Here are some quotes that have stuck with me. Each one I think holds an important truth and they do an excellent job in conveying that in just a few words.
===
The Renaissance was the time when Western Europeans lost their awe of the Ancients and realized that they had as much to contribute to civilization and society as the Greeks and Romans had contributed. To modern eyes, the puzzle is not that this should have occurred, but that it should have taken so long for people to lose their inferiority complex.
—J. Gribbin
A problem is grand in science if it lies before us unsolved and we see some way for us to make some headway into it.
—R. Feynman
Nobody made a greater mistake than he who did nothing because he could do only a little.
—E. Burke
Every kind of science, if it has only reached a certain degree of maturity, automatically becomes a part of mathematics.
—D. Hilbert
My rule these days is that if I see a 'new', I know I have to write a 'delete' somewhere. Therefore, I'll get it wrong. Therefore, I shouldn't write the 'new'.
—B. Stroustrup
The fastest computation is the one you don't do.
—Unknown
The chains of habit are too weak to be felt until they are too strong to be broken.
—S. Johnson
"I wear the chain I forged in life," replied the Ghost. "I made it link by link, and yard by yard; I girded it on of my own free-will, and of my own free-will I wore it."
—C. Dickens
The best theory is inspired by practice and the best practice is inspired by theory.
—D. Knuth [Source]
An idea which can be used once is a trick. If it can be used more than once it becomes a method.
—G. Pólya
Society is indeed a contract. It becomes a partnership not only between those who are living, but between those who are living, those who are dead, and those who are to be born.
—E. Burke
If men were angels, no government would be necessary. If angels were to govern men, neither external nor internal controls on government would be necessary. In framing a government which is to be administered by men over men, the great difficulty lies in this: you must first enable the government to control the governed; and in the next place oblige it to control itself.
—J. Madison
My brethren sometimes forget that we are not the Court of Last Resort because we are always right. We are always right because we are the Court of Last Resort.
—[U.S. Supreme Court Justice] R.H. Jackson
The past was erased, the erasure was forgotten, the lie became the truth.
—G. Orwell
The Party told you to reject the evidence of your eyes and ears. It was their final, most essential command.
—G. Orwell
A stupid man's report of what a clever man says can never be accurate, because he unconsciously translates what he hears into something he can understand.
—B. Russell
Nothing can stop an idea whose time has come.
—V. Hugo
More is different.
—P.W. Anderson
The ancients were hesitant to speak, fearing that their actions would not do justice to their words.
—Confucius
When asked why he went about with a lamp in broad daylight, Diogenes confessed, "I am looking for an honest man."
—Unknown
Luck favours the prepared mind.
—L. Pasteur
We must never neglect [to pay attention to] the patient's own use of his symptoms.
—A. Adler
An educator's most important task, one might say his holy duty, is to see to it that no child is discouraged at school, and that a child who enters school already discouraged regains his self-confidence through his school and his teacher.
—A. Adler
The journey is better than the inn.
—M. Cervantes
The abbot ought ever to bear in mind what he is and what he is called; he ought to know that to whom more is entrusted, from him more is exacted.
—St. Benedict
Between stimulus and response there is a space. In that space is our power to choose our response. In our response lies our growth and our freedom.
—V. Frankl
And yet it moves.
—G. Galilei
Give me a place to stand and with a lever I will move the whole world.
—Archimedes
The art of doing mathematics is finding that special case that contains all the germs of generality.
—D. Hilbert
Private victories precede public victories.
—S. Covey
Beware of false prophets, which come to you in sheep's clothing, but inwardly they are ravening wolves. Ye shall know them by their fruits.
—Matthew 7:15-16
A change in perspective is worth 80 IQ points.
—A. Kay
There is no royal road to geometry.
—Euclid
... before going farther I need to mention a few things in my life that have shaped my opinions. The first occurred at Los Alamos during WWII when we were designing atomic bombs. Shortly before the first field test (you realize no small scale experiment can be done―either you have critical mass or you do not), a man asked me to check some arithmetic he had done, and I agreed, thinking to fob it off on some subordinate. When I asked what it was, he said, "It is the probability that the test bomb will ignite the whole atmosphere." I decided I would check it myself! The next day when he came for the answers I remarked to him, "The arithmetic was apparently correct but I do not know about the formulas for the capture cross sections for oxygen and nitrogen―after all, there could be no experiments at the needed energy levels." He replied, like a physicist talking to a mathematician, that he wanted me to check the arithmetic not the physics, and left. I said to myself, "What have you done, Hamming, you are involved in risking all of life that is known in the Universe, and you do not know much of an essential part?" I was pacing up and down the corridor when a friend asked me what was bothering me. I told him. His reply was, "Never mind, Hamming, no one will ever blame you." Yes, we risked all the life we knew of in the known universe on some mathematics. Mathematics is not merely an idle art form, it is an essential part of our society.
—R. Hamming
[On Alonzo Church] The person lecturing us was logic incarnate.
—G.C. Rota
Zi Gong asked: "What do you think if all the people in town like someone?"
"Not too good", said Confucius.
"What if they all hate you?"
"Also not too good. It is better if the good people in town like you, and the evil ones hate you."
—Confucius
You've got to live right, too. It’s the way you live that predisposes you to avoid the traps and see the right facts. You want to know how to paint a perfect painting? It's easy. Make yourself perfect and then just paint naturally. That's the way all the experts do it. The making of a painting or the fixing of a motorcycle isn't separate from the rest of your existence. If you’re a sloppy thinker the six days of the week you aren't working on your machine, what trap avoidance, what gimmicks, can make you all of a sudden sharp on the seventh? It all goes together.
...
The real cycle you're working on is a cycle called yourself. The machine that appears to be "out there" and the person that appears to be "in here" are not two separate things. They grow toward Quality or fall away from Quality together.
—R. Pirsig
One can measure the importance of a scientific work by the number of earlier publications rendered superfluous by it.
—D. Hilbert
===
The Renaissance was the time when Western Europeans lost their awe of the Ancients and realized that they had as much to contribute to civilization and society as the Greeks and Romans had contributed. To modern eyes, the puzzle is not that this should have occurred, but that it should have taken so long for people to lose their inferiority complex.
—J. Gribbin
A problem is grand in science if it lies before us unsolved and we see some way for us to make some headway into it.
—R. Feynman
Nobody made a greater mistake than he who did nothing because he could do only a little.
—E. Burke
Every kind of science, if it has only reached a certain degree of maturity, automatically becomes a part of mathematics.
—D. Hilbert
My rule these days is that if I see a 'new', I know I have to write a 'delete' somewhere. Therefore, I'll get it wrong. Therefore, I shouldn't write the 'new'.
—B. Stroustrup
The fastest computation is the one you don't do.
—Unknown
The chains of habit are too weak to be felt until they are too strong to be broken.
—S. Johnson
"I wear the chain I forged in life," replied the Ghost. "I made it link by link, and yard by yard; I girded it on of my own free-will, and of my own free-will I wore it."
—C. Dickens
The best theory is inspired by practice and the best practice is inspired by theory.
—D. Knuth [Source]
An idea which can be used once is a trick. If it can be used more than once it becomes a method.
—G. Pólya
Society is indeed a contract. It becomes a partnership not only between those who are living, but between those who are living, those who are dead, and those who are to be born.
—E. Burke
If men were angels, no government would be necessary. If angels were to govern men, neither external nor internal controls on government would be necessary. In framing a government which is to be administered by men over men, the great difficulty lies in this: you must first enable the government to control the governed; and in the next place oblige it to control itself.
—J. Madison
My brethren sometimes forget that we are not the Court of Last Resort because we are always right. We are always right because we are the Court of Last Resort.
—[U.S. Supreme Court Justice] R.H. Jackson
The past was erased, the erasure was forgotten, the lie became the truth.
—G. Orwell
The Party told you to reject the evidence of your eyes and ears. It was their final, most essential command.
—G. Orwell
A stupid man's report of what a clever man says can never be accurate, because he unconsciously translates what he hears into something he can understand.
—B. Russell
Nothing can stop an idea whose time has come.
—V. Hugo
More is different.
—P.W. Anderson
The ancients were hesitant to speak, fearing that their actions would not do justice to their words.
—Confucius
When asked why he went about with a lamp in broad daylight, Diogenes confessed, "I am looking for an honest man."
—Unknown
Luck favours the prepared mind.
—L. Pasteur
We must never neglect [to pay attention to] the patient's own use of his symptoms.
—A. Adler
An educator's most important task, one might say his holy duty, is to see to it that no child is discouraged at school, and that a child who enters school already discouraged regains his self-confidence through his school and his teacher.
—A. Adler
The journey is better than the inn.
—M. Cervantes
The abbot ought ever to bear in mind what he is and what he is called; he ought to know that to whom more is entrusted, from him more is exacted.
—St. Benedict
Between stimulus and response there is a space. In that space is our power to choose our response. In our response lies our growth and our freedom.
—V. Frankl
And yet it moves.
—G. Galilei
Give me a place to stand and with a lever I will move the whole world.
—Archimedes
The art of doing mathematics is finding that special case that contains all the germs of generality.
—D. Hilbert
Private victories precede public victories.
—S. Covey
Beware of false prophets, which come to you in sheep's clothing, but inwardly they are ravening wolves. Ye shall know them by their fruits.
—Matthew 7:15-16
A change in perspective is worth 80 IQ points.
—A. Kay
There is no royal road to geometry.
—Euclid
... before going farther I need to mention a few things in my life that have shaped my opinions. The first occurred at Los Alamos during WWII when we were designing atomic bombs. Shortly before the first field test (you realize no small scale experiment can be done―either you have critical mass or you do not), a man asked me to check some arithmetic he had done, and I agreed, thinking to fob it off on some subordinate. When I asked what it was, he said, "It is the probability that the test bomb will ignite the whole atmosphere." I decided I would check it myself! The next day when he came for the answers I remarked to him, "The arithmetic was apparently correct but I do not know about the formulas for the capture cross sections for oxygen and nitrogen―after all, there could be no experiments at the needed energy levels." He replied, like a physicist talking to a mathematician, that he wanted me to check the arithmetic not the physics, and left. I said to myself, "What have you done, Hamming, you are involved in risking all of life that is known in the Universe, and you do not know much of an essential part?" I was pacing up and down the corridor when a friend asked me what was bothering me. I told him. His reply was, "Never mind, Hamming, no one will ever blame you." Yes, we risked all the life we knew of in the known universe on some mathematics. Mathematics is not merely an idle art form, it is an essential part of our society.
—R. Hamming
[On Alonzo Church] The person lecturing us was logic incarnate.
—G.C. Rota
Zi Gong asked: "What do you think if all the people in town like someone?"
"Not too good", said Confucius.
"What if they all hate you?"
"Also not too good. It is better if the good people in town like you, and the evil ones hate you."
—Confucius
You've got to live right, too. It’s the way you live that predisposes you to avoid the traps and see the right facts. You want to know how to paint a perfect painting? It's easy. Make yourself perfect and then just paint naturally. That's the way all the experts do it. The making of a painting or the fixing of a motorcycle isn't separate from the rest of your existence. If you’re a sloppy thinker the six days of the week you aren't working on your machine, what trap avoidance, what gimmicks, can make you all of a sudden sharp on the seventh? It all goes together.
...
The real cycle you're working on is a cycle called yourself. The machine that appears to be "out there" and the person that appears to be "in here" are not two separate things. They grow toward Quality or fall away from Quality together.
—R. Pirsig
One can measure the importance of a scientific work by the number of earlier publications rendered superfluous by it.
—D. Hilbert