M__________________________________________________________________________ Theorem : All positive integers are equal. Proof : Sufficient to show that for any two positive integers, A and B, A = B. Further, it is sufficient to show that for all N > 0, if A and B (positive integers) satisfy (MAX(A, B) = N) then A = B. Proceed by induction. If N = 1, then A and B, being positive integers, must both be 1. So A = B. Assume that the theorem is true for some value k. Take A and B with MAX(A, B) = k+1. Then MAX((A-1), (B-1)) = k. And hence (A-1) = (B-1). Consequently, A = B. M__________________________________________________________________________ From: Benjamin.J.Tilly@dartmouth.edu (Benjamin J. Tilly) Theorem : All numbers are equal to zero. Proof: Suppose that a=b. Then a = b a^2 = ab a^2 - b^2 = ab - b^2 (a + b)(a - b) = b(a - b) a + b = b a = 0 M__________________________________________________________________________ From: Michael_Ketzlick@h2.maus.de (Michael Ketzlick) Theorem : 3=4 Proof: Suppose: a + b = c This can also be written as: 4a - 3a + 4b - 3b = 4c - 3c After reorganising: 4a + 4b - 4c = 3a + 3b - 3c Take the constants out of the brackets: 4 * (a+b-c) = 3 * (a+b-c) Remove the same term left and right: 4 = 3 M__________________________________________________________________________ From: Benjamin.J.Tilly@dartmouth.edu (Benjamin J. Tilly) Theorem: 1$ = 1c. Proof: And another that gives you a sense of money disappearing... 1$ = 100c = (10c)^2 = (0.1$)^2 = 0.01$ = 1c Here $ means dollars and c means cents. This one is scary in that I have seen PhD's in math who were unable to see what was wrong with this one. Actually I am crossposting this to sci.physics because I think that the latter makes a very nice introduction to the importance of keeping track of your dimensions... M__________________________________________________________________________ From: clubok@physics11 (Kenneth S. Clubok) Theorem: 1 = -1 . Proof: 1 -1 -- = -- -1 1 1 -1 sqrt[ -- ] = sqrt[ -- ] -1 1 sqrt[1] sqrt[-1] ------- = ------- sqrt[-1] sqrt[1] 1=-1 (by cross-multiplication) And here's my personal favorite: Use integration by parts to find the anti-derivative of 1/x. One can get the amusing result that 0=1. (Until you realize you have to put in the limits.) M__________________________________________________________________________ From: jreimer@aol.com (JReimer) Theorem: 1 = -1 Proof: 1 = sqrt(1) = sqrt(-1 * -1) = sqrt(-1) * sqrt(-1) = 1^ = -1 Also one can disprove the axiom that things equal to the same thing are equal to each other. 1 = sqrt(1) -1 = sqrt(1) therefore 1 = -1 M__________________________________________________________________________ From: kdq@marsupial.jpl.nasa.gov (Kevin D. Quitt) Theorem: 4 = 5 Proof: 16 - 36 = 25 - 45 4^2 - 9*4 = 5^2 - 9*5 4^2 - 9*4 + 81/4 = 5^2 - 9*5 + 81/4 (4 - 9/2)^2 = (5 - 9/2)^2 4 - 9/2 = 5 - 9/2 4 = 5 M__________________________________________________________________________ baez@guitar.ucr.edu (john baez) writes: Theorem: 1 + 1 = 2 Proof: n(2n - 2) = n(2n - 2) n(2n - 2) - n(2n - 2) = 0 (n - n)(2n - 2) = 0 2n(n - n) - 2(n - n) = 0 2n - 2 = 0 2n = 2 n + n = 2 or setting n = 1 1 + 1 = 2 M__________________________________________________________________________ From: magidin@uclink.berkeley.edu (Arturo Viso Magidin) Theorem: In any finite set of women, if one has blue eyes then they all have blue eyes. Proof. Induction on the number of elements. if n= or n=1 it is immediate. Assume it is true for k Consider a group with k+1 women, and without loss of generality assume the first one has blue eyes. I will represent one with blue eyes with a '*' and one with unknown eye color as @. You have the set of women: {*,@,...,@} with k+1 elements. Consider the subset made up of the first k. This subset is a set of k women, of which one has blue eyes. By the induction hypothesis, all of them have blue eyes. We have then: {*,...,*,@}, with k+1 elements. Now consider the subset of the last k women. This is a set of k women, of which one has blue eyes (the next-to-last element of the set), hence they all have blue eyes, in particular the k+1-th woman has blue eyes. Hence all k+1 women have blue eyes. By induction, it follows that in any finite set of women, if one has blue eyes they all have blue eyes. QED M__________________________________________________________________________ From: Zorro Theorem: All positive integers are interesting. Proof: Assume the contrary. Then there is a lowest non-interesting positive integer. But, hey, that's pretty interesting! A contradiction. QED I heard this one from G. B. Thomas, but I don't know whether it is due to him. M__________________________________________________________________________ From: daniel@hagar.ph.utexas.edu (James Daniel) Aren't multi-valued functions fun? Once you realize what's going on, though, you can make them into silly proofs pretty much without thinking. Here's one I just made up: Object: to prove that i < 0 ( that is, sqrt(-1) < 0 ) Well, ( .5 + sqrt(3/4)*i )^3 = (-1)^3 (most would assert this to be a false statement -- mostly cuz they'll get the math wrong. It's a true statement. It's the next statement that is false.) which means that .5 + sqrt(3/4)*i = -1 So then 1 + sqrt(3)*i = -2 sqrt(3)*i = -1 i = -1/sqrt(3) Therefore i is a negative number. QED. M__________________________________________________________________________ From: julison@cco.caltech.edu (Julian C. Jamison) Theorem: All numbers are equal. Proof: Choose arbitrary a and b, and let t = a + b. Then a + b = t (a + b)(a - b) = t(a - b) a^2 - b^2 = ta - tb a^2 - ta = b^2 - tb a^2 - ta + (t^2)/4 = b^2 - tb + (t^2)/4 (a - t/2)^2 = (b - t/2)^2 a - t/2 = b - t/2 a = b So all numbers are the same, and math is pointless. M__________________________________________________________________________ From: pfc@math.ufl.edu (P. Fritz Cronheim) This one is from Jerry King's _Art of Mathematics_ 16/64=1/4 by cancelling the 6's. Here the result is true, but the method is not. Do the ends justify the means? :)_ M__________________________________________________________________________ Methods of Mathematical Proof This is from _A Random Walk in Science_ (by Joel E. Cohen?): To illustrate the various methods of proof we give an example of a logical system. THE PEJORATIVE CALCULUS Lemma 1. All horses are the same colour. (Proof by induction) Proof. It is obvious that one horse is the same colour. Let us assume the proposition P(k) that k horses are the same colour and use this to imply that k+1 horses are the same colour. Given the set of k+1 horses, we remove one horse; then the remaining k horses are the same colour, by hypothesis. We remove another horse and replace the first; the k horses, by hypothesis, are again the same colour. We repeat this until by exhaustion the k+1 sets of k horses have been shown to be the same colour. It follows that since every horse is the same colour as every other horse, P(k) entails P(k+1). But since we have shown P(1) to be true, P is true for all succeeding values of k, that is, all horses are the same colour. Theorem 1. Every horse has an infinite number of legs. (Proof by intimidation.) Proof. Horses have an even number of legs. Behind they have two legs and in front they have fore legs. This makes six legs, which is cer- tainly an odd number of legs for a horse. But the only number that is both odd and even is infinity. Therefore horses have an infinite num- ber of legs. Now to show that this is general, suppose that somewhere there is a horse with a finite number of legs. But that is a horse of another colour, and by the lemma that does not exist. Corollary 1. Everything is the same colour. Proof. The proof of lemma 1 does not depend at all on the nature of the object under consideration. The predicate of the antecedent of the uni- versally-quantified conditional 'For all x, if x is a horse, then x is the same colour,' namely 'is a horse' may be generalized to 'is anything' without affecting the validity of the proof; hence, 'for all x, if x is anything, x is the same colour.' Corollary 2. Everything is white. Proof. If a sentential formula in x is logically true, then any parti- cular substitution instance of it is a true sentence. In particular then: 'for all x, if x is an elephant, then x is the same colour' is true. Now it is manifestly axiomatic that white elephants exist (for proof by blatant assertion consult Mark Twain 'The Stolen White Ele- phant'). Therefore all elephants are white. By corollary 1 everything is white. Theorem 2. Alexander the Great did not exist and he had an infinite number of limbs. Proof. We prove this theorem in two parts. First we note the obvious fact that historians always tell the truth (for historians always take a stand, and therefore they cannot lie). Hence we have the historically true sentence, 'If Alexander the Great existed, then he rode a black horse Bucephalus.' But we know by corollary 2 everything is white; hence Alexander could not have ridden a black horse. Since the conse- quent of the conditional is false, in order for the whole statement to be true the antecedent must be false. Hence Alexander the Great did not exist. We have also the historically true statement that Alexander was warned by an oracle that he would meet death if he crossed a certain river. He had two legs; and 'forewarned is four-armed.' This gives him six limbs, an even number, which is certainly an odd number of limbs for a man. Now the only number which is even and odd is infinity; hence Alexander had an infinite number of limbs. We have thus proved that Alexander the Great did not exist and that he had an infinite number of limbs. M__________________________________________________________________________ Theorem: a cat has nine tails. Proof: No cat has eight tails. A cat has one tail more than no cat. Therefore, a cat has nine tails. M__________________________________________________________________________ From: rmaimon@husc9.Harvard.EDU (Ron Maimon) Theorem: All dogs have nine legs. Proof: would you agree that no dog has five legs? would you agree that _a_ dog has four legs more then _no_ dog? 4 + 5 = ? ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ =2.2 STATISTICS AND STATISTICANS M__________________________________________________________________________ Did you hear the one about the statistician? Probably.... M__________________________________________________________________________ Statistics means never having to say you're certain. [With apologies to Erich Segal] M__________________________________________________________________________ In earlier times, they had no statistics, and so they had to fall back on lies. - STEPHEN LEACOCK M__________________________________________________________________________ "The group was alarmed to find that if you are a labourer, cleaner or dock worker, you are twice as likely to die than a member of the professional classes" [The Sunday Times 31st August 1980] M__________________________________________________________________________ From: ph2008@mail.bris.ac.uk (CJ. Bradfield) Statistics is the art of never having to say you're wrong. Variance is what any two staticticians are at. (Not that I particularly dislike statisticians... I hate all mathematicians!!) [sorry mum!] M__________________________________________________________________________ 97.3% of all statistics are made up. M__________________________________________________________________________ it's like the tale of the roadside merchant who was asked to explain how he could sell rabbit sandwiches so cheap. "Well" he explained, "I have to put some horse-meat in too. But I mix them 50:50. One horse, one rabbit." [DARREL HUFF, How to lie with statistics] M__________________________________________________________________________ Are statisticians normal? M__________________________________________________________________________ From: joeshmoe@world.std.com (Jascha Franklin-Hodge) (List of Taglines) Smoking is a leading cause of statistics. I could prove God statistically. 43% of all statistics are worthless. "There are lies, damned lies, and statistics." -Mark Twain 3 out of 4 Americans make up 75% of the population. Death is 99 per cent fatal to laboratory rats. M__________________________________________________________________________ Did you know that the great majority of people have more than the average number of legs? [It's obvious really; amongst the 57 million people in Britain there are probably 5,000 people who have only got one leg. Therefore the average number of legs is (5000 * 1) + (56,995,000 * 2) ---------------------------------- = 1.9999123...... 57,000,000 Since most people have 2 legs....... ] M__________________________________________________________________________ A statistician is a person who draws a mathematically precise line from an unwarranted asumption to a foregone conclusion. M__________________________________________________________________________ A statistician can have his head in an oven and his feet in ice, and he will say that on the average he feels fine. M__________________________________________________________________________ From: Chris Morton (mortoncp@nextwork.rose-hulman.edu) do it collection Statisticians do it continuously but discretely. Statisticians do it when it counts. Statisticians do it with 95% confidence. Statisticians do it with large numbers. Statisticians do it with only a 5% chance of being rejected. Statisticians do it with two-tail T tests. Statisticians do it. After all, it's only normal. Statisticians probably do it. M__________________________________________________________________________ From: Mathematics Magazine, December 1990. Subject: Statisticians ( Excerpted from "Quotes, Damned Quotes" by John Bibby ) If there is a 50-50 chance that something can go wrong, then 9 times out of ten it will. (Paul Harvey News, 1979) ``Give us a copper Guv'' said the beggar to the Treasury statistician, when he waylaid him in Parliament square. ``I haven't eaten for three days.'' ``Ah,'' said the statistician, ``and how does that compare with the same period last year?'' (Russell Lewis) ``I gather, young man, that you wish to be a Member of Parliament. The first lesson that you must learn is, when I call for statistics about the rate of infant mortality, what I want is proof that fewer babies died when I was Prime Minister than when anyone else was Prime Minister. That is a political statistic.'' (Winston Churchill) ``You haven't told me yet,'' said Lady Nuttal, ``what it is your fiance does for a living.'' ``He's a statistician,'' replied Lamia, with an annoying sense of being on the defensive. Lady Nuttal was obviously taken aback. It had not occurred to her that statisticians entered into normal social relationships. The species, she would have surmised, was perpetuated in some collateral manner, like mules. ``But Aunt Sara, it's a very interesting profession,'' said Lamia warmly. ``I don't doubt it,'' said her aunt, who obviously doubted it very much. ``To express anything important in mere figures is so plainly impossible that there must be endless scope for well-paid advice on the how to do it. But don't you think that life with a statistician would be rather, shall we say, humdrum?'' Lamia was silent. She felt reluctant to discuss the surprising depth of emotional possibility which she had discovered below Edward's numerical veneer. ``It's not the figures themselves,'' she said finally. ``It's what you do with them that matters.'' (K.A.C. Manderville, The undoing of Lamia Gurdleneck) M__________________________________________________________________________ People who do very unusual jobs: the man who counts then number of people at public gatherings. You've probably seen his headlines, "Two million flock to see Pope.", "200 arrested as police find ounce of cannabis.", "Britain #3 billion in debt". You probably wondered who was responsible for producing such well rounded-up figures. What you didn't know was that it was all the work of one man, Rounder-Up to the media, John Wheeler. But how is he able to go on turning out such spot-on statistics? How can he be so accurate all the time? "We can't" admits Wheeler blithely. "Frankly, after the first million we stop counting, and round it up to the next million. I don't know if you've ever counted a papal flock, but, not only do they look a bit the same, they also don't keep still, what with all the bowing and crossing themselves." "The only way you could do it accurately is by taking an aerial photograph of the crowd and handing it to the computer to work out. But then you'd get a headline saying "1,678,163 [sic] flock to see Pope, not including 35,467 who couldn't see him", and, believe me, nobody wants that sort of headline." The art of big figures, avers Wheeler, lies in psychology, not statistics. The public like a figure it can admire. It likes millionaires, and million-sellers, and centuries at cricket, so Wheeler's international agency gives them the figures it wants, which involves not only rounding up but rounding down. "In the old days people used to deal with crowds on the Isle of Wight principle -- you know, they'd say that every day the population of the world increased by the number of people who could stand upright on the Isle of Wight, or the rain-forests were being decreased by an area the size of Rutland. This meant nothing. Most people had never been to the Isle of Wight for a start, and even if they had, they only had a vision of lots of Chinese standing in the grounds of the Cowes Yacht Club. And the Rutland comparison was so useless that they were driven to abolish Rutland to get rid of it. "No, what people want is a few good millions. A hundred million, if possible. One of our inventions was street value, for instance. In the old days they used to say that police had discovered drugs in a quantity large enough to get all of Rutland stoned for a fortnight. *We* started saying that the drugs had a street value of #10 million. Absolutely meaningless, but people understand it better." Sometimes they do get the figures spot on. "250,000 flock to see Royal two", was one of his recent headlines, and although the 250,000 was a rounded-up figure, the two was quite correct. in his palatial office he sits surrounded by relics of past headlines - a million-year-old fossil, a #500,000 Manet, a photograph of the Sultan of Brunei's #10,000,000 house - but pride of place goes to a pair of shoes framed on the wall. "Why the shoes? Because they cost me #39.99. They serve as a reminder of mankind's other great urge, to have stupid odd figures. Strange, isn't it? They want mass demos of exactly half a million, but they also want their gramophone records to go round at thirty-three-and-a-third, forty-five and seventy-eight rpm. We have stayed in business by remembering that below a certain level people want oddity. They don't a rocket costing #299 million and 99p, and they don't want a radio costing exactly #50." How does he explain the times when the figures clash - when, for example, the organisers of a demo claim 250,000 but the police put it nearer 100,000? "We provide both sets of figures; the figures the organisers want, and the figures the police want. The public believe both. If we gave the true figure, about 167,890, nobody would believe it because it doesn't sound believable." John Wheeler's name has never become well-known, as he is a shy figure, but his firm has an annual turnover of #3 million and his eye for the right figure has made him a rich man. His greatest pleasure, however, comes from the people he meets in the counting game. "Exactly two billion, to be precise." MILES KINGTON writing in The Observer, 3 November 1986 M__________________________________________________________________________ From: goble@infonaut.com (Clark Goble) You know how dumb the average guy is? Well, by definition, half of them are even dumber than that. -- J.R. "Bob" Dobbs *M_________________________________________________________________________ From: Kirk Lindberg (kalindberg@mmm.com) Q: What is the definition of a statistician? A: Someone who doesn't have the personality to be an accountant. *M_________________________________________________________________________ Did you hear about the Statistician that couldn't get laid? He decided a simulation was good enough. *M_________________________________________________________________________ From: rogers@sasuga.Hi.COM (Andrew Rogers) "She was only the statistician's daughter, but she knew all the standard deviations." *M_________________________________________________________________________ From: en4bmhd@bs47c.staffs.ac.uk (Hendrik De Vloed) All probabilities are 50% ... either something happens, or it doesn't! From: brc2@Lehigh.EDU Correction... My doctor told me I only have a 50% chance of making it- but he said there's only a 15% of even that. *M_________________________________________________________________________ From: ahilditc@awadi.com.au & ts@uwasa.fi (Timo Salmi) & Juhani Heino A:I'll bet that 99% of people who read the question don't! T:That's a mean thing to say. J:Yes, it was. I guess that person is too regressed. As a matter of fact, I'm 75.4 % sure about that. T:Incidentally, did you know that using non-linear regression in research is currently out of line. *M________________________________________________________________________ From: jlevine@rd.hydro.on.ca (Jody Levine) 80% of all statistics quoted to prove a point are made up on the spot. *M________________________________________________________________________ From: Sunita Saini A stats major was completely hung over the day of his final exam. It was a True/False test, so he decided to flip a coin for the answers. The stats professor watched the student the entire two hours as he was flipping the coin...writing the answer...flipping the coin...writing the answer. At the end of the two hours, everyone else had left the final except for the one student. The professor walks up to his desk and interrupts the student, saying: "Listen, I have seen that you did not study for this statistics test, you didn't even open the exam. If you are just flipping a coin for your answer, what is taking you so long? The student replies bitterly (as he is still flipping the coin): " Shhh! I am checking my answers!" ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ =2.3 MATHEMATICIANS From: Hugh Robinson Okay, here's mine. I am told that it's true, but... A certain well-known pure mathematician had a wife who, while intelligent, was not into mathematics. However, by continued practice, she learnt to distinguish between the conversations of algebraists and analysts. So when he had guests to dinner who were talking about mathematics, if they were analysts, she would introduce at a suitable pause in the conversation: "But what happens at the boundary?" Whereas, if they were algebraists, she would say: "But do the roots lie in the field?" By this means she was always able to impress his visitors by her knowledge of mathematics. (No, don't write and ask for the punchline. That's all.) M__________________________________________________________________________ Three men are in a hot-air balloon. Soon, they find themselves lost in a canyon somewhere. One of the three men says, "I've got an idea. We can call for help in this canyon and the echo will carry our voices far." So he leans over the basket and yells out, "Helllloooooo! Where are we?" (They hear the echo several times.) 15 minutes later, they hear this echoing voice: "Helllloooooo! You're lost!!" One of the men says, "That must have been a mathematician." Puzzled, one of the other men asks, "Why do you say that?" The reply: "For three reasons. (1) he took a long time to answer, (2) he was absolutely correct, and (3) his answer was absolutely useless." M__________________________________________________________________________ A small, 14-seat plane is circling for a landing in Atlanta. It's totally fogged in, zero visibility, and suddenly there's a small electrical fire in the cockpit which disables all of the instruments and the radio. The pilot continues circling, totally lost, when suddenly he finds himself flying next to a tall office building. He rolls down the window (this particular airplane happens to have roll-down windows) and yells to a person inside the building, "Where are we?" The person responds "In an airplane!" The pilot then banks sharply to the right, circles twice, and makes a perfect landing at Atlanta International. As the passengers emerge, shaken but unhurt, one of them says to the pilot, "I'm certainly glad you were able to land safely, but I don't understand how the response you got was any use." "Simple," responded the pilot. "I got an answer that was completely accurate and totally irrelevant to my problem, so I knew it had to be the IBM building." M__________________________________________________________________________ Mathematicians are like Frenchmen: whatever you say to them they translate into their own language and forthwith it is something entirely different. (Johann Wolfgang von Goethe) M__________________________________________________________________________ Old mathematicians never die; they just lose some of their functions. From: Tim.Nelson@Canada.ATTGIS.COM (list of Old * Never Die, they just) OLD MATH TEACHERS never die, they just reduce to lowest terms OLD MATHEMATICIANS never die, they just disintegrate OLD MATHEMATICIANS never die, they just go off on a tangent OLD NUMERICAL ANALYSTS never die, they just get disarrayed OLD TRIGONOMETRY TEACHERS never die, they just lose their identities M__________________________________________________________________________ From: banghar4@studentb.msu.edu (Rick Banghart) Two math professors are in a restaurant. One argues that the average person does not know any math beyond high school. The other argues that the average person knows some more advanced math. Just then, the first one gets up to use the rest room. The second professor calls over his waitress and says, "When you bring our food, I'm going to ask you a mathematical question. I want you to answer, 'One third x cubed.' Can you do that?" The waitress says, "I don't know if I can remember that. One thurr... um..." "One third x cubed," says the prof. "One thir dex cue?," asks the waitress. "One" "One" "Third" "Third" "X" "X" "Cubed" "Cubed" "One third X cubed" "One third X cubed" The waitress leaves, and the other professor comes back. They resume their conversation until a few minutes later when the waitress brings their food. The professor says to the waitress, "Say, do you mind if I ask you something?" "Not at all" "Can you tell me what the integral of x squared dx is?" The waitress pauses, then says, "One third x cubed." As she walks away, she stops, turns, and adds, "Plus a constant!" M__________________________________________________________________________ Some famous mathematician was to give a keynote speech at a conference. Asked for an advance summary, he said he would present a proof of Fermat's Last Theorem -- but they should keep it under their hats. When he arrived, though, he spoke on a much more prosaic topic. Afterwards the conference organizers asked why he said he'd talk about the theorem and then didn't. He replied this was his standard practice, just in case he was killed on the way to the conference. M__________________________________________________________________________ How many mathematicians does it take to screw in a lightbulb? One, who gives it to six Californians, thereby reducing it to an earlier riddle. -- from a button I bought at Nancy Lebowitz's table at Boskone Q: How many topologists does it take to change a light bulb? A: It really doesn't matter, since they'd rather knot. From:BRIAN6@VAXC.MDX.AC.UK (who has a lightbulb collection) Q: How many mathematicians does it take to screw in a lightbulb? A: None. It's left to the reader as an exercise. A: Just one, once you've managed to present the problem in terms he/she is familiar with. In earlier work, Wiener [1] has shown that one mathematician can change a light bulb. If k mathematicians can change a light bulb, and if one more simply watches them do it, then k+1 mathematicians will have changed the light bulb. Therefore, by induction, for all n in the positive integers, n mathematicians can change a light bulb. Bibliography: [1] Weiner, Matthew P., <11485@ucbvax>, "Re: YALBJ", 1986 Q: How many statisticians does it take to change a lightbulb ? A: This should be determined using a nonparametric procedure, since statisticians are NOT NORMAL. A: Walt Pirie to hold the bulb and one psychologist, one economist, one sociologist and one anthroplogist to pull away the ladder. A: One -- plus or minus three (small sample size). (Notes: Someone has been asking this as a bonus question on statistics exam papers for quite a while. Judging from some of his own students' exam answers, it depends on whether the lightbulb is negatively or positively screwed.) Q: How many light bulbs does it take to change a light bulb? A: One, if it knows its own Goedel number. (Could somebody please explain this one to me ! I think it's something to do with the maths/logic theories of Kurt Goedel, about it being impossible to prove things.) M__________________________________________________________________________ "A mathematician is a device for turning coffee into theorems" -- P. Erdos M__________________________________________________________________________ Moebius always does it on the same side. Statisticians probably do it Algebraists do it in groups. (Logicians do it) or [not (logicians do it)]. From: Chris Morton (mortoncp@nextwork.rose-hulman.edu) do it collection Logicians do it consistently and completely. Mathematicians do it associatively. Mathematicians do it commutatively. Mathematicians do it constantly. Mathematicians do it continuously. Mathematicians do it discretely. Mathematicians do it exponentially. Mathematicians do it forever if they can do one and can do one more. Mathematicians do it functionally. Mathematicians do it homologically. Mathematicians do it in fields. Mathematicians do it in groups. Mathematicians do it in imaginary planes. Mathematicians do it in numbers. Mathematicians do it in theory. Mathematicians do it on smooth contours. Mathematicians do it over and under the curves. Mathematicians do it parallel and perpendicular. Mathematicians do it partially. Mathematicians do it rationally. Mathematicians do it reflexively. Mathematicians do it symmetrically. Mathematicians do it to prove themselves. Mathematicians do it to their limits. Mathematicians do it totally. Mathematicians do it transcendentally. Mathematicians do it transitively. Mathematicians do it variably. Mathematicians do it with Nobel's wife. Mathematicians do it with a Minkowski sausage. Mathematicians do it with imaginary parts. Mathematicians do it with linear pairs. Mathematicians do it with odd functions. Mathematicians do it with prime roots. Mathematicians do it with relations. Mathematicians do it with rings. Mathematicians do it with their real parts. Mathematicians do it without limit. Mathematicians do over an open unmeasurable interval. Mathematicians have to prove they did it. Set theorists do it with cardinals. M__________________________________________________________________________ A mathematician is a person who says that, when 3 people are supposed to be in a room but 5 came out, 2 have to go in so the room gets empty... M__________________________________________________________________________ My geometry teacher was sometimes acute, and sometimes obtuse, but always, he was right. MP_________________________________________________________________________ From: lyon@netcom.com (Lyman Lyon) Physics professor is walking across campus, runs into Math Professor. Physics professor has been doing an experiment, and has worked out an emphirical equation that seems to explain his data, and asks the Math professor to look at it. A week later, they meet again, and the Math professor says the equation is invalid. By then, the Physics professor has used his equation to predict the results of further experiments, and he is getting excellent results, so he askes the Math professor to look again. Another week goes by, and they meet once more. The Math professor tells the Physics professor the equation does work, "But only in the trivial case where the numbers are real and positive." M__________________________________________________________________________ From: gw@molly.informatik.Uni-Koeln.DE (Georg Wambach) What is the difference between an applied mathematician and a pure mathematician? Suppose a mathematician parks his car, locks it with his key and walks away. After walking about 50 yards the mathematician realizes that he has dropped his key somewhere along the way. What does he do? If he is an applied mathematician he walks back to the car along the path he has previously traveled looking for his key. If he is a pure mathematician he walks to the other end of the parking lot where there is better light and looks for his key there. I told this joke to my brother (he is a "pure"). He answers: "But we have not dropped our keys!" Hence, I suggest a slight modification: Suppose a _tax_payer_ parks his car, locks it with his key and walks away. After walking about 50 yards the tax payer realizes that he has dropped his key somewhere along the way. He asked a mathematician to help him. What does the mathematician do? (...) +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ =2.4 POETRY M__________________________________________________________________________ From: chrisman@ucdmath.ucdavis.edu (Mark Chrisman) "Aleph-0 bottles of beer on the wall, Aleph-0 bottles of beer; Take one down, pass it around, Aleph-0 bottles of beer on the wall! Aleph-0 bottles of beer on the wall..." M__________________________________________________________________________ One and one make two, But if one and one should marry, Isn't it queer- Within a year There's two and one to carry. M__________________________________________________________________________ Geometry keeps you in shape. Decimals make a point. Einstein was ahead of his time. Lobachevski was out of line. M__________________________________________________________________________ "IF" (School Maths version) =========================== If you can solve a literal equation And rationalise denominator surds, Do grouping factors (with a transformation) And state the factor theorem in words; If you can plot the graph of any function And do a long division (with gaps), Or square binomials without compunction Or work cube roos with logs without mishaps. If you possess a sound and clear-cut notion Of interest sums with P and I unknown; If you can find the speed of trains in motion, Given some lengths and "passing-times" alone; If you can play with R (both big and little) And feel at home with l (or h) and Pi, And learn by cancellation how to whittle Your fractions down till they delight the eye. If you can recognise the segment angles Both at the centre and circumference; If you can spot equivalent triangles And Friend Pythagoras (his power's immmense); If you can see that equiangularity And congruence are two things and not one, You may pick up a mark or two in charity And, what is more, you may squeeze through, my son. [Times Educational Supplement 19th July 1947] M__________________________________________________________________________ This poem was written by Jon Saxton (an author of math textbooks). ((12 + 144 + 20 + (3 * 4^(1/2))) / 7) + (5 * 11) = 9^2 + 0 Or for those who have trouble with the poem: A Dozen, a Gross and a Score, plus three times the square root of four, divided by seven, plus five times eleven, equals nine squared and not a bit more. M__________________________________________________________________________ 'Tis a favorite project of mine A new value of pi to assign. I would fix it at 3 For it's simpler, you see, Than 3 point 1 4 1 5 9. ("The Lure of the Limerick" by W.S. Baring-Gould, p.5. Attributed to Harvey L. Carter). M__________________________________________________________________________ If inside a circle a line Hits the center and goes spine to spine And the line's length is "d" the circumference will be d times 3.14159 M__________________________________________________________________________ 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... M__________________________________________________________________________ Here's a limerick I picked up off the net a few years back - looks better on paper. 3_ \/3 / | 2 3 X pi 3_ | z dz X cos(--------) = ln (\/e ) | 9 / 1 Which, of course, translates to: Integral z-squared dz from 1 to the cube root of 3 times the cosine of three pi over 9 equals log of the cube root of 'e'. And it's correct, too. M__________________________________________________________________________ Not a joke, but a humorous ditty I heard from some guys in an engineering fraternity (to the best of my recollection): I'll do it phonetically: ee to the ex dee ex, ee to the why dee why, sine x, cosine x, natural log of y, derivative on the left derivative on the right integrate, integrate, fight! fight! fight! M__________________________________________________________________________ Other cheers: E to the x dx dy radical transcendental pi secant cosine tangent sine 3.14159 2.71828 come on folks let's integrate!! M__________________________________________________________________________ E to the i dx dy E to y dy cosine secant log of pi disintegrate em RPI !!! M__________________________________________________________________________ square root, tangent hyperbolic sine, 3.14159 e to the x, dy, dx, sliderule, slipstick, TECH TECH TECH! M__________________________________________________________________________ e to the u, du/dx e to the x dx cosine, secant, tangent, sine, 3.14159 integral, radical, u dv, slipstick, slide rule, MIT! M__________________________________________________________________________ E to the X D-Y, D-X E to the X D-X. Cosine, Secant, Tangent, Sine 3.14159 E-I, Radical, Pi Fight'em, Fight'em, WPI! Go Worcester Polytechnic Institute!!!!!! M__________________________________________________________________________ Hiawatha Designs an Experiment Hiawatha, mighty hunter, He could shoot ten arrows upward, Shoot them with such strength and swiftness That the last had left the bow-string Ere the first to earth descended. This was commonly regarded As a feat of skill and cunning. Several sarcastic spirits Pointed out to him, however, That it might be much more useful If he sometimes hit the target. "Why not shoot a little straighter And employ a smaller sample?" Hiawatha, who at college Majored in applied statistics, Consequently felt entitled To instruct his fellow man In any subject whatsoever, Waxed exceedingly indignant, Talked about the law of errors, Talked about truncated normals, Talked of loss of information, Talked about his lack of bias, Pointed out that (in the long run) Independent observations, Even though they missed the target, Had an average point of impact Very near the spot he aimed at, With the possible exception of a set of measure zero. "This," they said, "was rather doubtful; Anyway it didn't matter. What resulted in the long run: Either he must hit the target Much more often than at present, Or himself would have to pay for All the arrows he had wasted." Hiawatha, in a temper, Quoted parts of R. A. Fisher, Quoted Yates and quoted Finney, Quoted reams of Oscar Kempthorne, Quoted Anderson and Bancroft (practically in extenso) Trying to impress upon them That what actually mattered Was to estimate the error. Several of them admitted: "Such a thing might have its uses; Still," they said, "he would do better If he shot a little straighter." Hiawatha, to convince them, Organized a shooting contest. Laid out in the proper manner Of designs experimental Recommended in the textbooks, Mainly used for tasting tea (but sometimes used in other cases) Used factorial arrangements And the theory of Galois, Got a nicely balanced layout And successfully confounded Second order interactions. All the other tribal marksmen, Ignorant benighted creatures Of experimental setups, Used their time of preparation Putting in a lot of practice Merely shooting at the target. Thus it happened in the contest That their scores were most impressive With one solitary exception. This, I hate to have to say it, Was the score of Hiawatha, Who as usual shot his arrows, Shot them with great strength and swiftness, Managing to be unbiased, Not however with a salvo Managing to hit the target. "There!" they said to Hiawatha, "That is what we all expected." Hiawatha, nothing daunted, Called for pen and called for paper. But analysis of variance Finally produced the figures Showing beyond all peradventure, Everybody else was biased. And the variance components Did not differ from each other's, Or from Hiawatha's. (This last point it might be mentioned, Would have been much more convincing If he hadn't been compelled to Estimate his own components From experimental plots on Which the values all were missing.) Still they couldn't understand it, So they couldn't raise objections. (Which is what so often happens with analysis of variance.) All the same his fellow tribesmen, Ignorant benighted heathens, Took away his bow and arrows, Said that though my Hiawatha Was a brilliant statistician, He was useless as a bowman. As for variance components Several of the more outspoken Make primeval observations Hurtful of the finer feelings Even of the statistician. In a corner of the forest Sits alone my Hiawatha Permanently cogitating On the normal law of errors. Wondering in idle moments If perhaps increased precision Might perhaps be sometimes better Even at the cost of bias, If one could thereby now and then Register upon a target. W. E. Mientka, "Professor Leo Moser -- Reflections of a Visit" American Mathematical Monthly, Vol. 79, Number 6 (June-July, 1972) M__________________________________________________________________________ A mathematician named Klein Thought the Mobius Band was divine. Said he, "If you glue The edges of two You get a weird bottle like mine." M__________________________________________________________________________ A challenge for many long ages Had baffled the savants and sages. Yet at last came the light: Seems old Fermat was right-- To the margin add 200 pages. -- Paul Chernoff M__________________________________________________________________________ _There Once Was a Breathy Baboon_ by Sir Arthur Eddington There once was a breathy baboon Who always breathed down a bassoon, For he said, "It appears That in billions of years I shall certainly hit on a tune." +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ =2.5 QUOTES M__________________________________________________________________________ From: ph2008@mail.bris.ac.uk (CJ. Bradfield)philosophy: A few of my favourite quotes about mathematics: "A mathematician is a blind man in a dark room looking for a black cat which isn't there" - Charles Darwin M__________________________________________________________________________ "A person who can, within a year, solve x^2 - 92y^2 = 1 is a mathematician." -- Brahmagupta M__________________________________________________________________________ Anyone who cannot cope with mathematics is not fully human. At best he is a tolerable subhuman who has learned to wear shoes, bathe and not make messes in the house. -- Lazarus Long, "Time Enough for Love" M__________________________________________________________________________ Sex is the mathematics urge sublimated. -- M. C. Reed. M__________________________________________________________________________ "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 P.S. Augustine did really say that, but in his time there was no difference between mathematicans and astrologists. Astrologists told the future, which was diabolic. M__________________________________________________________________________ As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality. -- Albert Einstein M__________________________________________________________________________ Mathematics contains much that will neither hurt one if one does not know it nor help one if one does know it. - J.B. Mencken +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ -- Joachim Verhagen Email:J.C.D.Verhagen@fys.ruu.nl Department of molecular biofysics, University of Utrecht Utrecht, The Netherlands.