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."
Mathematician: Pi is the number expressing the relationship between the circumference of a circle and its diameter.
Physicist: Pi is 3.1415927 plus or minus 0.000000005
Engineer: Pi is about 3.
David Harr, Occidental College
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...."
Q: What's the title of this picture ?
.. .. ____ .. .. \\===/======\\== || | | || || |____| || || ( ) || || \____/ || || || || || || || || || || || || || || || || || || || || (\ || || ) ) || || //||\\ ||A: Hypotenuse
/\ /\ /\ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /______\ /______\ /______\ || || || || || ||A: 9, tree + tree + tree
Q: A dust storm blows through, now how much do you have?
A: 99, dirty tree + dirty tree + dirty tree
Q: Some birds go flying by and leave their droppings, one per tree, how many is that ?
A: 100, dirty tree and a turd + dirty tree and a turd + dirty tree and a turd
Naoto Kimura, Cal State-Northridge
\/3 / | 2 3 x 3.14 3_ | z dz x cos( ----------) = ln (\/e ) | 9 / 1Which, of course, translates to:
Integral z-squared dz
from 1 to the square root of 3
times the cosine
of three pi over 9
equals log of the cube root of 'e'.
And it's correct, too.
Doug Walker, SAS Institute
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
1 + 1 = 3, for large values of 1Rob Gardner, HP Ft. Collins, CO
lim ---- 8-->9 \/ 8 = 3Donald Chinn, UC-Berkeley
lim 3 = 8 w->oo(It is more obvious when handwritten...)
Jorge Stolfi, DEC Systems Research Center, Palo Alto, CA
Michael Plapp, NOSC
Jim Lewis, UC-Berkeley
Answer: Zero, because all the Poles are in Eastern Europe! Addendum: Actually, there ARE some Poles in Western Europe, but they are removable!
Do you believe in one God? Answer: Yes, up to isomorphism!
It's a city that can be guarded by finitely many near-sighted policemen!
Q: What's yellow, and equivalent to the Axiom of Choice?
A: Zorn's Lemon.
James Currie
Q: Why is it that the more accuracy you demand from an interpolation
function, the more expensive it becomes to compute?
A: That's the Law of Spline Demand.
Steve Friedl, V-Systems, Inc.
Philippe Schnoebelen
Heisenberg might have slept here.
Aaron Avery, University of Wisconsin
A month later, returning, the mad scientist went to the engineer's cell and found it long empty. The engineer had constructed a can opener from pocket trash, used aluminum shavings and dried sugar to make an explosive, and escaped.
The physicist had worked out the angle necessary to knock the lids off the tin cans by throwing them against the wall. She was developing a good pitching arm and a new quantum theory.
The mathematician had stacked the unopened cans into a surprising
solution to the kissing problem; his dessicated corpse was propped calmly
against a wall, and this was inscribed on the floor in blood:
Theorem: If I can't open these cans, I'll die.(name unknown), Reed College, Portland, ORProof: assume the opposite...
He tried a test to narrow the area of specialty. He put each man in a room with a stove, a table, and a pot of water on the table. He said "Boil the water". Both men moved the pot from the table to the stove and turned on the burner to boil the water. Next, he put them into a room with a stove, a table, and a pot of water on the floor. Again, he said "Boil the water". The first man put the pot on the stove and turned on the burner. The counselor told him to be an Engineer, because he could solve each problem individually. The second man moved the pot from the floor to the table, and then moved the pot from the table to the stove and turned on the burner. The counselor told him to be a mathematician because he reduced the problem to a previously solved problem.
The great logician Betrand Russell (or was it A.N. Whitehead?) once claimed that he could prove anything if given that 1+1=1.
So one day, some smarty-pants asked him, "Ok. Prove that you're the Pope."
He thought for a while and proclaimed, "I am one. The Pope is one. Therefore, the Pope and I are one."
Donald Chinn, UC-Berkeley
In the beginning there was only one kind of Mathematician, created by the Great Mathamatical Spirit form the Book: the Topologist. And they grew to large numbers and prospered.
One day they looked up in the heavens and desired to reach up as far as the eye could see. So they set out in building a Mathematical edifice that was to reach up as far as "up" went. Further and further up they went ... until one night the edifice collapsed under the weight of paradox.
The following morning saw only rubble where there once was a huge
structure reaching to the heavens. One by one, the Mathematicians climbed
out from under the rubble. It was a miracle that nobody was killed; but
when they began to speak to one another, SUPRISE of all suprises! they
could not understand each other. They all spoke different languages. They
all fought amongst themselves and each went about their own way. To this
day the Topologists remain the original Mathematicians.
- adapted from an American Indian legend of the Mound Of BabelMark William Hopkins, U. Wisconsin-Milwaukee
Rolan Christofferson, U.Colorado, Boulder
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.Theorem: All horses have an infinite number of legs.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.
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.
QEDJerry Weldon, Livermore Labs
---
Lumberjacks make good musicians because of their natural logarithms.
---
Pie are not square. Pie are round. Cornbread are square.
---
"The integral of e to the x is equal to f of the quantity u to
the n."
/ x n | e = f(u ) /---
A physics joke:
"Energy equals milk chocolate square"Naoto Kimura, Cal State-Northridge
Dennis Healy, Dartmouth
The lawyer says: "For sure a mistress is better. If you have a wife and want a divorce, it causes all sorts of legal problems."
The doctor says: "It's better to have a wife because the sense of security lowers your stress and is good for your health."
The mathematician says: " You're both wrong. It's best to have both so that when the wife thinks you're with the mistress and the mistress thinks you're with your wife --- you can do some mathematics."
Bruce Bukiet, Los Alamos National Lab
Algebraists do it in groups.
Al Sethuraman, Calma Company, San Diego
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
(Logicians do it) or [not (logicians do it)].
Scott Horne
Proof:
No cat has eight tails. A cat has one tail more than no cat. Therefore, a cat has nine tails.
Arndt Jonasson
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
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.Keith GoldfarbProceed 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.
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!!>
Lyle Levine, Washington University, St. Louis
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"
Dave Seaman, Purdue
"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
John C. George, U.Illinois Urbana-Champaign
"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
Mobius Dick.
Jeff Dalton, U. of Edinburgh, UK
"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
Jogging girl scout = Brownian motion.Ilan Vardi, Stanford
Proof: cancel the n in the numerator and denominator.
Micah Fogel, UC-Berkeley
The first one says to the second that the average person knows very little about basic mathematics.
The second one disagrees, and claims that most people can cope with a reasonable amount of math.
The first mathematicien goes off to the washroom, and in his absence the second calls over the waitress.
He tells her that in a few minutes, after his friend has returned, he will call her over and ask her a question. All she has to do is answer one third x cubed.
She repeats `one thir -- dex cue'? He repeats `one third x cubed'.
Her: `one thir dex cuebd'? Yes, that's right, he says. So she agrees, and goes off mumbling to herself, `one thir dex cuebd...'.
The first guy returns and the second proposes a bet to prove his point, that most people do know something about basic math.
He says he will ask the blonde waitress an integral, and the first laughingly agrees.
The second man calls over the waitress and asks `what is the integral of x squared?'.
The waitress says `one third x cubed' and while walking away, turns back and says over her shoulder `plus a constant'!
Lynn Marshall, Universite Catholique de Louvain, Belgium