**Some good quotes:**

**General:**

**"Not everything that counts can be counted;
and not everything that can be counted counts." - Albert Einstein **

**"The real danger is not that computers will
begin to think like men, but that men will begin to think like computers."
- Sydney Harris**

In H. Eves *Return to Mathematical Circles*, Boston: Prindle, Weber and
Schmidt, 1988.

**"A man is like a fraction whose numerator
is what he is and whose denominator is what he thinks of himself. The larger
the denominator the smaller the fraction."** **- [Count] Lev
Nikolgevich Tolstoy**

In H. Eves *Return to Mathematical Circles*, Boston: Prindle, Weber and
Schmidt, 1989.

**On Mathematics and Science:**

**Referee's report: "This paper contains much
that is new and much that is true. Unfortunately, that which is true is not
new and that which is new is not true." - Anonymous **

In H.Eves *Return to Mathematical Circles*, Boston: Prindle, Weber, and
Schmidt, 1988.

**"An expert is a man who has made all the
mistakes, which can be made, in a very narrow field." - Niels Bohr **

**"A Mathematician is a machine for turning
coffee into theorems." - Paul Erdos**

[upon losing the use of his right eye]

**"Now I will have less distraction."- Leonard Euler**

In H. Eves In *Mathematical Circles*, Boston: Prindle, Weber and Schmidt,
1969.

**"Since the mathematicians have invaded the
theory of relativity, I do not understand it myself anymore.**"
**- Albert Einstein**

In A. Sommerfelt "To Albert Einstein's Seventieth Birthday" in Paul
A. Schilpp (ed.) Albert Einstein, Philosopher-Scientist, Evanston, 1949.

**"Everything should be made as simple as
possible, but not simpler.**" **- Albert Einstein **

*Reader's Digest*. Oct. 1977.

**"The mathematician's patterns, like the
painter's or the poet's must be beautiful; the ideas, like the colors or the
words must fit together in a harmonious way. Beauty is the first test: there
is no permanent place in this world for ugly mathematics."- G.H. Hardy**

*A Mathematician's Apology*, London, Cambridge University Press, 1941.

**"One can measure the importance of a scientific
work by the number of earlier publications rendered superfluous by it."-
David Hilbert**

In H. Eves *Mathematical Circles Revisited*, Boston: Prindle, Weber and
Schmidt, 1971

**"Number theorists are like lotus-eaters
-- having once tasted of this food they can never give it up."- Leopold
Kronecker**

In H. Eves *Mathematical Circles Squared*, Boston: Prindle, Weber and
Schmidt, 1972.

[Asked for a testimony to the effect that Emmy Noether
was a great woman mathematician, he said:]

**"I can testify that she is a great mathematician, but that she
is a woman, I cannot swear.**"**- E. Landau**

J.E. Littlewood, *A Mathematician's Miscellany*, Methuen and Co ltd.,
1953.

**"In symbols one observes an advantage in
discovery which is greatest when they express the exact nature of a thing briefly
and, as it were, picture it; then indeed the labor of thought is wonderfully
diminished."- Gottfried Whilhem Leibniz**

In G. Simmons *Calculus Gems*, New York: McGraw Hill Inc., 1992.

**"No human investigation can be called real
science if it cannot be demonstrated mathematically." - Leonardo Da Vinci**

**I read in the proof sheets of Hardy on Ramanujan:
"As someone said, each of the positive integers was one of his personal
friends." My reaction was, "I wonder who said that; I wish I had."
In the next proof-sheets I read (what now stands), "It was Littlewood who
said..."- J.E. Littlewood**

*A Mathematician's Miscellany*, Methuen Co. Ltd, 1953.

**"The mathematician's best work is art, a
high perfect art, as daring as the most secret dreams of imagination, clear
and limpid. Mathematical genius and artistic genius touch one another."
- Gösta Mittag-Leffler**

In N. Rose *Mathematical Maxims and Minims*, Raleigh NC:Rome Press Inc.,
1988.

**"Neither you nor I nor anybody else knows
what makes a mathematician tick. It is not a question of cleverness. I know
many mathematicians who are far abler than I am, but they have not been so lucky.
An illustration may be given by considering two miners. One may be an expert
geologist, but he does not find the golden nuggets that the ignorant miner does."
- , L. J.** **Mordell**

In H. Eves *Mathematical Circles Adieu*, Boston: Prindle, Weber and Schmidt,
1977.

**"...from the same principles, I now demonstrate
the frame of the System of the World."- Isaac Newton**

*Principia Mathematica.*

[On the attention he received after finding the flaw
in Intel's Pentium chip in 1994]

**"Usually mathematicians have to shoot somebody to get this much
publicity.**" **- Thomas R. Nicely**

Cincinnati Enquirer, December 18, 1994, Section A, page 19.

**"We arrive at truth, not by reason only,
but also by the heart." - Blaise Pascal**

Pensees. 1670.

**"Chance favors only the prepared mind."
- Louis Pasteur**

In H. Eves *Return to Mathematical Circles*, Boston: Prindle, Weber and
Schmidt, 1988

**"Science is built up with facts, as a house
is with stones. But a collection of facts is no more a science than a heap of
stones is a house." - Jules Henri Poincaré**

*La Science et l'hypothèse. *

**"Mathematical discoveries, small or great
are never born of spontaneous generation. They always presuppose a soil seeded
with preliminary knowledge and well prepared by labour, both conscious and subconscious."-
Jules Henri Poincaré**

**"A good notation has a subtlety and suggestiveness
which at times make it almost seem like a live teacher." - Bertrand Russell**

In J. R. Newman (ed.) *The World of Mathematics*, New York: Simon and
Schuster, 1956

**"This paper gives wrong solutions to trivial
problems. The basic error, however, is not new." - Clifford Truesdell**

*Mathematical Reviews* 12, p561.

**"Every mathematician worthy of the name
has experienced ... the state of lucid exaltation in which one thought succeeds
another as if miraculously... this feeling may last for hours at a time, even
for days. Once you have experienced it, you are eager to repeat it but unable
to do it at will, unless perhaps by dogged work..." - Andre Weil **

*The Apprenticeship of a Mathematician.*

**"My work has always tried to unite the true
with the beautiful and when I had to choose one or the other, I usually chose
the beautiful.**" **- Hermann Weyl**

In an obituary by Freeman J. Dyson in *Nature*, March 10, 1956.

**On Teaching:**

**"Everything should be made as simple as
possible, but not simpler.**" **- Albert Einstein **

*Reader's Digest*. Oct. 1977.

**"When introduced at the wrong time or place,
good logic may be the worst enemy of good teaching." - George Polyá
**

**"We are not very pleased when we are forced
to accept a mathematical truth by virtue of a complicated chain of formal conclusions
and computations, which we traverse blindly, link by link, feeling our way by
touch. We want first an overview of the aim and of the road; we want to understand
the idea of the proof, the deeper context." - Hermann Weyl**

*Unterrichtsblätter für Mathematik und Naturwissenschaften*,
38, 177-188 (1932). Translation by Abe Shenitzer appeared in The American Mathematical
Monthly, v. 102, no. 7 (August-September 1995), p. 646.

**On Ability and Creativity**:

**"Natural abilities are like natural plants
that need pruning by study.**" **- Francis Bacon**

**"The creative person is both more primitive
and more cultivated, more destructive and more constructive, a lot madder and
a lot saner, than the average person." - Frank Barron**

**"There is no one definitive creative path.
There are many ways to be creative – not only intuitive ways but organized,
logical ways, too." - Theresa Bayer**

**"The essential ingredient for creativity
is wasting time." - Anonymous**

**"The infinitely competent can be uncreative."
- J. E. Littlewood**

In H. Eves *Mathematical Circles Squared*, Boston: Prindle, Weber and
Schmidt, 1972.

**Chase and Max Quotes**:

**"Rewind. Rewind." - Chase Holdener, Age 1**

After learning that his favorite parts of movies could be seen again by rewinding
the video, Chase began requesting that we "rewind" real life so that
he could experience happy moments again and again.

**"If I drop a ball, is it falling
or is it felling?" - Chase Holdener, Age 2**

**"But I have things that I have to do."
- Chase Holdener, Age 2 **

Chase's response
to Mom's statement that he needed to go to bed earlier.

**"Mommy, I love you infinity, but I love
myself infinity infinities." - Chase Holdener, Age 3**

**"Mathematics is for girls. Mommy studies
mathematics. I'm going to be a rockamatician like Daddy." - Chase Holdener,
Age 3 **

**"I don't want to be the same thing as a
moose!" - Chase Holdener, Age 3
**Chase was clearly upset (we're talking
real tears!) to learn that he was a mammal just like a moose.

**"Is George Bush real?" - Chase Holdener,
Age 3
**This question came shortly after Chase
went to his first baseball game (Colorado Rockies vs. Kansas City Royals in
Denver). At the game he kept saying "these baseball players are real."
It wasn't until the next day that I realized he had made the connection that
some things on TV are real and others aren't. While watching Bush give a speech
the following evening, Chase asked this question. Then he assured me that Clifford
the big red dog is not real.

**"Someday everybody
here will be dead, and all of the buildings will be dust." - Chase Holdener,
Age 3
**Chase's exclamation to his preschool teacher after his visit
to Elizabethtown, a ghost town in New Mexico.

**"Zombies are dead people who come back to
life. *** Pause. *** Jesus
came back to life, so Jesus is a zombie." - Chase Holdener, Age 4**

**"Mommy, I'm frustrated. How do I know if
I am real?" - Chase Holdener, Age 4**

**"They might as well charge $20" - Chase
Holdener, Age 5
**Chase's observation after seeing that a product was priced at
$19.99.

**"Five hundred and ninety five dollars is
*a lot* for a dinner." - Chase Holdener, Age 5
**Chase's statement after noticing the one missing decimal point
among a list of $5.95 meals advertised on a restaurant's white board.

**"Ah-goo" - Max Holdener, Age 3 months.**

**"Emma says that a googolplex is the biggest
number. I told her that a googolplex plus one is bigger." - Chase Holdener,
Age 6
**