在一個普普通通的定義上較勁，卻又不肖理會一下整個數學界的基本共識。這就是中國人的任性之處。事實上，在所有的真命題當中，能夠滿足其逆命題也為真的比率應當等於零（溪大炮知道為什麼嗎？）。這樣的東西很少，畢德格拉斯定理（勾股定理）恰好是這樣的一個定理，即其逆定理也成立。因此，溪大炮的說法純屬瞎掰。不過，俺挺喜歡溪大炮的，就像革命黨人喜歡孫大炮的道理差不多。
以下是網上（http://mathworld.wolfram.com/Theorem.html）關於定理（theorem）的定義，並沒有要求其逆定理也必須成立，才配稱為定理一說。 A theorem is a statement that can be demonstrated to be true by accepted mathematical operations and arguments. In general, a theorem is an embodiment of some general principle that makes it part of a larger theory. The process of showing a theorem to be correct is called a proof. Although not absolutely standard, the Greeks distinguished between "problems" (roughly, the construction of various figures) and "theorems" (establishing the properties of said figures; Heath 1956, pp. 252, 262, and 264)。 According to the Nobel Prize-winning physicist Richard Feynman (1985), any theorem, no matter how difficult to prove in the first place, is viewed as "trivial" by mathematicians once it has been proven. Therefore, there are exactly two types of mathematical objects: trivial ones, and those which have not yet been proven. 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). R. Graham has estimated that upwards of  mathematical theorems are published each year (Hoffman 1998, p. 204). |
