In mathematics, a proposition which terminates in theory, and which considers the properties of things already made or done; or it is a speculative proposition deduced from several definitions compared together. A theorem is a proposition to be proved by a chain of reasoning. A theorem is something to be proved; a problem is something to be done.

In algebra or analysis, it is sometimes used to denote a rule, particularly when that rule is expressed by symbols. A universal theorem, extends to any quantity without restriction. A particular theorem, extends only to a particular quantity. A negative theorem, expresses the impossibility of any assertion. A local theorem, is that which relates to a surface. A solid theorem, is that which considers a space terminated by a solid, that is, by any of the three conic sections.