Alphabetical by Author
Friendship is nonlinear.
much used, familiar, and clunky.
Little brains ... have only room for thoughts of
bread and butter.
in "The South Pole".
Question: How would you like me to cut your hair?
Answer: Silently. Lost in antiquity.
In mathematics the art of asking questions is more
valuable than solving problems. Title of
Ph.D. thesis (translated from Latin).
I offer nothing but blood, sweat, toil, and tears.
addressing the British people upon declaring war on
Sir, if I was married to you I would poison your
tea! (A forgotten enemy to Winston Churchill.)
Madam, if I was married to you I would drink it!
Democracy is the worst form of government, with the
exception of all others.
Becoming sufficiently familiar with something is a
substitute for understanding it.
, in a talk
Knots and Numbers, Tangles and Bangles
, May 15, 1996, University of Utah Frontiers of Science
40 minutes of continuous country music an hour -
it adds up to well over 1,000 minutes a day!
Slogan of KKAT,
a Salt Lake country music station, repeated several times a day
Fortunately, creative minds forget dogmatic
philosophical beliefs whenever adherence to them would
impede constructive achievement. For scholars and
layman alike it is not philosophy but active experience
in mathematics itself that alone can answer the
question: What is Mathematics?
Courant and Robbins (in "What is
A year ago we were standing at the edge of a
precipice. Since then we have taken a large step
forward. Effect of a too literal translation of a
Mao Ze Dong.
Do not worry about your difficulties in
mathematics. I can assure you that mine are still
I have little patience with scientists who pick a
board of wood, find its thinnest part, and drill a great
many holes where the drilling is easy.
Many writers have acquired the dexterity of
spreading a few critical thoughts over several hundred
Britannica, 1st edition, 1771, v.1,, in the article on
Life is too short, and so crowded with cares, that but
little time is left for any single man to employ himself in
unfolding the mysteries of nature.
Encyclopedia Britannica, 1st edition, 1771, v.2,
Eventually you reach the point where you have to
draw the line.
Euclid's Last Theorem
(Network Humor, source unknown).
Classification of mathematical problems as linear
and nonlinear is like classification of the Universe
as bananas and non-bananas.
(Network Humor, source unknown).
I think I can safely say that nobody understands
I couldn't do it. I couldn't reduce it to the
freshman level. That means we don't really understand
(on why spine one-half particles obey Fermi-Dirac
The paradox is only a conflict between reality and
your feeling of what reality ought to be.
If you treat individuals as they are they will
remain as they are, but if you treat them as if they
were what they ought to be and could be, they will
become what they ought to be and could be.
Johann Wolfgang von Goethe.
The purpose of computing is insight, not numbers.
Botany is simple. I divide plants into two kinds:
those that you can eat and those you cannot eat.
A ship in port is safe, but that's not what ships
are built for.
Grace Brewster Murray Hopper.
(The use of the word "bug" is also due to
Grace Hopper. She traced a computer problem to a dead
bug in the hardware and taped that bug into her
University politics are vicious precisely because
the stakes are so small.
Being able to recognize the negation of a
statement involving a quantifier is one of the most
important skills in logic. For instance, consider the
statement "All dogs are brown." In order for this
statement to be false, you do not have to show that
all dogs are not brown, you must simply find at
least one dog that is not brown. So, the negation of
the statement is "Some dogs are brown."
(page A45 of the third edition of Larson, Hostetler,
and Heyd, Intermediate Algebra, Houghton Mifflin Co.,
I have climbed so many mountains/just to reach the
(The opening lines of the lead song of "When fallen
Angles fly", the 1995 Country Music album of the
year, a very beautiful album indeed.)
I try to contemplate the cosmos.
(in the same album).
The trouble with the truth / is it always begs for
in "The trouble with the truth", from the 1996
album by the same name.
I think I may fairly make two postulata. First,
That food is necessary to the existence of man.
Secondly, That the passion between the sexes is
necessary and will remain nearly in its present state.
An Essay on the Principle of Population, 1798.
... alas! alas! life is full of disappointments;
as one reaches one ridge there is always another and a
higher one beyond which blocks the view.
(in "The First Crossing of Greenland")
A vulgar Mechanick can practice what he has been
taught or seen done, but if he is in an error he knows
not how to find it out and correct it, and if you put
him out of his road, he is at a stand; Whereas he that
is able to reason nimbly and judiciously about figure,
force and motion, is never at rest till he gets over
to Nathaniel Hawes, 25 May 1694, quoted in
In theory, there is no
difference between theory and practice. But, in practice, there is.
Richard M. Nixon
A wise man knows everything, a shrewd one,
everybody. Peking Noodle Company
Our intelligence is finite, so probably there must
come a time at which we approach an inherent human
intellectual limit and progress grinds to a halt. Is
there such a limit? Is this it? University of Utah
as quoted in the Salt Lake Tribune of March 22,
1996. (He was talking in the context of quantum
We have nothing to fear but fear itself.
Franklin D. Roosevelt.
Sacred cows make the best hamburger. Marine General
Jack Sheehan, quoted in Newsweek of July 14,
1997, p. 35.
In every game there must be losers and winners.
Part of the art of playing a game well is to be a "
good" loser or a gracious winner. Let the other
fellow be the good loser. As for you, just accept your
victory casually and naturally, as befits a player who
has finished reading this entire book.
5 Weeks to winning Bridge
Logic is in the eye of the logician.
He loves mathematics, and he loves his students.
An anonymous student in an evaluation of a course I taught.
Because someone with a foreign accent told us so.
An anonymous student, in response to the
question Why do we multiply matrices this way?
It's a cosmic law. Another anonymous
student, in response to the question Why do we
multiply matrices this way?
There are three kinds of mathematicians, those who
can count and those who can't. University of Utah
Math Professor Don Tucker (holding up four
It ain't what you don't know that gets you into
trouble. It's what you know for sure that just ain't so.
Always do right- this will gratify some and
astonish the rest.
The difference between the right word and the
almost right word is the difference between lightning
and the lightning bug.
She [the boat] shuddered as if she had
hit a continent.
(in Old Times on the Mississippi.) Now,
that's vivid writing!
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