In mathematics, a lemma is a proven statement, typically named as such to distinguish it as a truth used as a stepping stone to a larger result rather than an important statement in and of itself. Of course, some of the most powerful statements in mathematics are known as lemmas, including Zorn's lemma, Bezout's lemma , Gauss' lemma , Fatou's lemma, etc. There is no technical distinction between a lemma, a proposition, and a theorem.
The Greek word "lemma" (λεμμα) itself means "anything which is received, such as a gift, profit, or a bribe." According to [1], the plural "lemmas" is commonly used. The correct Greek plural of lemma, however, is lemmata (λεμματα). The Greek "theoria" (θεορηα) means "view, or vision" and is linguistically related to the word "theatre." The apparent relation is that a theorem is a mathematical fact which you see to be true.
See also
References
- N. Higham, Handbook of writing for the mathematical sciences, Society for Industrial and Applied Mathematics, 1998. (pp. 16)
In linguistics, and particularly in morphology, a lemma comprises the canonical form of a word. Lemmas have especial significance in highly inflected languages such as Czech.
In Terry Pratchett's Discworld series, the shadowing lemma is an animal which exists in only 2 dimensions and eats mathematicians.
