult.
2) If the object/theorem is exotic or contains an exotic object like $\star$-independence, google and other search engines suppress special characters and the situation defaults to that in (1). Finally, I find it especially hopeless if you are looking to find say, class number computations of $\mathbb{Q}[\sqrt{2},\sqrt{7}]$.
I would like to know if anyone has any thoughts on getting around these problems. If it's a misplaced question, I would be happy to delete it.
Best Answer
In addition to google, google scholar, and google books, I sometimes find the following to be useful:
sciencedirect.com --- to search through the journals, and thus by analogy several other publishers' websites
latexsearch.com --- still in beta, but it takes TeX / LaTeX code as input, so might be useful for addressing the point raised in your Observation 2.
Another very recent, though not relevant for you website might be: sciverse.com (for image / illustration search in published articles)