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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. He
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
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...."
and here's another version of the same joke:
Mathematician: 3 is a prime, 5 is a prime, 7 is a prime,
9 is not a prime - counter-example - claim is false.
Physicist: 3 is a prime, 5 is a prime, 7 is a prime,
9 is an experimental error, 11 is a prime, ...
Engineer: 3 is a prime, 5 is a prime, 7 is a prime,
9 is a prime, 11 is a prime, ...
Computer scientist: 3's a prime, 5's a prime, 7's a prime, 7's a prime,
7's a prime, ...
Computer scientist using Unix: 3's a prime, 5's a prime, 7's a prime,
Theorem: a cat has nine tails.
No cat has eight tails. A cat has one tail more than no cat.
Therefore, a cat has nine tails.
An assemblage of the most gifted minds in the world were all posed the
"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.
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
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
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."
There are three kinds of people in the world;
those who can count and those who can't.
And the related:
There are two groups of people in the world;
those who believe that the world can be
divided into two groups of people,
and those who don't.
There are two groups of people in the world:
Those who can be categorized into one of two
groups of people, and those who can't.
The world is divided into two classes:
people who say "The world is divided into two classes",
and people who say
The world is divided into two classes:
people who say: "The world is divided into two classes",
and people who say:
The world is divided into two classes:
people who say ...
97.3% of all statistics are made up.
TOP TEN EXCUSES FOR NOT DOING THE MATH HOMEWORK
1. I accidentally divided by zero and my paper burst into flames.
2. Isaac Newton's birthday.
3. I could only get arbitrarily close to my textbook. I couldn't
actually reach it.
4. I have the proof, but there isn't room to write it in this margin.
5. I was watching the World Series and got tied up trying to prove
that it converged.
6. I have a solar powered calculator and it was cloudy.
7. I locked the paper in my trunk but a four-dimensional dog got in
and ate it.
8. I couldn't figure out whether i am the square of negative one or
i is the square root of negative one.
9. I took time out to snack on a doughnut and a cup of coffee.
I spent the rest of the night trying to figure which one to dunk.
10. I could have sworn I put the homework inside a Klein bottle, but
this morning I couldn't find it.
Definitions of Terms Commonly Used in Higher Math
The following is a guide to the weary student of mathematics who
is often confronted with terms which are commonly used but rarely
defined. In the search for proper definitions for these terms we
found no authoritative, nor even recognized, source. Thus, we
followed the advice of mathematicians handed down from time
immortal: "Wing It."
CLEARLY: I don't want to write down all the "in-
TRIVIAL: If I have to show you how to do this, you're
in the wrong class.
OBVIOUSLY: I hope you weren't sleeping when we discussed
this earlier, because I refuse to repeat it.
RECALL: I shouldn't have to tell you this, but for
those of you who erase your memory tapes
after every test...
WLOG (Without Loss Of Generality): I'm not about to do all the
possible cases, so I'll do one and let you
figure out the rest.
IT CAN EASILY BE SHOWN: Even you, in your finite wisdom, should
be able to prove this without me holding your
CHECK or CHECK FOR YOURSELF: This is the boring part of the
proof, so you can do it on your own time.
SKETCH OF A PROOF: I couldn't verify all the details, so I'll
break it down into the parts I couldn't
HINT: The hardest of several possible ways to do a
BRUTE FORCE (AND IGNORANCE): Four special cases, three counting
arguments, two long inductions, "and a
partridge in a pair tree."
SOFT PROOF: One third less filling (of the page) than
your regular proof, but it requires two extra
years of course work just to understand the
ELEGANT PROOF: Requires no previous knowledge of the subject
matter and is less than ten lines long.
SIMILARLY: At least one line of the proof of this case is
the same as before.
CANONICAL FORM: 4 out of 5 mathematicians surveyed
recommended this as the final form for their
students who choose to finish.
TFAE (The Following Are Equivalent): If I say this it means that,
and if I say that it means the other thing,
and if I say the other thing...
BY A PREVIOUS THEOREM: I don't remember how it goes (come to
think of it I'm not really sure we did this
at all), but if I stated it right (or at
all), then the rest of this follows.
TWO LINE PROOF: I'll leave out everything but the conclusion,
you can't question 'em if you can't see 'em.
BRIEFLY: I'm running out of time, so I'll just write
and talk faster.
LET'S TALK THROUGH IT: I don't want to write it on the board lest
I make a mistake.
PROCEED FORMALLY: Manipulate symbols by the rules without any
hint of their true meaning (popular in pure
QUANTIFY: I can't find anything wrong with your proof
except that it won't work if x is a moon of
Jupiter (Popular in applied math courses).
PROOF OMITTED: Trust me, It's true.
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
What do you call a young eigensheep?
A lamb, duh!!!
One day a farmer called up an engineer, a physicist, and a mathematician
and asked them to fence of the largest possible area with the least
amount of fence. The engineer made the fence in a circle and
proclaimed that he had the most efficient design. The physicist made
a long, straight line and proclaimed 'We can assume the length is
infinite...' and pointed out that fencing off half of the Earth was
certainly a more efficient way to do it. The Mathematician just
laughed at them. He built a tiny fence around himself and said 'I
declare myself to be on the outside.'
An engineer thinks that his equations are an approximation to reality.
A physicist thinks reality is an approximation to his equations.
A mathematician doesn't care.
Why is the number 10 afraid of seven?
-- because seven ate nine.
A group of scientists were doing an investigation into problem-solving
techniques, and constructed an experiment involving a physicist, an
engineer, and a mathematician.
The experimental apparatus consisted of a water spigot and two identical
pails, one of which was fastened to the ground ten feet from the spigot.
Each of the subjects was given the second pail, empty, and told to fill the
pail on the ground.
The physicist was the first subject: he carried his pail to the spigot,
filled it there, carried it full of water to the pail on the ground, and
poured the water into it. Standing back, he declared, "There: I have
solved the problem."
The engineer and the mathematician each approached the problem similarly.
Upon finishing, the engineer noted that the solution was exact, since the
volumes of the pails were equal. The mathematician merely noted that he
had proven that a solution exists.
Now, the experimenters altered the parameters of the task a bit: the pail
on the ground was still empty, but the subjects were presented with a pail
that was already half-filled with water.
The physicist immediately carried his pail over to the one on the ground,
emptied the water into it, went back to the spigot, *filled* the pail, and
finally emptied the entire contents into the pail on the ground,
overflowing it and spilling some of the water. Upon finishing, he
commented that the problem should have been better stated.
The engineer, in turn, thought for some time before going into action. He
then took his half-filled pail to the spigot, filled it to the brim, and
filled the pail on the ground from it. Again he noted that the problem had
an exact solution, which of course he had found.
The mathematician thought for a long time before stirring. At last he
stood up, emptied his pail onto the ground, and declared, "The problem has
been reduced to one already solved."
Three Laws of Thermodynamics (paraphrased):
First Law: You can't get anything without working for it.
Second Law: The most you can accomplish by work is to break even.
Third Law: You can't break even.
The upgrade path to the most powerful and satisfying computer:
* Pocket calculator
* Commodore Pet / Apple II / TRS 80 / Commodore 64 / Timex Sinclair
(Choose any of the above)
* IBM PC
* Fastest workstation of the time (HP, DEC, IBM, SGI: your choice)
* Minicomputer (HP, DEC, IBM, SGI: your choice)
* Mainframe (IBM, Cray, DEC: your choice)
And then you reach the pinnacle of modern computing facilities:
******* G R A D U A T E S T U D E N T S ********
Yes, you just sit back and do all of your computing through lowly
graduate students. Imagine the advantages:
* Multi-processing, with as many processes as you have
students. You can easily add more power by promising more
desperate undergrads that they can indeed escape college
through your guidance. Special student units can even
handle several tasks *on*their*own*!
* Full voice recognition interface. Never touch a keyboard or
mouse again. Just mumble commands and they *will* be
understood (or else!).
* No hardware upgrades and no installation required. Every
student comes complete with all hardware necessary. Never
again fry a chip or $10,000 board by improper installation!
Just sit that sniveling student at a desk, give it writing
utensils (making sure to point out which is the dangerous
end) and off it goes.
* Low maintenance. Remember when that hard disk crashed in
your Beta 9900, causing all of your work to go the great bit
bucket in the sky? This won't happen with grad. students.
All that is required is that you give them a good *whack!*
upside the head when they are acting up, and they will run
good as new.
* Abuse module. Imagine yelling expletives at your computer.
Doesn't work too well, because your machine just sits there
and ignores you. Through the grad student abuse module you
can put the fear of god in them, and get results to boot!
* Built-in lifetime. Remember that awful feeling two years
after you bought your GigaPlutz mainframe when the new
faculty member on the block sneered at you because his
FeelyWup workstation could compute rings around your
dinosaur? This doesn't happen with grad. students. When
they start wearing and losing productivity, simply give them
the PhD and boot them out onto the street to fend for
themselves. Out of sight, out of mind!
* Cheap fuel: students run on Coca Cola (or the high-octane
equivalent -- Jolt Cola) and typically consume hot spicy
chinese dishes, cheap taco substitutes, or completely
synthetic macaroni replacements. It is entirely unnecessary
to plug the student into the wall socket (although this does
get them going a little faster from time to time).
* Expansion options. If your grad. students don't seem to be
performing too well, consider adding a handy system manager
or software engineer upgrade. These guys are guaranteed to
require even less than a student, and typically establish
permanent residence in the computer room. You'll never know
they are around! (Which you certainly can't say for an
AXZ3000-69 150gigahertz space-heater sitting on your desk
with its ten noisy fans....) [Note however that the
engineering department still hasn't worked out some of the
idiosyncratic bugs in these expansion options, such as
incessant muttering at nobody in particular, occasionaly
screaming at your grad. students, and posting ridiculous
messages on world-wide bulletin boards.]
So forget your Babbage Engines and abacuses (abaci?) and PortaBooks
and DEK 666-3D's and all that other silicon garbage. The wave of the
future is in wetware, so invest in graduate students today! You'll never
Dean, to the physics department. "Why do I always have to give you
guys so much money, for laboratories and expensive equipment and
stuff. Why couldn't you be like the math department - all they need
is money for pencils, paper and waste-paper baskets. Or even better,
like the philosophy department. All they need are pencils and paper."
A mathematician, a physicist, and an engineer were
travelling through Scotland when they saw a black sheep through the
window of the train.
"Aha," says the engineer, "I see that Scottish sheep are black."
"Hmm," says the physicist, "You mean that some Scottish sheep are
"No," says the mathematician, "All we know is that there is at least
one sheep in Scotland, and that at least one side of that one sheep is
What is "pi"?
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 0.00000005
Engineer: Pi is about 3.