I do not think -- therefore I am not. Philosophy is a game with objectives and no rules. Mathematics is a game with rules and no objectives The good Christian should beware of mathematicians and all those who make empty prophecies. The danger already exists that mathematicians have made a covenant with the devil to darken the spirit and confine man in the bonds of Hell. (St. Augustine) A math professor is one who talks in someone else's sleep. "The problems for the exam will be similar to the discussed in the class. Of course, the numbers will be different. But not all of them. Pi will still be 3.14159... " How to prove it. Guide for lecturers. Proof by vigorous handwaving: Works well in a classroom or seminar setting. Proof by forward reference: Reference is usually to a forthcoming paper of the author, which is often not as forthcoming as at first. Proof by funding: How could three different government agencies be wrong? Proof by example: The author gives only the case n = 2 and suggests that it contains most of the ideas of the general proof. Proof by omission: "The reader may easily supply the details" "The other 253 cases are analogous" Proof by deferral: "We'll prove this later in the course". Proof by picture: A more convincing form of proof by example. Combines well with proof by omission. Proof by intimidation: "Trivial." Proof by seduction: "Convince yourself that this is true! " Proof by cumbersome notation: Best done with access to at least four alphabets and special symbols. Proof by exhaustion: An issue or two of a journal devoted to your proof is useful. Proof by obfuscation: A long plotless sequence of true and/or meaningless syntactically related statements. Proof by wishful citation: The author cites the negation, converse, or generalization of a theorem from the literature to support his claims. Proof by eminent authority: "I saw Karp in the elevator and he said it was probably NP- complete." Proof by personal communication: "Eight-dimensional colored cycle stripping is NP-complete [Karp, personal communication]." Proof by reduction to the wrong problem: "To see that infinite-dimensional colored cycle stripping is decidable, we reduce it to the halting problem." Proof by reference to inaccessible literature: The author cites a simple corollary of a theorem to be found in a privately circulated memoir of the Slovenian Philological Society, 1883. Proof by importance: A large body of useful consequences all follow from the proposition in question. Proof by accumulated evidence: Long and diligent search has not revealed a counterexample. Proof by cosmology: The negation of the proposition is unimaginable or meaningless. Popular for proofs of the existence of God. Proof by mutual reference: In reference A, Theorem 5 is said to follow from Theorem 3 in reference B, which is shown to follow from Corollary 6.2 in reference C, which is an easy consequence of Theorem 5 in reference A. Proof by metaproof: A method is given to construct the desired proof. The correctness of the method is proved by any of these techniques. Proof by vehement assertion: It is useful to have some kind of authority relation to the audience. Proof by ghost reference: Nothing even remotely resembling the cited theorem appears in the reference given. Q: how many times can you subtract 7 from 83, and what is left afterwards? A: I can subtract it as many times as I want, and it leaves 76 every time. Q: Why did the chicken cross the Moebius strip? A: To get to the other ... er, um ... Q: Did you hear the one about the statistician? A: Probably.... How many mathematical logicians does it take to replace a lightbulb?? None: They can't do it, but they can prove that it can be done. How many numerical analysts does it take to replace a lightbulb?? 3.9967: (after six iterations). How many classical geometers does it take to replace a lightbulb?? None: You can't do it with a straight edge and a compass. A SLICE OF PI ****************** 3.14159265358979 1640628620899 23172535940 881097566 5432664 09171 036 5 If (1+x) (real close to 1) Is raised to the power of 1 Over x, you will find Here's the value defined: 2.718281...