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...."

-----------------------------------------------------------------------------

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,
                               segmentation fault

Gosh, they all overlooked that even 2's a prime!!

I figure that 2 is the oddest prime of all, because it's the
only one that's even!

------------------------------------------------------------------------------

An engineer, a physicist and a mathmetician were driving in the country 
when they came upon pasture after pasture with only black cows in them. 
The engineer said, "There seem to be only cows colored black in this 
area." The physicist said, "That doesn't quite follow. The only cows we 
have seen are black." Then the mathemetician said, "I don't think you 
are right there. The only cows we have seen are black on one side."


(Submitted by Ed Howland, ehowland@cyber.net)

------------------------------------------------------------------------------

Factorials were invented to make math look more exciting.

(Submitted by Steven Wright, afelson@rmii.com)

------------------------------------------------------------------------------
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.

------------------------------------------------------------------------------

My geometry teacher was sometimes acute, and sometimes
obtuse, but always, he was right.

------------------------------------------------------------------------------

And now, for some really bad picture jokes (that I heard at Cal Poly SLO) :

    Q:  What's the title of this picture ?

              ..  .. ____ ..  ..
               \\===/======\\==
                ||  |    |  ||
                ||  |____|  ||
                || (      ) ||
                ||  \____/  ||
                ||          ||
                ||          ||
                ||          ||
                ||          ||
                ||          ||
                ||          ||
                ||          ||
                ||          ||
                ||          ||
                ||    (\    ||
                ||    ) )   ||
                ||  //||\\  ||

    A:  Hypotenuse

-------

    Q:  What quantity is represented by this ?

                 /\         /\         /\
                /  \       /  \       /  \
                /  \       /  \       /  \
               /    \     /    \     /    \
               /    \     /    \     /    \
              /______\   /______\   /______\
                 ||         ||         ||
                 ||         ||         ||

    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

------------------------------------------------------------------------------

I saw the following scrawled on a math office blackboard in college:

        1 + 1 = 3, for large values of 1

------------------------------------------------------------------------------
      lim      ----
      8->9   \/ 8   = 3

Along the same lines:

     lim   sqrt (3) = 2
     3->4

------------------------------------------------------------------------------

Asked how his pet parrot died, the mathematician answered
    "Polynomial.  Polygon."

------------------------------------------------------------------------------


Lumberjacks make good musicians because of their natural logarithms.

------------------------------------------------------------------------------

Q: What is Quayle-o-phobia?

A: The fear of natural logarithms.
        (Hint: Quayle and the letter "e" made news.)

------------------------------------------------------------------------------

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"

------------------------------------------------------------------------------
Russell to Whitehead: "My Godel is killing me!"

------------------------------------------------------------------------------
A doctor, a lawyer and a mathematician were discussing the relative
merits of having a wife or a mistress.

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.

------------------------------------------------------------------------------
Von Neumann and Norbert Wiener 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".

Wiener 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 Wiener 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...

------------------------------------------------------------------------------
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 horrible 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......"

------------------------------------------------------------------------------
An engineer, a mathematician, and a physicist went to the races one
Saturday and laid their money down.  Commiserating in the bar after
the race, the engineer says, "I don't understand why I lost all my
money.  I measured all the horses and calculated their strength and
mechanical advantage and figured out how fast they could run..."

The physicist interrupted him: "...but you didn't take individual
variations into account.  I did a statistical analysis of their
previous performances and bet on the horses with the highest
probability of winning..."

"...so if you're so hot why are you broke?" asked the engineer.  But
before the argument can grow, the mathematician takes out his pipe and
they get a glimpse of his well-fattened wallet.  Obviously here was a
man who knows something about horses.  They both demanded to know his
secret.

"Well," he says, between puffs on the pipe, "first I assumed all the
horses were identical and spherical..."

------------------------------------------------------------------------------
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.

------------------------------------------------------------------------------
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."

------------------------------------------------------------------------------
A group of Polish tourists is flying on a small airplane through the
Grand Canyon on a sightseeing tour.  The tour guide announces: "On the
right of the airplane, you can see the famous Bright Angle Falls."
The tourists leap out of their seats and crowd to the windows on the
right side.  This causes a dynamic imbalance, and the plane violently
rolls to the side and crashes into the canyon wall.  All aboard are
lost.  The moral to this episode is:  always keep your poles off the
right side of the plane.

------------------------------------------------------------------------------
                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)

See also "Applied Dynamic Programming" by Bellman and Dreyfuss, prior to 1962.

------------------------------------------------------------------------------
An assemblage of the most gifted minds in the world were all posed the
following question:

"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.

------------------------------------------------------------------------------
Economist: Someone who is good with numbers but lacks the personality
           to be an accountant.

------------------------------------------------------------------------------
Old mathematicians never die; they just lose some of their functions.

------------------------------------------------------------------------------
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, ..."

-------------------------------------------------------------------------------
What's non-orientable and lives in the sea?

Mobius Dick.

------------------------------------------------------------------------------
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!"

-------------------------------------------------------------------------------
Definition:

   Jogging girl scout = Brownian motion.

------------------------------------------------------------------------------
      lim      sin(x)
    n --> oo   ------ = 6
                 n

Proof: cancel the n in the numerator and denominator.

-------------------------------------------------------------------------------
Two male mathematicians are in a bar.

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 mathematician 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'!

------------------------------------------------------------------------------
This was made by Mike Bender and Sarah Herr:

                          MATHEMATICS PURITY TEST

          Count the number of yes's, subtract from 60, and divide by 0.6.

----------

                                The Basics

1)  Have you ever been excited about math?
2)  Had an exciting dream about math?
3)  Made a mathematical calculation?
4)  Manipulated the numerator of an equation?
5)  Manipulated the denominator of an equation?
6)  On your first problem set?
7)  Worked on a problem set past 3:00 a.m.?
8)  Worked on a problem set all night?
9)  Had a hard problem?
10) Worked on a problem continuously for more than 30 minutes?
11) Worked on a problem continuously for more than four hours?
12) Done more than one problem set on the same night (i.e. both
    started and finished them)?
13) Done more than three problem sets on the same night?
14) Taken a math course for a full year?
15) Taken two different math courses at the same time?
16) Done at least one problem set a week for more than four months?
17) Done at least one problem set a night for more than one month
    (weekends excluded)?
18) Done a problem set alone?
19) Done a problem set in a group of three or more?
20) Done a problem set in a group of 15 or more?
21) Was it mixed company?
22) Have you ever inadvertently walked in upon people doing a problem set?
23) And joined in afterwards?
24) Have you ever used food doing a problem set?
25) Did you eat it all?
26) Have you ever had a domesticated pet or animal walk over you while you
    were doing a problem set?
27) Done a problem set in a public place where you might be discovered?
28) Been discovered while doing a problem set?


                           Kinky Stuff

29) Have you ever applied your math to a hard science?
30) Applied your math to a soft science?
31) Done an integration by parts?
32) Done two integration by parts in a single problem?
33) Bounded the domain and range of your function?
34) Used the domination test for improper integrals?
35) Done Newton's Method?
36) Done the Method of Frobenius?
37) Used the Sandwich Theorem?
38) Used the Mean Value Theorem?
39) Used a Gaussian surface?
40) Used a foreign object on a math problem (eg: calculator)?
41) Used a program to improve your mathematical technique (eg: MACSYMA)?
42) Not used brackets when you should have?
43) Integrated a function over its full period?
44) Done a calculation in three-dimensional space?
45) Done a calculation in n-dimensional space?
46) Done a change of bases?
47) Done a change of bases specifically in order to magnify your vector?
48) Worked through four complete bases in a single night (eg: using the
    Graham-Schmidt method)?
49) Inserted a number into an equation?
50) Calculated the residue of a pole?
51) Scored perfectly on a math test?
52) Swallowed everything your professor gave you?
53) Used explicit notation in your problem set?
54) Purposefully omitted important steps in your problem set?
55) Padded your own problem set?
56) Been blown away on a test?
57) Blown away your professor on a test?
58) Have you ever multiplied 23 by 3?
59) Have you ever bounded your Bessel function so that the membrane
    did not shoot to infinity?
69) Have you ever understood the following quote:
       "The relationship between Z^0 to C_0, B_0, and H_0
        is an example of a general principle which we have
        encountered:  the kernel of the adjoint of a linear
        transformation is both the annihilator space of the
        image of the transformation and also the dual space
        of the quotient of the space of which the image is
        a subspace by the image subspace."
        (Sternberg & Bamberg's _A "Course" in Mathematics for
        Students of Physics_, vol. 2)


-------------------------------------------------------------------------------

A somewhat advanced society has figured how to package basic knowledge
in pill form.

A student, needing some learning, goes to the pharmacy and asks what
kind of knowledge pills are available.  The pharmacist says "Here's a
pill for English literature."  The student takes the pill and swallows
it and has new knowledge about English literature!

"What else do you have?" asks the student.

"Well, I have pills for art history, biology, and world history,"
replies the pharmacist.

The student asks for these, and swallows them and has new knowledge
about those subjects.

Then the student asks, "Do you have a pill for math?"

The pharmacist says "Wait just a moment", and goes back into the
storeroom and brings back a whopper of a pill and plunks it on the
counter.

"I have to take that huge pill for math?" inquires the student.

The pharmacist replied "Well, you know math always was a little hard
to swallow."

-------------------------------------------------------------------------------
"A mathematician is a device for turning coffee into theorems"
  -- P. Erdos

-------------------------------------------------------------------------------

Three standard Peter Lax jokes (heard in his lectures) :

1. What's the contour integral around Western Europe?
        Answer: Zero, because all the Poles are in Eastern Europe!
        Addendum: Actually, there ARE some Poles in Western Europe, but
                  they are removable!

2. An English mathematician (I forgot who) was asked by his very religious
   colleague:
        Do you believe in one God?
        Answer: Yes, up to isomorphism!

3. What is a compact city?
        It's a city that can be guarded by finitely many near-sighted
        policemen!

-------------------------------------------------------------------------------
"Algebraic symbols are used when you do not know what you are talking about."

-------------------------------------------------------------------------------
Heisenberg might have slept here.

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)].

-------------------------------------------------------------------------------
A promising PhD candidate was presenting his thesis at his final
examination.  He proceeded with a derivation and ended up with
something like:

        F = -MA

He was embarrassed, his supervising professor was embarrassed, and the
rest of the committee was embarrassed.  The student coughed nervously
and said "I seem to have made a slight error back there somewhere."

One of the mathematicians on the committee replied dryly, "Either that
or an odd number of them!"

-------------------------------------------------------------------------------
There was a mad scientist ( a mad ...social... scientist ) who
kidnapped  three colleagues, an engineer, a physicist, and a
mathematician, and locked  each of them in seperate cells with plenty
of canned food and water but no can opener.

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 desiccated 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.

        Proof: assume the opposite...

-------------------------------------------------------------------------------
Problem: To Catch a Lion in the Sahara Desert.

(Hunting lions in Africa was originally published as "A contribution
to the mathematical theory of big game hunting" in the American
Mathematical Monthly in 1938 by "H. Petard, of Princeton NJ" [actually
the late Ralph Boas].  It has been reprinted several times.

1. Mathematical Methods

1.1 The Hilbert (axiomatic) method

We place a locked cage onto a given point in the desert.  After that
we introduce the following logical system:
   Axiom 1: The set of lions in the Sahara is not empty.
   Axiom 2: If there exists a lion in the Sahara, then there exists a
            lion in the cage.
   Procedure: If P is a theorem, and if the following is holds:
              "P implies Q", then Q is a theorem.
   Theorem 1: There exists a lion in the cage.

1.2 The geometrical inversion method

We place a spherical cage in the desert, enter it and lock it from
inside.  We then perform an inversion with respect to the cage.  Then
the lion is inside the cage, and we are outside.

1.3 The projective geometry method

Without loss of generality, we can view the desert as a plane surface.
We project the surface onto a line and afterwards the line onto an
interior point of the cage. Thereby the lion is mapped onto that same
point.

1.4 The Bolzano-Weierstrass method

Divide the desert by a line running from north to south.  The lion is
then either in the eastern or in the western part.  Let's assume it is
in the eastern part.  Divide this part by a line running from east to
west.  The lion is either in the northern or in the southern part.
Let's assume it is in the northern part.  We can continue this process
arbitrarily and thereby constructing with each step an increasingly
narrow fence around the selected area.  The diameter of the chosen
partitions converges to zero so that the lion is caged into a fence of
arbitrarily small diameter.

1.5 The set theoretical method

We observe that the desert is a separable space.  It therefore
contains an enumerable dense set of points which constitutes a
sequence with the lion as its limit.  We silently approach the lion in
this sequence, carrying the proper equipment with us.

1.6 The Peano method

In the usual way construct a curve containing every point in the
desert.  It has been proven [1] that such a curve can be traversed in
arbitrarily short time.  Now we traverse the curve, carrying a spear,
in a time less than what it takes the lion to move a distance equal to
its own length.

1.7 A topological method

We observe that the lion possesses the topological gender of a torus.
We embed the desert in a four dimensional space.  Then it is possible
to apply a deformation [2] of such a kind that the lion when returning
to the three dimensional space is all tied up in itself.  It is then
completely helpless.

1.8 The Cauchy method

We examine a lion-valued function f(z). Be \zeta the cage.  Consider
the integral

          1    [   f(z)
       ------- I --------- dz
       2 \pi i ] z - \zeta

               C

where C represents the boundary of the desert.  Its value is f(zeta),
i.e. there is a lion in the cage [3].

1.9 The Wiener-Tauber method

We obtain a tame lion, L_0, from the class L(-\infinity,\infinity),
whose fourier transform vanishes nowhere.  We put this lion somewhere
in the desert.  L_0 then converges toward our cage.  According to the
general Wiener-Tauner theorem [4] every other lion L will converge
toward the same cage.  (Alternatively we can approximate L arbitrarily
close by translating L_0 through the desert [5].)

2 Theoretical Physics Methods

2.1 The Dirac method

We assert that wild lions can ipso facto not be observed in the Sahara
desert.  Therefore, if there are any lions at all in the desert, they
are tame.  We leave catching a tame lion as an exercise to the reader.

2.2 The Schroedinger method

At every instant there is a non-zero probability of the lion being in
the cage.  Sit and wait.

2.3 The Quantum Measurement Method

We assume that the sex of the lion is _ab initio_ indeterminate.  The
wave function for the lion is hence a superposition of the gender
eigenstate for a lion and that for a lioness.  We lay these eigenstates
out flat on the ground and orthogonal to each other.  Since the (male)
lion has a distinctive mane, the measurement of sex can safely be made
from a distance, using binoculars.  The lion then collapses into one of
the eigenstates, which is rolled up and placed inside the cage.

2.4 The nuclear physics method

Insert a tame lion into the cage and apply a Majorana exchange
operator [6] on it and a wild lion.

As a variant let us assume that we would like to catch (for argument's
sake) a male lion.  We insert a tame female lion into the cage and
apply the Heisenberg exchange operator [7], exchanging spins.

2.5 A relativistic method

All over the desert we distribute lion bait containing large amounts
of the companion star of Sirius.  After enough of the bait has been
eaten we send a beam of light through the desert.  This will curl
around the lion so it gets all confused and can be approached without
danger.

3 Experimental Physics Methods

3.1 The thermodynamics method

We construct a semi-permeable membrane which lets everything but lions
pass through.  This we drag across the desert.

3.2 The atomic fission method

We irradiate the desert with slow neutrons.  The lion becomes
radioactive and starts to disintegrate. Once the disintegration
process is progressed far enough the lion will be unable to resist.

3.3 The magneto-optical method

We plant a large, lense shaped field with cat mint (nepeta cataria)
such that its axis is parallel to the direction of the horizontal
component of the earth's magnetic field.  We put the cage in one of the
field's foci . Throughout the desert we distribute large amounts of
magnetized spinach (spinacia oleracea) which has, as everybody knows,
a high iron content.  The spinach is eaten by vegetarian desert
inhabitants which in turn are eaten by the lions.  Afterwards the
lions are oriented parallel to the earth's magnetic field and the
resulting lion beam is focussed on the cage by the cat mint lense.

[1] After Hilbert, cf. E. W. Hobson, "The Theory of Functions of a Real
    Variable and the Theory of Fourier's Series" (1927), vol. 1, pp 456-457
[2] H. Seifert and W. Threlfall, "Lehrbuch der Topologie" (1934), pp 2-3
[3] According to the Picard theorem (W. F. Osgood, Lehrbuch der
    Funktionentheorie, vol 1 (1928), p 178) it is possible to catch every lion
    except for at most one.
[4] N. Wiener, "The Fourier Integral and Certain of its Applications" (1933),
    pp 73-74
[5] N. Wiener, ibid, p 89
[6] cf e.g. H. A. Bethe and R. F. Bacher, "Reviews of Modern Physics", 8
    (1936), pp 82-229, esp. pp 106-107
[7] ibid

----------

4 Contributions from Computer Science.

4.1 The search method

We assume that the lion is most likely to be found in the direction to
the north of the point where we are standing.  Therefore the REAL
problem we have is that of speed, since we are only using a PC to
solve the problem.

4.2 The parallel search method.

By using parallelism we will be able to search in the direction to the
north much faster than earlier.

4.3 The Monte-Carlo method.

We pick a random number indexing the space we search.  By excluding
neighboring points in the search, we can drastically reduce the number
of points we need to consider.  The lion will according to probability
appear sooner or later.

4.4 The practical approach.

We see a rabbit very close to us.  Since it is already dead, it is
particularly easy to catch.  We therefore catch it and call it a lion.

4.5 The common language approach.

If only everyone used ADA/Common Lisp/Prolog, this problem would be
trivial to solve.

4.6 The standard approach.

We know what a Lion is from ISO 4711/X.123.  Since CCITT have specified
a Lion to be a particular option of a cat we will have to wait for a
harmonized standard to appear.  $20,000,000 have been funded for
initial investigations into this standard development.

4.7 Linear search.

Stand in the top left hand corner of the Sahara Desert.  Take one step
east.  Repeat until you have found the lion, or you reach the right
hand edge.  If you reach the right hand edge, take one step
southwards, and proceed towards the left hand edge.  When you finally
reach the lion, put it the cage.  If the lion should happen to eat you
before you manage to get it in the cage, press the reset button, and
try again.

4.8 The Dijkstra approach:

The way the problem reached me was: catch a wild lion in the Sahara
Desert. Another way of stating the problem is:

       Axiom 1: Sahara elem deserts
       Axiom 2: Lion elem Sahara
       Axiom 3: NOT(Lion elem cage)

We observe the following invariant:

       P1:     C(L) v not(C(L))

where C(L) means: the value of "L" is in the cage.

Establishing C initially is trivially accomplished with the statement

       ;cage := {}

Note 0:
This is easily implemented by opening the door to the cage and shaking
out any lions that happen to be there initially.
(End of note 0.)

The obvious program structure is then:

       ;cage:={}
       ;do NOT (C(L)) ->
               ;"approach lion under invariance of P1"
               ;if P(L) ->
                       ;"insert lion in cage"
                [] not P(L) ->
                       ;skip
               ;fi
       ;od

where P(L) means: the value of L is within arm's reach.

Note 1:
Axiom 2 ensures that the loop terminates.
(End of note 1.)

Exercise 0:
Refine the step "Approach lion under invariance of P1".
(End of exercise 0.)

Note 2:
The program is robust in the sense that it will lead to
abortion if the value of L is "lioness".
(End of note 2.)

Remark 0: This may be a new sense of the word "robust" for you.
(End of remark 0.)

Note 3:

>From observation we can see that the above program leads to the
desired goal. It goes without saying that we therefore do not have to
run it.
(End of note 3.)
(End of approach.)

----------

For other articles, see also:

A Random Walk in Science - R.L. Weber and E. Mendoza
More Random Walks In Science - R.L. Weber and E. Mendoza
In Mathematical Circles (2 volumes) - Howard Eves
Mathematical Circles Revisited - Howard Eves
Mathematical Circles Squared - Howard Eves
Fantasia Mathematica - Clifton Fadiman
The Mathematical Magpi - Clifton Fadiman
Seven Years of Manifold - Jaworski
The Best of the Journal of Irreproducible Results - George H. Scheer
Mathematics Made Difficult - Linderholm
A Stress-Analysis of a Strapless Evening Gown - Robert Baker
The Worm-Runners Digest
Knuth's April 1984 CACM article on The Space Complexity of Songs
Stolfi and ?? SIGACT article on Pessimal Algorithms and Simplexity Analysis

-------------------------------------------------------------------------------
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!

------------------------------------------------------------------------------
The Programmers' Cheer --

Shift to the left, shift to the right!
Pop up, push down, byte, byte, byte!

------------------------------------------------------------------------------
Other cheers:

E to the x dx dy
radical transcendental pi
secant cosine tangent sine
3.14159
2.71828
come on folks let's integerate!!

----------

E to the i dx dy
E to y dy
cosine secant log of pi
disintegrate em RPI !!!

----------

square root, tangent
hyperbolic sine,
3.14159
e to the x, dy, dx,
sliderule, slipstick, TECH TECH TECH!

----------

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!

----------

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!!!!!!

------------------------------------------------------------------------------
Words in {} should be interpreted as greek letters:

Q: I M A {pi}{rho}Maniac.  R U  1,2?
                              o         <- read as "U-not"
A: Y ?
    o

("I am a pyromaniac.  Are you not one, too?"  "Why not?")

F U \{can\} \{read\} Ths U \{Mst\} \{use\} TeX
("If you can read this, you must use TeX")

------------------------------------------------------------------------------
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."

-------------------------------------------------------------------------------
Actually, I prefer the IBM version of this joke...

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."

-------------------------------------------------------------------------------
 (I'm not sure if the following one is a true story or not)
    The great logician Bertrand 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."

[NOTE: The following is from merritt@Gendev.slc.paramax.com (Merritt).
The story about 1+1=1 causing ridiculous consequences was, I believe,
originally the product of a conversation at the Trinity High Table.
It is recorded in Sir Harold Jeffreys' Scientific Inference, in a note
to chapter one.  Jeffreys remarks that the fact that everything
followed from a single contradiction had been noticed by Aristotle (I
doubt this way of putting it is quite correct, but that is beside the
point).  He goes on to say that McTaggart denied the consequence: "if
2+2=5, how can you prove that I am the pope?"  Hardy is supposed to
have replied: "if 2+2=5, 4=5; subtract 3; then 1=2; but McTaggart and
the pope are two; therefore McTaggart and the pope are one."  When I
consider this story, I am astonished at how much more brilliant some
people are than I (quite independent of the fallacies in the
argument).

Since McTaggart, Hardy, Whitehead, and Russell (the last two of whom
were credited with a variant of Hardy's argument in your post) were
all fellows of Trinity and Jeffreys (their exact contemporary) was a
fellow of St. Johns, I suspect that (whatever the truth of Jeffreys'
story) it is very unlikely that Whitehead or Russell had anything to do
with it.  The extraordinary point to me about the story is that Hardy
was able to snap this argument out between mouthfuls, so to speak, and
he was not even a logician at all.  This is probably why it came in
some people's minds to be attributed to one or other of the famous
Trinity logicians.

-----------------------------------------------------------------------------
THE STORY OF BABEL:

In the beginning there was only one kind of Mathematician, created by
the Great Mathematical 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
surprises! 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 Babel

------------------------------------------------------------------------------
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.


-------------------------------------------------------------------------------

Not precisely pure-math, but ...

Fuller's Law of Cosmic Irreversability:

                1 pot T --> 1 pot P
but
                1 pot P -/-> 1 pot T

------------------------------------------------------------------------------
A tribe of Native Americans generally referred to their woman by the
animal hide with which they made their blanket.  Thus, one woman might
be known as Squaw of Buffalo Hide, while another might be known as
Squaw of Deer Hide.  This tribe had a particularly large and strong
woman, with a very unique (for North America anyway) animal hide for
her blanket.  This woman was known as Squaw of Hippopotamus hide, and
she was as large and powerful as the animal from which her blanket was
made.

Year after year, this woman entered the tribal wrestling tournament,
and easily defeated all challengers; male or female.  As the men of
the tribe admired her strength and power, this made many of the other
woman of the tribe extremely jealous.  One year, two of the squaws
petitioned the Chief to allow them to enter their sons together as a
wrestling tandem in order to wrestle Squaw of the Hippopotamus hide as
a team.  In this way, they hoped to see that she would no longer be
champion wrestler of the tribe.

As the luck of the draw would have it, the two sons who were wrestling
as a tandem met the squaw in the final and championship round of the
wrestling contest.  As the match began, it became clear that the squaw
had finally met an opponent that was her equal.  The two sons wrestled
and struggled vigorously and were clearly on an equal footing with the
powerful squaw.  Their match lasted for hours without a clear victor.
Finally the chief intervened and declared that, in the interests of
the health and safety of the wrestlers, the match was to be terminated
and that he would declare a winner.

The chief retired to his teepee and contemplated the great struggle he
had witnessed, and found it extremely difficult to decide a winner.
While the two young men had clearly outmatched the squaw, he found it
difficult to force the squaw to relinquish her tribal championship.
After all, it had taken two young men to finally provide her with a
decent match.  Finally, after much deliberation, the chief came out
from his teepee, and announced his decision.  He said...

"The Squaw of the Hippopotamus hide is equal to the sons of the squaws
of the other two hides"

-------------------------------------------------------------------------------
A topologist is a man who doesn't know the difference between a coffee
cup and a doughnut.

-------------------------------------------------------------------------------
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.

------------------------------------------------------------------------------
A guy decided to go to the brain transplant clinic to refreshen his
supply of brains.  The secretary informed him that they had three
kinds of brains available at that time.  Doctors' brains were going
for $20 per ounce and lawyers' brains were getting $30 per ounce.  And
then there were mathematicians' brains which were currently fetching
$1000 per ounce.

"A 1000 dollars an ounce!" he cried.  "Why are they so expensive?"

"It takes more mathematicians to get an ounce of brains," she explained.

-------------------------------------------------------------------------------
A topologist walks into a bar and orders a drink.  The bartender,
being a number theorist, says, "I'm sorry, but we don't serve
topologists here."

The disgruntled topologist walks outside, but then gets an idea and
performs Dahn surgery upon herself.  She walks into the bar, and the
bartender, who does not recognize her since she is now a different
manifold, serves her a drink.  However, the bartender thinks she looks
familiar, or at least locally similar, and asks, "Aren't you that
topologist that just came in here?"

To which she responds, "No, I'm a frayed knot."

-------------------------------------------------------------------------------
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.

And then:

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 ...

------------------------------------------------------------------------------
What follows is a "quiz" a student of mine once showed me (which she'd
gotten from a previous teacher, etc...).  It's multiple choice, and if
you sort the letters (with upper and lower case disjoint) questions
and answers will come out next to each other.  Enjoy...

 S. What the acorn said when he grew up
 N.                                                     bisects
 u. A dead parrot
 g.                                                     center
 F. What you should do when it rains
 R.                                                     hypotenuse
 m. A geometer who has been to the beach
 H.                                                     coincide
 h. The set of cards is missing
 y.                                                     polygon
 A. The boy has a speech defect
 t.                                                     secant
 K. How they schedule gym class
 p.                                                     tangent
 b. What he did when his mother-in-law wanted to go home
 D.                                                     ellipse
 O. The tall kettle boiling on the stove
 W.                                                     geometry
 r. Why the girl doesn't run a 4-minute mile
 j.                                                     decagon

-------------------------------------------------------------------------------
___  1. That which Noah built.
___  2. An article for serving ice cream.
___  3. What a bloodhound does in chasing a woman.
___  4. An expression to represent the loss of a parrot.
___  5. An appropriate title for a knight named Koal.
___  6. A sunburned man.
___  7. A tall coffee pot perking.
___  8. What one does when it rains.
___  9. A dog sitting in a refrigerator.
___ 10. What a boy does on the lake when his motor won't run.
___ 11. What you call a person who writes for an inn.
___ 12. What the captain said when the boat was bombed.
___ 13. What a little acorn says when he grows up.
___ 14. What one does to trees that are in the way.
___ 15. What you do if you have yarn and needles.
___ 16. Can George Washington turn into a country?


A. hypotenuse              I. circle
B. polygon                 J. axiom
C. inscribe                K. cone
D. geometry                L. coincide
E. unit                    M. cosecant
F. center                  N. tangent
G. decagone                O. hero
H. arc                     P. perpendicular

------------------------------------------------------------------------------

A team of engineers were required to measure the height of a flag
pole. They only had a measuring tape, and were getting quite
frustrated trying to keep the tape along the pole.  It kept falling
down, etc.

A mathematician comes along, finds out their problem, and proceeds to
remove the pole from the ground and measure it easily.

When he leaves, one engineer says to the other:  "Just like a
mathematician!  We need to know the height, and he gives us the
length!"

-------------------------------------------------------------------------------
A man camped in a national park, and noticed Mr. Snake and Mrs. Snake
slithering by.  "Where are all the little snakes?" he asked.  Mr.
Snake replied, "We are adders, so we cannot multiply."

The following year, the man returned to the same camping spot.  This
time there were a whole batch of little snakes.  "I thought you said
you could not multiply," he said to Mr. Snake.  "Well, the park ranger
came by and built a log table, so now we can multiply by adding!"

------------------------------------------------------------------------------
Einstein dies and goes to heaven only to be informed that his room is
not yet ready.  "I hope you will not mind waiting in a dormitory.  We
are very sorry, but it's the best we can do and you will have to share
the room with others." he is told by the doorman (say his name is
Pete).  Einstein says that this is no problem at all and that there is
no need to make such a great fuss.  So Pete leads him to the dorm.
They enter and Albert is introduced to all of the  present
inhabitants.  "See, Here is your first room mate.  He has an IQ of
180!"
"Why that's wonderful!"  Says Albert.  "We can discuss mathematics!"
"And here is your second room mate.  His IQ is 150!"
"Why that's wonderful!" Says Albert.  "We can discuss physics!"
"And here is your third room mate. His IQ is 100!"
"That Wonderful!  We can discuss the latest plays at the theater!"
Just then another man moves out to capture Albert's hand and shake it.
"I'm your last room mate and I'm sorry, but my IQ is only 80."
Albert smiles back at him and says, "So, where to you think interest
rates are headed?"

------------------------------------------------------------------------------
97.3% of all statistics are made up.

-------------------------------------------------------------------------------
Did you hear the one about the statistician?

Probably....

-------------------------------------------------------------------------------
There was once a very smart horse.  Anything that was shown it, it
mastered easily, until one day, its teachers tried to teach it about
rectangular coordinates and it couldn't understand them.  All the
horse's acquaintances and friends tried to figure out what was the
matter and couldn't.  Then a new guy (what the heck, a computer
engineer) looked at the problem and said,

"Of course he can't do it.  Why, you're putting Descartes before the
horse!"

-------------------------------------------------------------------------------
        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.

-------------------------------------------------------------------------------
The guy gets on a bus and starts threatening everybody: "I'll integrate
you!  I'll differentiate you!!!"  So everybody gets scared and runs
away.  Only one person stays.  The guy comes up to him and says:
"Aren't you scared, I'll integrate you, I'll differentiate you!!!"  And
the other guy says; "No, I am not scared, I am e to the x."

-------------------------------------------------------------------------------
A mathematician went insane and believed that he was the
differentiation operator.  His friends had him placed in a mental
hospital until he got better.  All day he would go around  frightening
the other patients by staring at them and saying "I differentiate
you!"

One day he met a new patient; and true to form he stared at him and
said "I differentiate you!", but for once, his victim's  expression
didn't change.  Surprised, the mathematician marshalled his energies,
stared fiercely at the new patient and said loudly "I differentiate
you!", but still the other man had no reaction.  Finally, in
frustration, the mathematician screamed out "I DIFFERENTIATE YOU!" --
at which point the new patient calmly looked up and said, "You can
differentiate me all you like: I'm e to the x."

------------------------------------------------------------------------------
   /
  |   1
  | -----  = log cabin
  | cabin
 /

        Oops, you forgot your constant of integration.


   /
  |   1
  | -----  = log cabin + C
  | cabin
 /

        And, as we all know,

           log cabin + C = houseboat

------------------------------------------------------------------------------
        8                                      5
If lim  - = oo (infinity),  then what does lim - = ?
  x->0  x                                 x->0 x

answer: (write 5 on it's side)

------------------------------------------------------------------------------
Why did the cat fall off the roof?

Because he lost his mu.  (mew=sound cats make, mu=coeff of friction)

------------------------------------------------------------------------------
Boy's Life, May 1973:

Ralph:  Dad, will you do my math for me tonight?
Dad:    No, son, it wouldn't be right.
Ralph:  Well, you could try.

------------------------------------------------------------------------------
Mrs. Johnson the elementary school math teacher was having children do
problems on the blackboard that day.

``Who would like to do the first problem, addition?''

No one raised their hand.  She called on Tommy, and with some help he
finally got it right.

``Who would like to do the second problem, subtraction?''

Students hid their faces.  She called on Mark, who got the problem but
there was some suspicion his girlfriend Lisa whispered it to him.

``Who would like to do the third problem, division?''

Now a low collective groan could be heard as everyone looked at
nothing in particular.  The teacher called on Suzy, who got it right
(she has been known to hold back sometimes in front of her friends).

``Who would like to do the last problem, multiplication?''

Tim's hand shot up, surprising everyone in the room.  Mrs. Johnson
finally gained her composure in the stunned silence.  ``Why the
enthusiasm, Tim?''

``God said to go fourth and multiply!''

-------------------------------------------------------------------------------
                  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-
                              between" steps.

          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
                              hand.

          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
                              prove.

          HINT:               The hardest of several possible ways to do a
                              proof.

          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
                              terms.

          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
                              math courses).

          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.

-------------------------------------------------------------------------------
In the bayous of Louisiana, there is a small river called the Dirac.
Many wealthy people have their mansions near its mouth.  One of the
social leaders decided to have a  grand ball.  Being a cousin of the
Governor, she arranged  for a detachment of the state militia to serve
as guards and traffic directors for the big doings.  A captain was
sent over with a small company; naturally he asked if there was enough
room for him and his unit.  The social leader replied, "But of course,
Captain!  It is well known that the Dirac delta function has unit
area."

-------------------------------------------------------------------------------
Albert Einstein, who fancied himself as a violinist, was rehearsing a
Haydn string quartet.  When he failed for the fourth time to get his
entry in the second movement, the cellist looked up and said, "The
problem with you, Albert, is that you simply can't count."

------------------------------------------------------------------------------
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.

-------------------------------------------------------------------------------
When I was a Math/Chem grad student at Princeton in 1973-74, there was
a story going around about a grad student.  This guy was always late.
One day he stumbled into class late, saw seven problems written on the
board, and wrote them down.  As the week went on he began to panic:
the math department at Princeton is fiercely competitive, and here he
was unable to do most of a simple homework assignment!  When the next
class rolled around he only had solved two of the problems, although
he had a pretty good idea of how to solve a third but not enough time
to complete it.

When he dejectedly flung his partial assignment on the prof's desk,
the prof asked him "What's that?"  "The homework."  "What homework?"
Eventually it came out that what the prof had written on the board
were the seven most important unsolved problems in the field.

This is largely an academic legend, at least according to Jan Harold
Brunvand, the author of a series of books on so-called Urban Legends.
He talks about it in his latest book _Curses!  Broiled Again!_ in the
chapter entitled "The Unsolvable Math Problem."  It is, however, based
in some fact.  The Stanford mathematician, George B. Danzig,
apparently managed to solve two statistics problems previously
unsolved under similar circumstances.

-------------------------------------------------------------------------------
The following problem can be solved either the easy way or the hard way.

Two trains 200 miles apart are moving toward each other; each one is
going at a speed of 50 miles per hour.  A fly starting on the front of
one of them flies back and forth between them at a rate of 75 miles
per hour.  It does this until the trains collide and crush the fly to
death.  What is the total distance the fly has flown?

The fly actually hits each train an infinite number of times before it
gets crushed, and one could solve the problem the hard way with pencil
and paper by summing an infinite  series of distances.  The easy way
is as follows:  Since the trains are 200 miles apart and each train is
going 50 miles an hour, it takes 2 hours for the trains to collide.
Therefore the fly was flying for two hours.  Since the fly was flying
at a rate of 75 miles per hour, the fly must have flown 150 miles.
That's all there is to it.

When this problem was posed to John von Neumann, he immediately
replied, "150 miles."

"It is very strange," said the poser, "but nearly everyone tries to
sum the infinite series."

"What do you mean, strange?" asked Von Neumann.  "That's how I did it!"

-------------------------------------------------------------------------------
Mathematicians are like Frenchmen: whatever you say to them, they
translate it into their own language, and forthwith it means something
entirely different.
                -- Johann Wolfgang von Goethe

-------------------------------------------------------------------------------
"The reason that every major university maintains a department of
mathematics is that it is cheaper to do this than to institutionalize
all those people."

-------------------------------------------------------------------------------
Three mathematicians and a physicist walk into a bar.
You'd think the second one would have ducked.  (Ha, that quack's me up!)

-------------------------------------------------------------------------------
What do you call a young eigensheep?

A lamb, duh!!!

-------------------------------------------------------------------------------
"The world is everywhere dense with idiots."
                - LFS

-------------------------------------------------------------------------------
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, a mathematician, and a computer programmer are driving
down the road when the car they are in gets a flat tire.  The engineer
says that they should buy a new car.  The mathematician says they
should sell the old tire and buy a new one.  The computer programmer
says they should drive the car around the block and see if the tire
fixes itself.

------------------------------------------------------------------------------
A math/computer science convention was being held.  On the train to
the convention, a bunch of math majors and a bunch of computer science
majors were on the train.  Each of the math majors had his/her train
ticket.  The group of computer science majors had only ONE ticket for
all of them.  The math majors started laughing and snickering.

Then, one of the CS majors said "here comes the conductor" and then
all of the CS majors went into the bathroom.  The math majors were
puzzled.  The conductor came aboard and said "tickets please" and got
tickets from all the math majors.  He then went to the bathroom and
knocked on the door and said "ticket please" and the CS majors stuck
the ticket under the door.  The conductor took it and then the CS
majors came out of the bathroom a few minutes later.  The math majors
felt really stupid.

So, on the way back from the convention, the group of math majors had
one ticket for the group.  They started snickering at the CS majors,
for the whole group had no tickets amongst them.  Then, the CS major
lookout said "Conductor coming!".  All the CS majors went to the
bathroom.  All the math majors went to another bathroom.  Then, before
the conductor came on board, one of the CS majors left the bathroom,
knocked on the other bathroom, and said "ticket please."

------------------------------------------------------------------------------
The following is supposedly a true story about Russell.  It isn't
really a math joke since it makes fun of the British hierarchy, but
it's funny anyway....

Around the time when Cold War started, Bertrand Russell was giving a
lecture on politics in England.  Being a leftist in a conservative
women's club, he was not received well at all: the ladies came up to
him and started attacking him with whatever they could get their hands
on.  The guard, being an English gentleman, did not want to be rough
to the ladies and yet needed to save Russell from them.  He said, "But
he is a great mathematician!"  The ladies ignored him.  The guard said
again, "But he is a great philosopher!"  The ladies ignore him again.
In desperation, finally, he said, "But his brother is an earl!"  Bert
was saved.

------------------------------------------------------------------------------
Another "true" story, kinda like the aforementioned urban legend:

Enrico Fermi, while studying in college, was bored by his math
classes.  He walked up to the professor and said, "My classes are too
easy!"  The professor looked at him, and said, "Well, I'm sure you'll
find this interesting."  Then the professor copied 9 problems from a
book to a paper and gave the paper to Fermi.  A month later, the
professor ran into Fermi, "So how are you doing with the problems I
gave you?"  "Oh, they are very hard.  I only managed to solve 6 of
them."  The professor was visibly shocked, "What!? But those are
unsolved problems!"

-------------------------------------------------------------------------------
An engineer, a physicist, and a mathematician find themselves in an
anecdote, indeed an anecdote quite similar to many that you have no
doubt already heard.  After some observations and rough calculations,
the engineer realizes the situation and starts laughing.  A few
minutes later the physicist understands, too, and chuckles to himself
happily as he now has enough experimental evidence to publish a paper.
This leaves the mathematician somewhat perplexed, as he had observed
right away that he was the subject of an anecdote, and deduced quite
rapidly the presence of humour from similar anecdotes, but considers
this anecdote to be too trivial a corollary to be significant, let
alone funny.


-------------------------------------------------------------------------------
"A person who can, within a year, solve x^2 - 92y^2 = 1 is a mathematician."
   -- Brahmagupta

-------------------------------------------------------------------------------
Math and Alcohol don't mix, so...

PLEASE DON'T DRINK AND DERIVE

Then there's every parent's scream when their child walks into the
room dazed and staggering:

OH NO...YOU'VE BEEN TAKING DERIVATIVES!!

-------------------------------------------------------------------------------
MADD =  Mathematicians
        Against
        Drunk
        Deriving

-------------------------------------------------------------------------------
[This limerick was previously posted incorrectly.
 The integral limit has been changed.]

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.

-------------------------------------------------------------------------------
This poem was written by John Saxon (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.

-------------------------------------------------------------------------------
        '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).

-------------------------------------------------------------------------------
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

-------------------------------------------------------------------------------

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...

-------------------------------------------------------------------------------
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.

-------------------------------------------------------------------------------
We use epsilons and deltas in mathematics because mathematicians tend
to make errors.

------------------------------------------------------------------------------

What's big, grey, and proves the uncountability of the reals?
Cantor's Diagonal Elephant!

How can you tell that Harvard was layed out by a mathematician?
The div school [divinity school] is right next to the grad school...

-------------------------------------------------------------------------------
The Stanford Linear Accelerator Center was known as SLAC, until the
big earthquake, when it became known as SPLAC.

SPLAC?  Stanford Piecewise Linear Accelerator.

-------------------------------------------------------------------------------
Q:  How many topologists does it take to change a light bulb?
A:  It really doesn't matter, since they'd rather knot.

------------------------------------------------------------------------------

A mathematician decides he wants to learn more about practical
problems.  He sees a seminar with a nice title: "The Theory of Gears."
So he goes.  The speaker stands up and begins, "The theory of gears
with a real number of teeth is well known ..."

-------------------------------------------------------------------------------
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."

-------------------------------------------------------------------------------
Professor Dirac, a famous Applied Mathematician-Physicist, had a horse
shoe over his desk.  One day a student asked if he really believed
that a horse shoe brought luck.  Professor Dirac replied, "I
understand that it brings you luck if you believe in it or not."

-------------------------------------------------------------------------------
First of all let me make it clear that I have nothing against
contravariant functors.  Some of my best friends are cohomology
theories!  But now you aren't supposed to call them contravariant
anymore.  It's Algebraically Correct to call them 'differently
arrowed'!!

In the same way that transcendental numbers are polynomially
challenged?

Manifolds are personifolds (humanifolds).

Neighborhoods are neighbor victims of society.

It's the Asian Remainder Theorem.

It isn't PC to use "singularity" - the function is "convergently
challenged" there.

-------------------------------------------------------------------------------
Why did the computer scientist die in the shower?
Because he read the instructions on the shampoo bottle,  "Lather,
rinse, repeat."

Why did the calculus student have so much trouble making Kool-Aid?
Because he couldn't figure out how to get a quart of water into the
little package.

Q: Why do computer scientists confuse Christmas and Halloween?
A: Because Oct 31 = Dec 25

-------------------------------------------------------------------------------
Here are some phrases used to remember SIN, COS, and TAN.
(SIN = Opposite/Hypotenuse, COS = Adjacent/H, TAN = O/A).

1.      SOHCAHTOA       (sock-a-toe-a)

2.      The Cat    Sat
        On  An     Orange
        And Howled Hard

3.      Some Old Hulks
        Carry A Huge
        Tub Of Ale

4.      Silly Old Hitler
        Caused Awful Headaches
        To Our Airmen

5.      Some Old Hag
        Cracked All Her
        Teeth On Asparagus

6.      Some Old Hairy
        Camels Are Hairier
        Than Others Are

7.      Silly Old Harry
        Caught A Herring
        Trawling Off America

8.      SOPHY, CADHY, TOAD

--------------------------------units and dimensions-------------

2 monograms                                             1 diagram
8 nickles                                               2 paradigms
2 wharves                                               1 paradox

10E5 bicycles                                           2 megacycles

1 unit of suspense in an Agatha Christie novel          1 whod unit

-------------------------------------------------------------------------------
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.

-------------------------------------------------------------------------------
Q: What goes "Pieces of seven! Pieces of seven!"?
A: A parroty error!!

Q: What did the circle say to the tangent line?
A: "Stop touching me!"

-------------------------------------------------------------------------------
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...

-------------------------------------------------------------------------------
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

    * Apple Macintosh

    * 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
go back!

-------------------------------------------------------------------------------
If I have seen farther than others, it is because I was
standing on the shoulder of giants.
   -- Isaac Newton

If I have not seen as far as others, it is because giants
were standing on my shoulders.
   -- Hal Abelson

In computer science, we stand on each other's feet.
   -- Brian K. Reid

-------------------------------------------------------------------------------
He thinks he's really smooth, but he's only C^1.
He's always going off on a tangent.

-------------------------------------------------------------------------------
A mathematician and a physicist agree to a psychological experiment.
The mathematician is put in a chair in a large empty room and a
beautiful naked woman is placed on a bed at the other end of the room.
The psychologist explains, "You are to remain in your chair.  Every
five minutes, I will move your chair to a position halfway between its
current location and the woman on the bed."  The mathematician looks
at the psychologist in disgust.  "What? I'm not going to go through
this.  You know I'll never reach the bed!"  And he gets up and storms
out.  The psychologist makes a note on his clipboard and ushers the
physicist in.  He explains the situation, and the physicist's eyes
light up and he starts drooling.  The psychologist is a bit confused.
"Don't you realize that you'll never reach her?"  The physicist smiles
and replied, "Of course!  But I'll get close enough for all practical
purposes!"

-------------------------------------------------------------------------------
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."

-------------------------------------------------------------------------------
An engineer, physicist, and mathematician are all challenged with a
problem: to fry an egg when there is a fire in the house.  The
engineer just grabs a huge bucket of water, runs over to the fire, and
puts it out.  The physicist thinks for a long while, and then measures
a precise amount of water into a container.  He takes it over to the
fire, pours it on, and with the last drop the fire goes out. The
mathematician pores over pencil and paper.  After a few minutes he
goes "Aha!  A solution exists!" and goes back to frying the egg.

Sequel:  This time they are asked simply to fry an egg (no fire).  The
engineer just does it, kludging along; the physicist calculates
carefully and produces a carefully cooked egg; and the mathematician
lights a fire in the corner, and says "I have reduced it to the
previous problem."

-------------------------------------------------------------------------------
A physicist and a mathematician setting in a faculty lounge.
Suddenly, the coffee machine catches on fire.  The physicist grabs a
bucket and leaps towards the sink, fills the bucket with water and
puts out the fire.  The second day, the same two sit in the same
lounge.  Again, the coffee machine catches on fire.  This time, the
mathematician stands up, gets a bucket, hands the bucket to the
physicist, thus reducing the problem to a previously solved one.

-------------------------------------------------------------------------------
An engineer, a mathematician, and a physicist are staying in three
adjoining cabins at a decrepit old motel.

First the engineer's coffee maker catches fire on the bathroom vanity.
He smells the smoke, wakes up, unplugs it, throws it out the window,
and goes back to sleep.

Later that night the physicist smells smoke too.  He wakes up and sees
that a cigarette butt has set the trash can on fire.  He says to
himself, "Hmm. How does one put out a fire?  One can reduce the
temperature of the fuel below the flash point, isolate the burning
material from oxygen, or both.  This could be accomplished by applying
water."  So he picks up the trash can, puts it in the shower stall,
turns on the water, and, when the fire is out, goes back to sleep.

The mathematician, of course, has been watching all this out the
window.  So later, when he finds that his pipe ashes have set the
bedsheet on fire, he is not in the least taken aback.  He immediately
sees that the problem reduces to one that has already been solved and
goes back to sleep.

-------------------------------------------------------------------------------
A mathematician and a physicist were asked the following question:

        Suppose you walked by a burning house and saw a hydrant and
        a hose not connected to the hydrant.  What would you do?

P: I would attach the hose to the hydrant, turn on the water, and put out
   the fire.

M: I would attach the hose to the hydrant, turn on the water, and put out
   the fire.

Then they were asked this question:

        Suppose you walked by a house and saw a hose connected to
        a hydrant.  What would you do?

P: I would keep walking, as there is no problem to solve.

M: I would disconnect the hose from the hydrant and set the house on fire,
   reducing the problem to a previously solved form.

-------------------------------------------------------------------------------
There were two men trying to decide what to do for a living.  They
went to see a counselor, and he decided that they had good problem
solving skills.

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.

-------------------------------------------------------------------------------
So a mathematician, an engineer, and a physicist are out hunting
together.  They spy a deer(*) in the woods.

The physicist calculates the velocity of the deer and the effect of
gravity on the bullet, aims his rifle and fires.  Alas, he misses; the
bullet passes three feet behind the deer.  The deer bolts some yards,
but comes to a halt, still within sight of the trio.

"Shame you missed," comments the engineer, "but of course with an
ordinary gun, one would expect that."  He then levels his special
deer-hunting gun, which he rigged together from an ordinary rifle, a
sextant, a compass, a barometer, and a bunch of flashing lights which
don't do anything but impress onlookers, and fires.  Alas, his bullet
passes three feet in front of the deer, who by this time wises up and
vanishes for good.

"Well," says the physicist, "your contraption didn't get it either."

"What do you mean?" pipes up the mathematician.  "Between the two of
you, that was a perfect shot!"

----------

(*) How they knew it was a deer:

The physicist observed that it behaved in a deer-like manner, so it
must be a deer.

The mathematician asked the physicist what it was, thereby reducing it
to a previously solved problem.

The engineer was in the woods to hunt deer, therefore it was a deer.

-------------------------------------------------------------------------------
A computer scientist, 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
black."

"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
black!"

"Oh, no!" shouts the computer scientist, "A special case!"

-------------------------------------------------------------------------------
A Mathematician (M) and an Engineer (E) attend a lecture by a
Physicist. The topic concerns Kulza-Klein theories involving physical
processes that occur in spaces with dimensions of 11, 12 and even
higher.  The M is sitting, clearly enjoying the lecture, while the E
is frowning and looking generally confused and puzzled.  By the end
the E has a terrible headache.  At the end, the M comments about the
wonderful lecture.  The E says "How do you understand this stuff?"
M: "I just visualize the process."
E: "How can you POSSIBLY visualize something that occurs in
11-dimensional space?"
M: "Easy, first visualize it in N-dimensional space, then let N go to 11."

-------------------------------------------------------------------------------
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.

-------------------------------------------------------------------------------
When considering the behaviour of a howitzer:

A mathematician will be able to calculate where the shell will land.

A physicist will be able to explain how the shell gets there.

An engineer will stand there and try to catch it.

-------------------------------------------------------------------------------
An engineer, a physicist and a mathematician find themselves in an
anecdote, indeed an anecdote quite similar to many that you have no
doubt already heard.  After some observations and rough calculations
the engineer realizes the situation and starts laughing.  A few
minutes later the physicist understands too and chuckles to himself
happily as he now has enough experimental evidence to publish a paper.

This leaves the mathematician somewhat perplexed, as he had observed
right away that he was the subject of an anecdote, and deduced quite
rapidly the presence of humour from similar anecdotes, but considers
this anecdote to be too trivial a corollary to be significant, let
alone funny.

-------------------------------------------------------------------------------
Q: What's purple and commutes?
A: An abelian grape.

Q: Why did the mathematician name his dog "Cauchy"?
A: Because he left a residue at every pole.

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.

Q: How many mathematicians does it take to screw in a lightbulb?
A: 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: What do a mathematician and a physicist [or engineer, or musician,
   or whatever the profession of the person addressed] have in common?
A: They are both stupid, with the exception of the mathematician.

Q: What do you call a teapot of boiling water on top of mount everest?
A: A high-pot-in-use

Q: What do you call a broken record?
A: A Decca-gone

Q: What do you get when you cross 50 female pigs and 50 male deer?
A: One hundred sows-and-bucks

Q: Why did the chicken cross the Moebius strip?
A: To get to the other ... er, um ...

Q: What is the world's longest song?
A: "Aleph-nought Bottles of Beer on the Wall."

Q: What does a mathematician do when he's constipated?
A: He works it out with a pencil.

Q: What's yellow and equivalent to the Axiom of Choice.
A: Zorn's Lemon.

Q: What do you get if you cross an elephant with a zebra.
A: Elephant zebra sin theta.

Q: What do you get if you cross an elephant with a mountain climber.
A: You can't do that.  A mountain climber is a scalar.

Q: What do you get when you cross an elephant with a banana?
A: Elephant banana sine theta in a direction mutually perpendicular to
   the two as determined by the right hand rule.

Q: To what question is the answer "9W."
A: "Dr. Wiener, do you spell your name with a V?"
