I have found that wikipedia is not a coherent, exhaustive, or detailed reference. I would like to find a similar resource that explains academic/scientific terms and methodologies clearly, briefly, and in a detailed manner. Ideally, this resource would be freely available on the Internet and provide descriptions that clarify these sorts of terms e.g: theory, theorem, hypothesis, assumption, conjecture, lemma, corollary, law, rule, principle, etc.
Here is a short list of resources, for different fields, which I frequently use for reference:
- Springer, Encyclopedia of mathematics
- IEC, Electropedia: The World's Online Electrotechnical Vocabulary
- IUPAC, Compendium of Chemical Terminology - The Gold book
- IUPAC, Quantities, Units and Symbols in Physical Chemistry (pdf)
- JCGM, International Vocabulary of Metrology
- IEEE, The Authoritative Dictionary of IEEE Standards Terms (requires subscription)
If you find wikipedia not clear and brief enough, try wiktionary instead. Instead of a full scale encyclopedia type site, wiktionary only provides definition and examples.
Here is the result for entering "theorem" into Wolfram alpha:
A theorem is a statement that can be demonstrated to be true by accepted mathematical operations and arguments. In general, a theorem is an embodiment of some general principle that makes it part of a larger theory. The process of showing a theorem to be correct is called a proof.
Although not absolutely standard, the Greeks distinguished between "problems" (roughly, the construction of various figures) and "theorems" (establishing the properties of said figures; Heath 1956, pp. 252, 262, and 264).
According to the Nobel Prize-winning physicist Richard Feynman, any theorem, no matter how difficult to prove in the first place, is viewed as "trivial" by mathematicians once it has been proven. Therefore, there are exactly two types of mathematical objects: trivial ones, and those which have not yet been proven.