The origin and immediate purpose of the introduction of complex magnitudes into mathematics lie in the theory of simple laws of dependence between variable magnitudes expressed by means of operations on magnitudes. If we enlarge the scope of applications of these laws by assigning to the variables they involve complex values, then there appears an otherwise hidden harmony and regularity. | |

Ebbinghaus, quoted in "Thinking the Unthinkable: The Story of Complex
Numbers (with a Moral)," by Israel Kleiner, Mathematics Teacher, Oct. 1988. |
96 |

Life would be stunted and narrow if we could feel no significance in the world around us beyond that which can be weighed and measured with the tools of the physicist or described by the metrical symbols of the mathematician. | |

Sir Arthur Eddington, |
1576 |

There was just one place where [Einstein's] theory did not seem to work properly, and that was -- infinity. I think Einstein showed his greatness in the simple and drastic way in which he disposed of difficulties at infinity. He abolished infinity. He slightly altered his equations so as to make space at great distances bend round until it closed up. So that, if in Einstein's space you keep going right on in one direction, you do not get to infinity; you find yourself back at your starting-point again. Since there was no longer infinity, there could be no difficulties at infinity. | |

Sir Arthur Eddington, quoted in To Infinity and Beyond by Eli Maor. |
658 |

Proof is an idol before which the mathematician tortures himself. | |

Sir Arthur Eddington, quoted in Bridges to Infinity by Michael Guillen. |
533 |

Not only is the universe stranger than we imagine, it is stranger than we can imagine. | |

Sir Arthur Eddington, |
1281 |

If we don't stand up for children, then we don't stand for much. | |

Marian Wright Edelman, |
1017 |

There ain't no rules around here! We're trying to accomplish something! | |

Thomas Edison, quoted in The Fourth, and By Far the Most Recent, 637 Best
Things Anybody Ever Said, by Robert Byrne. |
95 |

There is great value in disaster. All our mistakes are burned up. Thank God we can start again. [Dec. 10, 1914, the night after a fire destroyed his life work, Edison Industries of West Orange, N.J.] | |

Thomas Alva Edison, |
937 |

I have not failed. I have just found 10,000 ways that won't work. | |

Thomas Edison, |
1766 |

Opportunity is missed by most because it is dressed in overalls and looks like work. | |

Thomas Edison, |
1583 |

He [Glenn Draper] got me reading these calculus books in the old Newtonian style, the infinitesimal way, and this nonsense with Dedekind cuts and real numbers, and he got me to reading non-Euclidean geometry and so on. Well, boy, this was heady stuff for a fifteen year old!... Hell, I had been kept in at recess all my life for not being able to do my arithmetic. But this idea of proving [theorems in Euclidean geometry] was really thrilling. | |

Jack Edmonds, from "A Glimpse of Heaven," from History of Mathematical Programming: A Collection of Personal Reminiscences edited by Lenstra, Rinnooy Kan, and Schrijver. |
1237 |

O, Youth: Do you know that yours is not the first generation to yearn for a life full of beauty and freedom? Do you know that all your ancestors have felt the same as you do -- and fell victim to trouble and hatred? Do you know also that your fervent wishes can only find fulfillment if you succeed in attaining love and understanding of people, and animals, and plants, and stars, so that every joy becomes your joy and every pain your pain? | |

Albert Einstein, quoted in The Quotable Einstein edited by Alice Calaprice. |
644 |

The state of mind which enables a man to do work of this kind [scientific research]... is akin to that of the religious worshiper or the lover; the daily effort comes from no deliberate intention or program, but straight from the heart. | |

Albert Einstein, quoted in The Quotable Einstein edited by Alice Calaprice. |
637 |

After a certain high level of technical skill is achieved, science and art tend to coalesce in esthetics, plasticity, and form. The greatest scientists are always artists as well. | |

Albert Einstein, quoted in The Quotable Einstein edited by Alice Calaprice. |
638 |

The grand aim of all science is to cover the greatest number of empirical facts by logical deduction from the smallest number of hypotheses or axioms. | |

Albert Einstein, quoted in The Quotable Einstein edited by Alice Calaprice. |
639 |

Science is a wonderful thing if one does not have to earn a living at it. One should earn one's living by work of which one is sure one is capable. Only when we do not have to be accountable to anyone can we find joy in scientific endeavor. | |

Albert Einstein, quoted in The Quotable Einstein edited by Alice Calaprice. |
640 |

In the beginning (if there was such a thing), God created Newton's laws of motion together with the necessary masses and forces. This is all; everything beyond this follows from the development of appropriate mathematics methods by means of deduction. | |

Albert Einstein, quoted in The Quotable Einstein edited by Alice Calaprice. |
641 |

I believe that older people who have scarcely anything to lose ought to be willing to speak out on behalf of those who are young and who are subject to much greater restraint. | |

Albert Einstein, quoted in The Quotable Einstein edited by Alice Calaprice. |
643 |

Teaching should be such that what is offered is perceived as a valuable gift and not as a hard duty. | |

Albert Einstein, quoted in The Quotable Einstein edited by Alice Calaprice. |
636 |

Whoever undertakes to set himself up as a judge of Truth and Knowledge is shipwrecked by the laughter of the gods. | |

Albert Einstein, |
983 |

The truth of a theory is in your mind, not in your eyes. | |

Albert Einstein, |
862 |

Logic will get you from A to B. Imagination will take you everywhere. | |

Albert Einstein, |
833 |

People like you and I, though mortal of course, like everyone else, do not grow old no matter how long we live. What I mean is that we never cease to stand like curious children before the great Mystery into which we were born. | |

Albert Einstein, quoted in The Quotable Einstein edited by Alice Calaprice. |
642 |

We never cease to stand like curious children before the great mystery into which we are born. | |

Albert Einstein, quoted in From Agnesi to Zeno, by Sanderson Smith |
106 |

Pure mathematics is, in its way, the poetry of logical ideas. | |

Albert Einstein, |
97 |

But there is another reason for the high repute of mathematics, it is mathematics that offers the exact natural sciences a certain measure of security which, without mathematics, they could not attain. | |

Albert Einstein, |
98 |

Imagination is more important than knowledge. | |

Albert Einstein, |
99 |

Since the mathematicians have invaded the theory of relativity, I do not understand it myself anymore. | |

Albert Einstein, quoted in The World of Mathematics, by J.R. Newman. |
100 |

Whatever your difficulties in mathematics, I can assure you mine are far greater. | |

Albert Einstein, |
101 |

How can it be that mathematics, being after all a product of human thought independent of experience, is so admirably adapted to the objects of reality? | |

Albert Einstein, |
102 |

As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality. | |

Albert Einstein, quoted in A Mathematical Sampler: Topics for Liberal Arts,
by W.P. Berlinghoff and K.E. Grant. |
103 |

It is not so very important for a person to learn facts. For that he does not really need a college. He can learn them from books. The value of an education in a liberal arts college is not the learning of many facts but the training of the mind to think something that cannot be learned from textbooks. | |

Albert Einstein, quoted in The Quotable Einstein edited by Alice Calaprice. |
634 |

Most of the fundamental ideas of a science are essentially simple, and may, as a rule, be expressed in a language comprehensible to everyone. | |

Albert Einstein, |
105 |

Humiliation and mental oppression by ignorant and selfish teachers wreak havoc in the youthful mind that can never be undone and often exert a baleful influence in later life. | |

Albert Einstein, quoted in The Quotable Einstein edited by Alice Calaprice. |
635 |

Science is the attempt to make the chaotic diversity of our sense-experiments correspond to a logically uniform system of thought. | |

Albert Einstein, |
107 |

It is in fact nothing short of a miracle that the modern methods of instruction have not entirely strangled the holy curiosity of inquiry; for this delicate little plant, aside from stimulation, stands mainly in need of freedom; without this it goes to wrack and ruin without fail. | |

Albert Einstein, |
108 |

It is the supreme art of the teacher to awaken joy in creative expression and knowledge. | |

Albert Einstein, quoted in A Teacher's Treasury of Quotations, by Bernard E. Farber. |
109 |

Great spirits have always encountered violent opposition from mediocre minds. | |

Albert Einstein, quoted in A Teacher's Treasury of Quotations, by Bernard
E. Farber. |
110 |

The most beautiful thing we can experience is the mysterious. It is the source of all true art and science. | |

Albert Einstein, quoted in The Magic of Mathematics, by Theoni Pappas. |
487 |

Teaching should be such that what is offered is perceived as a valuable gift rather than a hard duty. | |

Albert Einstein, from the Quotable Einsetin. |
498 |

The series of integers is obviously an invention of the human mind, a self-created tool which simplifies the ordering of certain sensory experiences. | |

Albert Einstein, |
611 |

In the middle of difficulty lies opportunity. | |

Albert Einstein, |
1051 |

I have no particular talent. I am only inquisitive. | |

Albert Einstein, quoted in From Agnesi to Zeno, by Sanderson Smith. |
104 |

Never regard study as a duty, but as the enviable opportunity to learn to know the liberating influence of beauty in the realm of the spirit for your own personal joy and to the profit of the community to which your later work belongs. | |

Albert Einstein, |
1592 |

The most beautiful thing we can experience is the mysterious. It is the source of all true art and all science. He to whom this emotion is a stranger, who can no longer pause to wonder and stand rapt in awe, is as good as dead: his eyes are closed. | |

Albert Einstein, |
1444 |

[On his Father showing him a compass:] [It] made a deep and lasting impression on me. Something deeply hidden had to be behind things. | |

Albert Einstein, quoted in The Ten Most Beautiful Experiments by George Johnson. |
1301 |

My dear children: I rejoice to see you before me today, happy youth of a sunny and fortunate land. Bear in mind that the wonderful things that you learn in your schools are the work of many generations, produced by enthusiastic effort and infinite labour in every country of the world. All this is put into your hands as your inheritance in order that you may receive it, honour it, and add to it, and one day faithfully hand it on to your children. Thus do we mortals achieve immortality in the permanent things which we create in common. If you always keep that in mind you will find meaning in life and work and acquire the right attitude towards other nations and ages. | |

Albert Einstein, to a group of school children in 1934. |
1289 |

When, after several hours reading, I came to myself again, I asked myself what it was that had so fascinated me. The answer is simple. The results were not presented as ready-made, but scientific curiosity was first aroused by presenting contrasting possibilities of conceiving matter. Only then the attempt was made to clarify the issue by thorough argument. The intellectual honesty of the author makes us share the inner struggle in his mind. It is this which is the mark of the born teacher. Knowledge exists in two forms - lifeless, stored in books, and alive, in the consciousness of men. The second form of existence is after all the essential one; the first, indispensable as it may be, occupies only an inferior position. | |

Albert Einstein, |
1287 |

Somebody who only reads newspapers and at best books of contemporary authors looks to me like an extremely near-sighted person who scorns eyeglasses. He is completely dependent on the prejudices and fashions of his times, since he never gets to see or hear anything else. And what a person thinks on his own without being stimulated by the thoughts and experiences of other people is even in the best case rather paltry and monotonous. There are only a few enlightened people with a lucid mind and style and with good taste within a century. What has been preserved of their work belongs among the most precious possessions of mankind. We owe it to a few writers of antiquity (Plato, Aristotle, etc.) that the people in the Middle Ages could slowly extricate themselves from the superstitions and ignorance that had darkened life for more than half a millennium. Nothing is more needed to overcome the modernist's snobbishness. | |

Albert Einstein, 1954. |
1286 |

A human being is part of the whole called by us universe, a part limited in time and space. We experience ourselves, our thoughts and feelings as something separate from the rest. A kind of optical delusion of consciousness. This delusion is a kind of prison for us, restricting us to our personal desires and to affection for a few persons nearest to us. Our task must be to free ourselves from the prison by widening our circle of compassion to embrace all living creatures and the whole of nature in its beauty. We shall require a substantially new manner of thinking if mankind is to survive. | |

Albert Einstein, |
1285 |

People like us, who believe in physics, know that the distinction between past, present, and future is only a stubbornly persistent illusion. | |

Albert Einstein, |
1451 |

A human being is a part of a whole, called by us 'universe', a part limited in time and space. He experiences himself, his thoughts and feelings as something separated from the rest... a kind of optical delusion of his consciousness. This delusion is a kind of prison for us, restricting us to our personal desires and to affection for a few persons nearest to us. Our task must be to free ourselves from this prison by widening our circle of compassion to embrace all living creatures and the whole of nature in its beauty. | |

Albert Einstein, |
1452 |

The most beautiful and most profound experience is the sensation of the mystical. It is the power of all true science. He to whom this emotion is a stranger, who can no longer wonder and stand rapt in awe, is as good as dead. To know that what is impenetrable to us really exists, manifesting itself as the highest wisdom and the most radiant beauty which our dull faculties can comprehend only in their primitive forms - this knowledge, this feeling is at the center of true religiousness. | |

Albert Einstein, from The Merging of Spirit and Science. |
1284 |

There are two ways to live your life - one is as though nothing is a miracle, the other is as though everything is a miracle. | |

Albert Einstein, |
1453 |

In your schooldays most of you who read this book made acquaintance with the noble building of Euclid's geometry, and you remember -- perhaps with more respect than love -- the magnificent structure, on the lofty staircase of which you were chased about for uncounted hours by conscientious teachers. | |

Albert Einstein, from Relativity: The Special and General Theory |
1555 |

Every reference-body (co-ordinate system) has its own particular time; unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an event. | |

Albert Einstein, from Relativity: The Special and General Theory |
1557 |

The world is a dangerous place, not because of those who do evil, but because of those who look on and do nothing. | |

Albert Einstein, |
1378 |

The gift of fantasy has meant more to me than my talent for absorbing knowledge. | |

Albert Einstein, |
1686 |

The formulation of a problem is often more essential than its solution, which may be merely a matter of mathematical or experimental skill. | |

Albert Einstein, |
1758 |

We can't solve problems by using the same kind of thinking we used when we created them. | |

Albert Einstein, |
1745 |

All religions, arts and sciences are branches of the same tree. All these aspirations are directed toward ennobling man's life, lifting it from the sphere of mere physical existence and leading the individual towards freedom. | |

Albert Einstein, |
1739 |

Geometry sets out form certain conceptions such as plane, point, and straight line, with which we are able to associate more or less definite ideas, and from certain simple propositions (axioms) which, in virtue of these ideas, we are inclined to accept as true. Then, on the basis of a logical process, the justification of which we feel ourselves compelled to admit, all remaining propositions are shown to follow from those axioms, i.e. they are proven. A proposition is then correct (true) when it has been derived in the recognized manner from the axioms. The question of truth of the individual geometrical propositions is thus reduced to one of the truth of the axioms. Now it has long been known that the last question is not only unanswerable by the methods of geometry, but that it is in itself entirely without meaning. We cannot ask whether it is true that only one straight line goes through two points. We can only say that Euclidean geometry deals with things called straight lines, to each of which is ascribed the property of being uniquely determined by two points situated on it. The concept true does not tally with the assertions of pure geometry, because by the word true we are eventually in the habit of designating always the correspondence with a real object; geometry, however, is not concerned with the relation of the ideas involved in it to objects of experience, but only with the logical connection of these ideas among themselves. | |

Albert Einstein, from Relativity: The Special and General Theory. |
1556 |

We merely want to live in peace with all the world, to trade with them, to commune with them, to learn from their culture as they may learn from ours, so that the products of our toil may be used for our schools and our roads and our churches and not for guns and planes and tanks and ships of war. | |

Dwight D. Eisenhower, |
848 |

Every gun that is made, every warship launched, every rocket fired signifies in the final sense, a theft from those who hunger and are not fed, those who are cold and are not clothed. This world in arms is not spending money alone. It is spending the sweat of its laborers, the genius of its scientists, the hopes of its children. This is not a way of life at all in any true sense. Under the clouds of war, it is humanity hanging on a cross of iron. | |

Dwight D. Eisenhower, from American Society of Newspaper Editors, 16 April 1953 |
847 |

We shall not cease from exploration. And the end of all our exploring will be to arrive where we started and know the place for the first time. | |

T. S. Eliot, |
1734 |

Human kind cannot bear much reality. | |

T.S. Eliot, |
866 |

Knowledge is knowing that we cannot know. | |

Ralph Waldo Emerson, |
1700 |

Unless you try to do something beyond what you have already mastered, you will never grow. | |

Ralph Waldo Emerson, |
912 |

People wish to be settled: only as far as they are unsettled is there any hope for them. | |

Ralph Waldo Emerson, from Essays, 1841. |
1236 |

Every great and commanding moment in the annals of the world is the triumph of some enthusiasm. | |

Ralph Waldo Emerson, quoted in The Teacher's Quotation Book, edited by Wanda Lincoln and Murray Suid. |
629 |

The eye is the first circle; the horizon which it forms is the second; and throughout nature this primary figure is repeated without end. It is the highest emblem in the cipher of the world. | |

Ralph Waldo Emerson, quoted in Mathematically Speaking: A Dictionary of Quotations edited by C.C. Gaither and A.E. Cavazos-Gaither. |
1241 |

We are too civil to books. For a few golden sentences we will turn over and actually read a volume of four or five hundred pages. | |

Ralph Waldo Emerson, |
993 |

If the single man plants himself indomitably on his instincts, and there abides, the huge world will become round to him | |

Ralph Waldo Emerson, |
927 |

Do not go where the path may lead, go instead where there is no path and leave a trail. | |

Ralph Waldo Emerson, |
1330 |

Most of the shadows of this life are caused by standing in our own sunshine | |

Ralph Waldo Emerson, |
933 |

A day is a miniature eternity. | |

Ralph Waldo Emerson, |
871 |

When variable magnitudes entered mathematics and when their variability was extended to the infinitely small and infinitely large, then mathematics, usually so very moral, perpetrated the Fall: it ate the apple of knowledge and this opened for it it the road to gigantic achievements but also to delusions. The virgin state of absolute meaningfulness, of irrefutable provability of all things mathematical... belonged to the past. An era of discord had arrived. | |

Engels, quoted in In Search of Infinity by N.Ya. Vilenkin (translated by Abe Shenitzer). |
729 |

There are three signs of senility. The first sign is that a man forgets his theorems. The second sign is that he forgets to zip up. The third sign is that he forgets to zip down. | |

Paul Erdos, |
1390 |

Television is something the Russians invented to destroy American education. | |

Paul Erdos, |
1389 |

It will be another million years, at least, before we understand the primes. | |

Paul Erdos, quoted in "A Quote a Day Educates" by Monte Zerger, Mathematical Intelligencer, vol. 20, no. 2, Spring 1998. |
680 |

My brain is open. | |

Paul Erdos, |
1387 |

A mathematician is a device for turning coffee into theorems. | |

Paul Erdos, |
1385 |

If Hilbert could be so wrong about predicting [when the Riemann hypothesis, the transcendence of 2^(root 2), and Fermat's last theorem would be solved], I think it is even more risky to make predictions now [1993]. | |

Paul Erdos, quoted in Consortium [COMAP Newsletter], No. 71, Fall 1999. |
1195 |

Babies can ask questions about primes which grown [wo]men cannot answer. | |

Paul Erdos, quoted in In Code by Sarah Flannery and David Flannery. |
908 |

Another roof, another proof. | |

Paul Erdos, quoted in "To Prove and Conjecture: Paul Erdos and His Mathematics", by Bela Bollobas, American Mathematical Monthly, vol. 105, no. 3, March 1998. |
702 |

Every human activity, good or bad, except mathematics, must come to an end. | |

Paul Erdos, quoted in "To Prove and Conjecture: Paul Erdos and His Mathematics", by Bela Bollobas, American Mathematical Monthly, vol. 105, no. 3, March 1998. |
701 |

God may not play dice with the universe, but something strange is going on with the prime numbers. | |

Paul Erdos, |
1386 |

Property is a nuisance. | |

Paul Erdos, |
1388 |

Determination plus hard work plus concentration equals success, which equals ganas. | |

Jaime Escalante, quoted in Math Power: How to Help Your Children Love Math, Even if You Don't by Patricia Clark Kenschaft. |
1162 |

Only those who attempt the absurd will achieve the impossible. I think it's in my basement... let me go upstairs and check. | |

M.C. Escher, |
1630 |

Science and art sometimes can touch one another, like two pieces of the jigsaw puzzle which is our human life, and that contact may be made across the boderline between the two respective domains. | |

M.C. Escher, quoted in Notebooks, Periodic Drawings, and Related Works of M.C. Escher by Doris Schattschneider. |
693 |

Father [M.C. Escher] had difficulty comprehending that the working of his mind was akin to that of a mathematician. He greatly enjoyed the interest in his work by mathematicians and scientists, who readily understood him as he spoke, in his pictures, a common language. Unfortunately, the specialized language of mathematics hid from him the fact that mathematicians were struggling with the same concepts as he was. | |

George Escher, quoted in Notebooks, Periodic Drawings, and Related Works of M.C. Escher by Doris Schattschneider. |
692 |

After all I am happy about the contact and friendship of mathematicians that resulted from it all. They have often given me new ideas, and sometimes there even is an interaction between us. How playful they can be, those learned ladies and gentlemen! | |

M.C. Escher, quoted in To Infinity and Beyond by Eli Maor. |
655 |

I never got a pass mark in math... Just imagine - mathematicians now use my prints to illustrate their books. Funny me consorting with all these learned folks, as though I were their long lost brother. I guess they are unaware of the fact that I am ignorant about the whole thing. | |

M. C. Escher, |
112 |

By keenly confronting the enigmas that surround us, and by considering and analyzing the observations that I had made, I ended up in the domain of mathematics. Although I am absolutely without training in the exact sciences, I often seem to have more in common with mathematicians than with my fellow-artists. | |

M.C. Escher, quoted in To Infinity and Beyond by Eli Maor. |
654 |

The laws of mathematics are not merely human inventions or creations. They simply 'are'; they exist quite independently of the human intellect. The most that any man with a keen intellect can do is to find out that they are there and to take cognizance of them. | |

M.C. Escher, quoted in The Magic of Mathematics, by Theoni Pappas. |
488 |

Deep, deep infinity! Quietness. To dream away from the tensions of daily living; to sail over a calm sea at the prow of a ship, toward a horizon that always recedes; to stare at the passing waves and listen to their monotonous soft murmur; to dream away into unconsciousness. | |

M.C. Escher, in To Infinity and Beyond: A Cultural History of the Infinite by Eli Maor. |
1498 |

For since the fabric of the universe is most perfect and the work of a most wise Creator, nothing at all takes place in the universe in which some rule of maximum or minimum does not appear. | |

Leonhard Euler, quoted in Single Variable Calculus, by James Stewart. |
113 |

After exponential quantities the circular functions, sine and cosine, should be considered because they arise when imaginary quantities are involved in the exponential. | |

Leonhard Euler, quoted in Theory of Complex Functions, by Reinhold Remmert. |
114 |

The kind of knowledge which is supported only by observations and is not yet proved must be carefully distinguished from the truth; it is gained by induction, as we usually say. Yet we have seen cases in which mere induction led to error. Therefore, we should take great care not to accept as true such properties of the numbers which we have discovered by observation and which are supported by induction alone. Indeed, we should use such a discovery as an opportunity to investigate more exactly the properties discovered and to prove or disprove them; in both cases we may learn something useful. | |

Euler, |
1218 |

As we must refer the numbers to the pure intellect alone, we can hardly understand how observations and quasi-experiments can be of use in investigating the nature of the numbers. Yet, in fact, as I shall show here with very good reasons, the properties of the numbers known today have been mostly discovered by observation, and discovered long before their truth has been confirmed by rigid demonstrations. There are even many properties of the numbers with which we are well acquainted, but which we are not yet able to prove; only observations have led us to their knowledge. Hence we see that in the theory of numbers, which is still very imperfect, we can place our highest hopes in observations; they will lead us continually to new properties which we shall endeavor to prove afterwards. | |

Euler, |
1217 |

The King [Frederick II] calls me "my Professor," and I am the happiest man in the world! | |

Euler, quoted in Analysis by Its History by E. Hairer and G. Wanner. |
1109 |

Because all conceivable numbers are either greater than zero, less than zero or equal to zero, then it is clear that the square root of negative numbers cannot be included among the possible numbers… And this circumstance leads us to the concept of such numbers, which by their nature are impossible and ordinarily are called imaginary or fancied numbers, because they exist only in the imagination. | |

Leonhard Euler, quoted in "Thinking the Unthinkable: The Story of Complex Numbers (with a Moral" by Israel Kleiner, Mathematics Teacher, October 1988, pp. 583-92). |
1762 |

Mighty is geometry; joined with art, resistless. | |

Euripides, |
115 |

If it ain't from the heart then it can't be art;
If you ain't got proof it can't be truth; If it ain't got legs then it can't run; If it ain't never started then it can't be done. | |

Everlast, from "Whitey" on the album "Eat at Whitey's" [Whitey Ford's]. |
1185 |

There is a distinction between what may be called a problem and what may be considered an exercise. The latter serves to drill a student in some technique or procedure, and requires little if any, original thought... No exercise, then, can always be done with reasonbable dispatch and with a miniumum of creative thinking. In contrast to an exercise, a problem, if it is a good one for its level, should require thought on the part of the student. | |

Howard Eves, quoted in Out of the Mouths of Mathematicians, by Rosemary Schmalz |
445 |

It is impossible to overstate the imporance of problems in mathematics. It is by means of problems that mathematics develops and actually lifts itself by its own bootstraps... Every new discovery in mathematics, results from an attempt to solve some problem. | |

Howard Eves, quoted in Out of the Mouths of Mathematicians, by Rosemary Schmalz |
446 |

Getting [the] degree meant more to me than an NCAA title, being named All-American or winning an Olympic gold medal. | |

Patrick Ewing, quoted in My Soul Looks Back, 'Less I Forget, by Dorothy
Winbush Riley. |
116 |

108 quotes found and displayed.