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Not precisely pure-math, but ...
Fuller's Law of Cosmic Irreversability:
1 pot T --> 1 pot P
but
1 pot P -/-> 1 pot T
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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"
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A topologist is a man who doesn't know the difference between a coffee
cup and a doughnut.
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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.
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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.
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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."
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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.
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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 ...
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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, the questions and answers will come out next to
each other. Enjoy...
A. The boy has a speech defect
r. geometry
S. A dead parrot
j. bisects
M. The tall kettle boiling on the stove
d. center
O. Why the girl doesn't run a 4-minute mile
n. hypotenuse
E. What you should do when it rains
l. tangent
Q. What the acorn said when he grew up
f. coincide
G. The set of cards is missing
t. polygon
I. How they schedule gym class
h. decagon
K. A geometer who has been to the beach
p. secant
C. What he did when his mother-in-law wanted to go home
b. ellipse
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___ 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. What a boy does on the lake when his motor won't run.
___ 10. What you call a person who writes for an inn.
___ 11. What the captain said when the boat was bombed.
___ 12. What a little acorn says when he grows up.
___ 13. What one does to trees that are in the way.
___ 14. What you do if you have yarn and needles.
___ 15. 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. decagon O. hero
H. arc
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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!"
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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!"
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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's 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 do you think interest
rates are headed?"
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97.3% of all statistics are made up.
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Did you hear the one about the statistician?
Probably....
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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 (a computer engineer) looked
at the problem and said,
"Of course he can't do it. Why, you're putting Descartes before the horse!"
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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 root 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.
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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 that I'll integrate you, I'll differentiate you??"
And the other guy says; "No, I am not scared, I am e to the x."
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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."
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/
| 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
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Why did the cat fall off the roof?
Because he lost his mu. (mew=sound cats make, mu=coeff of friction)
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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!"
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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.
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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."
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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."
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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.
His first-person account can be found (along with many other
fascinating accounts) in the book "More Mathematical People".
Here is the full reference; this book is highly recommended....
Title: More mathematical people : contemporary conversations,
edited by Donald J. Albers, G.L. Alexanderson, Constance Reid.
Edition: 1st ed.
Pub. Info.: Boston : Harcourt Brace Jovanovich, c1990.
Phy Descript: 375 p.
Notes: Includes bibliographical references.
LC Subject: Mathematicians -- Interviews.
Mathematicians -- Biography.
Other Author: Albers, Donald J., 1941-.
Alexanderson, Gerald L.
Reid, Constance.
Status: QA28 .M67 1990
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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!"
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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
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"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."
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Three mathematicians and a physicist walk into a bar.
You'd think the second one would have ducked. (Ha, that quacks me up!)
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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.
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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."
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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.
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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!"
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Last modified 19-November-2001.