My daughter Lea's
Math Poem and
Math Poem II.
My nephew Jim Mullinax wrote
The Ghostly Buick of Highway 21
for his Differential Equations class.
Q. How do you know when a mathematician is extroverted?
A. He looks at YOUR shoes when he talks to you.
The first mathematician says, "It's obvious."
Three hours later, the second mathematician says,
"Of course, yes, it's obvious!"
Q. What is purple and commutes?
Standard answer: An Abelian Grape.
Answers from my Abstract Algebra class, Spring 2007:
1. Barney the purple dinosaur. He lives in Newark but works in
New York City, so he takes the subway every morning.
2. A sick, working, pink panther.
3. A suburban eggplant with a job in Atlanta.
4. A purple commutative ring.
5. The set {ab : a, b in Z} written in purple ink.
Seen on a public bathroom wall:
HEISENBERG MAY HAVE BEEN HERE.
Q. What is the physicist's definition of a vector space?
A. A set V satisfying the axiom that for any x in V, x has a little
arrow drawn over it.
One day a farmer called up an engineer, a physicist, and a mathematician and
asked them to fence off 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
built a tiny fence around himself and said "I declare myself to be on
the outside."
An engineer, a physicist, and a mathematician are jailed in three different
cells and after a week of not eating are each given a single unopened can
for food. The engineer fashions a can-opening device from some buttons on
his shirt and part of the commode in the cell and easily succeeds in neatly
opening the can. The physicist is found the next day in his cell with the
can smashed on the floor and food all over the place, but he succeeded in
opening the can and ate just enough food to survive. The mathematician is
found dead in his cell the next day, with the still unopened can sitting
next to him. Under the can is a scrap of paper with some writing scrawled
on it. It says "Suppose the can is open...."
Ancient and anonymous methods of proof: Proof by ______________
1. Handwaving.
2. Intimidation.
3. Referral to non-existent authority.
4. The method of least astonishment.
5. Reductio ad nauseum.
6. Reduction to a sequence of unrelated lemmas (also called the
method of convergent irrelevancies).
7. Deferral until later in the course.
8. Deferral until after the course is completed.
9. Assignment.
Top Ten Excuses For Not Doing Math Homework:
1. I accidentally divided by zero and my paper burst into flames.
2. It's Isaac Newton's birthday.
3. I could only get arbitrarily close to my textbook. I couldn't
actually reach it.
4. I have the proof, but there isn't room to write it in this margin.
5. I was watching the World Series and got tied up trying to prove
that it converged.
6. I have a solar powered calculator and it was cloudy.
7. I locked the paper in my trunk but a four-dimensional dog got in
and ate it.
8. I couldn't figure out whether i am the square of negative one or
i is the square root of negative one.
9. I took time out to snack on a doughnut and a cup of coffee. I
spent the rest of the night trying to figure which one to dunk.
10. I could have sworn I put the homework inside a Klein bottle, but
this morning I couldn't find it.
Definitions of Terms Commonly Used in Higher Math
The following is a guide to the weary student of mathematics who
is often confronted with terms which are commonly used but rarely defined.
In the search for proper definitions for these terms we found no
authoritative, nor even recognized, source. Thus, we followed the
advice of mathematicians handed down from time immortal: "Wing It."
CLEARLY: I don't want to write down all the "in-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.
"There are no good math jokes." – Anonymous
"I'm not losing—I'm just not currently winning."
– Andrew Heil
What is yellow and equivalent to the Axiom of Choice? Zorn's Lemon!
– Anonymous
What is yellow and vanishes at infinity? The Riemann-Lebesgue Lemon!
– Akram Aldroubi
"What is measured is not the truth."
– J. Tukey
"An expert is someone who knows some of the worst mistakes that can be
made in his subject, and how to avoid them."
– Werner Heisenberg
"Wavelet theory would have been impossible without TeX."
– Bernd Fischer (Luebeck)
"Do not worry about your difficulties in mathematics.
I can assure you that mine are even greater."
– Albert Einstein
"A man whose mind has gone astray should study mathematics."
– Francis Bacon
"All great theorems were discovered after midnight."
– Adrian Mathesis
"We have a habit in writing articles published in scientific journals to
make the work as finished as possible, to cover up all the tracks, to not
worry about the blind alleys or describe how you had the wrong idea first,
and so on. So there isn't any place to publish, in a dignified manner, what
you actually did in order to get to do the work."
– Richard Feynman
A tautology is a thing that is tautological.
If it happens, it must be possible.
"The good Christian should beware of mathematicians and all those who
make empty prophecies. The danger already exists that mathematicians
have made a covenant with the devil to darken the spirit and confine
man in the bonds of Hell."
– St. Augustine
It would just be terrible if it wasn't true, seeing as how I just proved it.
– George Cain
No question is so difficult as one to which the answer is obvious.
Math is like love—a simple idea but it can get complicated.
– R. Drabek
If you think the problem is bad now, just wait until we've solved it.
– Arthur Kasspe
Young man, in mathematics you don't understand things, you just get used
to them.
– von Neumann
Everything in this proof holds up to loss of generality.
– joey montgomery
In theory every theory works fine.
When it comes to professors, the following happens with a nontrivial
frequency: He/she will say one thing, write something else, mean a third
thing. A fourth thing will turn out to be correct.
"Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk."
– Leopold Kronecker
"Nobody wants to be the zero vector."
– Clark Alexander
"Want to meet Erdos? Just wait here and wait. He'll show up."
– referring to Erdos' nomadic tendency
"We mathematicians are all a bit crazy."
– Edmund Landau
"My brain is open."
– Erdos would often say this to mathematicians meeting him
"Beauty is the first test: there is no permanent place in the world for ugly
mathematics."
– G.H. Hardy
"It is a far finer gambit than any chess gambit, a chess player may offer the
sacrifice of a pawn or even a piece, but the mathematician offers the game."
– G.H. Hardy on proof by contradiction
"A mathematician is a machine for turning coffee into theorems."
"If numbers aren't beautiful, I don't know what is."
– Erdos
"Only professional mathematicians learn anything from proofs. Other people
learn from explanations."
– Ralph Boas
"An optimist sees a glass half full, a pessimist sees a glass half empty,
and an engineer sees a glass twice as big as it should be."
"God has a transfinite book with all the theorems and their best proofs. I
sometimes say, 'you don't really have to believe in God as long as you
believe in the book.' Of course, I do not really believe that The Book exists."
– Erdos
"The expression 'correct proof' is redundant. Mathematical proof does not
admit degrees. A sequence of steps in an argument is either a proof, or it
is meaningless."
– Gian-Carlo Rota
About George Burdell:
What else is left to say about the man? But I will try. He once counted to
infinity, Twice. When Google cant find the answer, they ask George. He can
lead a horse to water AND make him drink. He hits blackjack with just one card.
Superman wears George Burdell Pajamas. George checkmated Bobby Fisher, using
only his king.
– From "Rate My Professors"
"Mathematics is an experimental science, and definitions do not come first,
but later on."
– Oliver Heaviside