----------------------------------------------------------------------------- Q. What does a mathematician do when he's constipated? A. He works it out with a pencil. Joseph Costa, NOSC ------------------------------------------------------------------------ Three employees of NOSC (an engineer, a physicist and a mathematician) are staying in a hotel while attending a technical seminar. The engineer wakes up and smells smoke. He goes out into the hallway and sees a fire, so he fills a trashcan from his room with water and douses the fire. He goes back to bed. Later, the physicist wakes up and smells smoke. He opens his door and sees a fire in the hallway. He walks down the hall to a fire hose and after calculating the flame velocity, distance, water pressure, trajectory, etc. extinguishes the fire with the minimum amount of water and energy needed. Later, the mathematician wakes up and smells smoke. He goes to the hall, sees the fire and then the fire hose. He thinks for a moment and then exclaims, "Ah, a solution exists!" and then goes back to bed. Michael Plapp, NOSC ------------------------------------------------------------------------ "A mathematician is a device for turning coffee into theorems" -- P. Erdos Jim Lewis, UC-Berkeley ------------------------------------------------------------------------- James Currie "Algebraic symbols are used when you do not know what you are talking about." Philippe Schnoebelen ------------------------------------------------------------------------- Moebius always does it on the same side. Heisenberg might have slept here. Aaron Avery, University of Wisconsin ------------------------------------------------------------------------- ------------------------------------------------------------------------------- The ark lands after The Flood. Noah lets all the animals out. Says, "Go and multiply." Several months pass. Noah decides to check up on the animals. All are doing fine except a pair of snakes. "What's the problem?" says Noah. "Cut down some trees and let us live there", say the snakes. Noah follows their advice. Several more weeks pass. Noah checks on the snakes again. Lots of little snakes, everybody is happy. Noah asks, "Want to tell me how the trees helped?" "Certainly", say the snakes. "We're adders, and we need logs to multiply." Rolan Christofferson, U.Colorado, Boulder ------------------------------------------------------------------------------- What is "pi"? Mathematician: Pi is thenumber expressing the relationship between the circumference of a circle and its diameter. Physicist: Pi is 3.1415927plus or minus 0.000000005 Engineer: Pi is about 3. David Harr, Occidental College ------------------------------------------------------------------------------- Lemma: All horses are the same color. Proof (by induction): Case n=1: In a set with only one horse, it is obvious that all horses in that set are the same color. Case n=k: Suppose you have a set of k+1 horses. Pull one of these horses out of the set, so that you have k horses. Suppose that all of these horses are the same color. Now put back the horse that you took out, and pull out a different one. Suppose that all of the k horses now in the set are the same color. Then the set of k+1 horses are all the same color. We have k true => k+1 true; therefore all horses are the same color. Theorem: All horses have an infinite number of legs. Proof (by intimidation): Everyone would agree that all horses have an even number of legs. It is also well-known that horses have forelegs in front and two legs in back. 4 + 2 = 6 legs, which is certainly an odd number of legs for a horse to have! Now the only number that is both even and odd is infinity; therefore all horses have an infinite number of legs. However, suppose that there is a horse somewhere that does not have an infinite number of legs. Well, that would be a horse of a different color; and by the Lemma, it doesn't exist. QED Jerry Weldon, Livermore Labs ------------------------------------------------------------------------------ Several students were asked the following problem: Prove that all odd integers are prime. Well, the first student to try to do this was a math student. Hey says "hmmm... Well, 1 is prime, 3 is prime, 5 is prime, and by induction, we have that all the odd integers are prime." Of course, there are some jeers from some of his friends. The physics student then said, "I'm not sure of the validity of your proof, but I think I'll try to prove it by experiment." He continues, "Well, 1 is prime, 3 is prime, 5 is prime, 7 is prime, 9 is ... uh, 9 is an experimental error, 11 is prime, 13 is prime... Well, it seems that you're right." The third student to try it was the engineering student, who responded, "Well, actually, I'm not sure of your answer either. Let's see... 1 is prime, 3 is prime, 5 is prime, 7 is prime, 9 is ..., 9 is ..., well if you approximate, 9 is prime, 11 is prime, 13 is prime... Well, it does seem right." Not to be outdone, the computer science student comes along and says "Well, you two sort've got the right idea, but you'd end up taking too long doing it. I've just whipped up a program to REALLY go and prove it..." He goes over to his terminal and runs his program. Reading the output on the screen he says, "1 is prime, 1 is prime, 1 is prime, 1 is prime...." ------------ Ya' hear about the geometer who went to the beach to catch the rays and became a tangent ? ------------ My geometry teacher was sometimes acute, and sometimes obtuse, but always, he was right. ------------ ------------------------------------------------------------------------------- A biologist, a statistician, a mathematician and a computer scientist are on a photo-safari in africa. They drive out on the savannah in their jeep, stop and scout the horizon with their binoculars. The biologist : "Look! There's a herd of zebras! And there, in the middle : A white zebra! It's fantastic ! There are white zebra's ! We'll be famous !" The statistician : "It's not significant. We only know there's one white zebra." The mathematician : "Actually, we only know there exists a zebra, which is white on one side." The computer scientist : "Oh, no! A special case!" Niels Ull Jacobsen, U. of Copenhagen --------------------------------------------------------------------------- I saw the following scrawled on a math office blackboard in college: 1 + 1 = 3, for large values of 1 Rob Gardner, HP Ft. Collins, CO --------------------------------------------------------------------------- lim ---- 8-->9 \/ 8 = 3 Donald Chinn, UC-Berkeley --------------------------------------------------------------------------- Asked how his pet parrot died, the mathmatican answered "Polynomial. polygon." --- Lumberjacks make good musicians because of their natural logarithms. --- Pie are not square. Pie are round. Cornbread are square. --- Statisticians probably do it Algebraists do it in groups. Al Sethuraman, Calma Company, San Diego ----------------------------------------------------------------------------- Von Neumann and Nobert Weiner were both the subject of many dotty professor stories. Von Neumann supposedly had the habit of simply writing answers to homework assignments on the board (the method of solution being, of course, obvious) when he was asked how to solve problems. One time one of his students tried to get more helpful information by asking if there was another way to solve the problem. Von Neumann looked blank for a moment, thought, and then answered, "Yes.". Weiner was in fact very absent minded. The following story is told about him: When they moved from Cambridge to Newton his wife, knowing that he would be absolutely useless on the move, packed him off to MIT while she directed the move. Since she was certain that he would forget that they had moved and where they had moved to, she wrote down the new address on a piece of paper, and gave it to him. Naturally, in the course of the day, an insight occurred to him. He reached in his pocket, found a piece of paper on which he furiously scribbled some notes, thought it over, decided there was a fallacy in his idea, and threw the piece of paper away. At the end of the day he went home (to the old address in Cambridge, of course). When he got there he realized that they had moved, that he had no idea where they had moved to, and that the piece of paper with the address was long gone. Fortunately inspiration struck. There was a young girl on the street and he conceived the idea of asking her where he had moved to, saying, "Excuse me, perhaps you know me. I'm Norbert Weiner and we've just moved. Would you know where we've moved to?" To which the young girl replied, "Yes daddy, mommy thought you would forget." The capper to the story is that I asked his daughter (the girl in the story) about the truth of the story, many years later. She said that it wasn't quite true -- that he never forgot who his children were! The rest of it, however, was pretty close to what actually happened... Richard Harter, Computer Corp. of America, Cambridge, MA ----------------------------------------------------------------------------- C programmers do it with long pointers. (Logicians do it) or [not (logicians do it)]. Scott Horne ----------------------------------------------------------------------------- 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. Arndt Jonasson ----------------------------------------------------------------------------- The USDA once wanted to make cows produce milk faster, to improve the dairy industry. So, they decided to consult the foremost biologists and recombinant DNA technicians to build them a better cow. They assembled this team of great scientists, and gave them unlimited funding. They requested rare chemicals, weird bacteria, tons of quarantine equipment, there was a God-awful typhus epidemic they started by accident, and, 2 years later, they came back with the "new, improved cow." It had a milk production improvement of 2% over the original. They then tried with the greatest Nobel Prize winning chemists around. They worked for six months, and, after requisitioning tons of chemical equipment, and poisoning half the small town in Colorado where they were working with a toxic cloud from one of their experiments, they got a 5% improvement in milk output. The physicists tried for a year, and, after ten thousand cows were subjected to radiation therapy, they got a 1% improvement in output. Finally, in desperation, they turned to the mathematicians. The foremost mathematician of his time offered to help them with the problem. Upon hearing the problem, he told the delegation that they could come back in the morning and he would have solved the problem. In the morning, they came back, and he handed them a piece of paper with the computations for the new, 300% improved milk cow. The plans began: "A Proof of the Attainability of Increased Milk Output from Bovines: Consider a spherical cow......" Chet Murthy, Cornell -------------------------------------------------------------------------- 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. Keith Goldfarb -------------------------------------------------------------------------- A bunch of Polish scientists decided to flee their repressive government by hijacking an airliner and forcing the pilot to fly them to a western country. They drove to the airport, forced their way on board a large passenger jet, and found there was no pilot on board. Terrified, they listened as the sirens got louder. Finally, one of the scientists suggested that since he was an experimentalist, he would try to fly the aircraft. He sat down at the controls and tried to figure them out. The sirens got louder and louder. Armed men surrounded the jet. The would be pilot's friends cried out, "Please, please take off now!!! Hurry!!!!!!" The experimentalist calmly replied, "Have patience. I'm just a simple pole in a complex plane." Lyle Levine, Washington University, St. Louis -------------------------------------------------------------------------- ------------------------------------------------------------------------------- An assemblage of the most gifted minds in the world were all posed the following "What is 2 * 2 ?" The engineer whips out his slide rule (so it's old) and shuffles it back and forth, and finally announces "3.99". The physicist consults his technical references, sets up the problem on his computer, and announces "it lies between 3.98 and 4.02". The mathematician cogitates for a while, oblivious to the rest of the world, then announces: "I don't what the answer is, but I can tell you, an answer exists!". Philosopher: "But what do you _mean_ by 2 * 2 ?" Logician: "Please define 2 * 2 more precisely." Accountant: Closes all the doors and windows, looks around carefully, then asks "What do you _want_ the answer to be?" Computer Hacker: Breaks into the NSA super-computer and gives the answer. Dave Horsfall, Alcatel-STC Australia, North Sydney ------------------------------------------------------------------------------ Old mathematicians never die; they just lose some of their functions. John C. George, U.Illinois Urbana-Champaign ------------------------------------------------------------------------------ During a class of calculus my lecturer suddenly checked himself and stared intently at the table in front of him for a while. Then he looked up at us and explained that he thought he had brought six piles of papers with him, but "no matter how he counted" there was only five on the table. Then he became silent for a while again and then told the following story: "When I was young in Poland I met the great mathematician Waclaw Sierpinski. He was old already then and rather absent-minded. Once he had to move to a new place for some reason. His wife wife didn't trust him very much, so when they stood down on the street with all their things, she said: - Now, you stand here and watch our ten trunks, while I go and get a taxi. She left and left him there, eyes somewhat glazed and humming absently. Some minutes later she returned, presumably having called for a taxi. Says Mr Sierpinski (possibly with a glint in his eye): - I thought you said there were ten trunks, but I've only counted to nine. - No, they're TEN! - No, count them: 0, 1, 2, ..." Kai-Mikael, Royal Inst. of Technology, Stockholm, SWEDEN -------------------------------------------------------------------------- What's nonorientable and lives in the sea? Mobius Dick. Jeff Dalton, U. of Edinburgh, UK ----------------------------------------------------------------------------- Philosopher: "Resolution of the continuum hypothesis will have profound implications to all of science." Physicist: "Not quite. Physics is well on its way without those mythical `foundations'. Just give us serviceable mathematics." Computer Scientist: "Who cares? Everything in this Universe seems to be finite anyway. Besides, I'm too busy debugging my Pascal programs." Mathematician: "Forget all that! Just make your formulae as aesthetically pleasing as possible!" Keitaro Yukawa, U. of Victoria, B.C, CANADA ----------------------------------------------------------------------------- Definition: Jogging girl scout = Brownian motion. Ilan Vardi, Stanford ----------------------------------------------------------------------------- The limit as n goes to infinity of sin(x)/n is 6. Proof: cancel the n in the numerator and denominator. Micah Fogel, UC-Berkeley \ __ \ /..\ / / :: \ / /` .... '\ / o / \ :: / \ / __ ___ /\__/\ / / / / / /__ -/- -\- \/ / / /__/ ___/ / ______________________________ / cca89018@uk.ac.bham.ibm3090 / Reality .. what a concept