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:
“The little toy dog is covered with dust,
But sturdy and stanch he stands;
And the little toy soldier is red with rust,
And the musket moulds in his hands.
Time was when the little toy dog was new,
And the soldier was passing fair;
And that was the time when our Little Boy Blue
Kissed them and put them there.”
—Eugene Field (1850–1895)
“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)