Lemma

A short theorem used in proving a larger theorem. Related concepts are the axiom, porism, postulate, principle, and theorem.

The late mathematician P. Erdős has often been associated with the observation that "a mathematician is a machine for converting coffee into theorems" (e.g., Hoffman 1998, p. 7). However, this characterization appears to be due to his friend, Alfred Rényi (MacTutor, Malkevitch). This thought was developed further by Erdős' friend and Hungarian mathematician Paul Turán, who suggested that weak coffee was suitable "only for lemmas" (MacTutor, Malkevitch).

REFERENCES

Hoffman, P. The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical Truth. New York: Hyperion, 1998.

MacTutor History of Mathematics Archive. "Alfréd Rényi." http://www-history.mcs.st-andrews.ac.uk/Biographies/Renyi.html.Malkevitch, J. "The Erdős Graph." http://www.ams.org/featurecolumn/archive/networks6.html.