In mathematics, a toy theorem is a simplified version of a more general theorem. For instance, by introducing some simplifying assumptions in a theorem, one obtains a toy theorem.
Usually, a toy theorem is used to illustrate the claim of a theorem. It can also be insightful to study proofs of a toy theorem derived from a non-trivial theorem. Toy theorems can also have education value. After presenting a theorem (with, say, a highly non-trivial proof), one can sometimes give some assurance that the theorem really holds, by proving a toy version of the theorem.
For instance, a toy theorem of the Brouwer fixed point theorem is obtained by restricting the dimension to one. In this case, the Brouwer fixed point theorem follows almost immediately from the intermediate value theorem.
Famous quotes containing the words toy and/or theorem:
“As the creative adult needs to toy with ideas, the child, to form his ideas, needs toys—and plenty of leisure and scope to play with them as he likes, and not just the way adults think proper. This is why he must be given this freedom for his play to be successful and truly serve him well.”
—Bruno Bettelheim (20th century)
“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (1913–1960)