Trends, like horses, are easier to ride in the direction they are already going.
John Naisbitt, from Megatrends
1158
 
Being a true gentleman is an impossibility, trying to become one a dangerous task, yet living without the attempt a degrading lot.
Paik Nak-Chung,
266
 
The advancement and perfection of mathematics are intimately connected with the prosperity of the State.
Napoleon, quoted in A History of Mathematics, by Carl Boyer.
267
 
Concepts are the substance of mathematical knowledge.
National Council of Teachers of Mathematics, from the Curriculum and Evaluation Standards for School Mathematics.
268
 
The need for curricular reform in K-4 mathematics is clear. Such reform must address both the content and emphasis of the curriculum as well as approaches to instruction. A long-standing preoccupation with computation and other traditional skills has dominated both what mathematics is taught and the way mathematics is taught at this level. As a result, the present K-4 curriculum is narrow in scope; fails to foster mathematical insight, reasoning, and problem solving; and emphasizes rote activities. Even more significant is that children begin to lose their belief that mathematics is a sense-making experience. They become passive receivers of rules and procedures rather than active participants in creating knowledge.
National Council of Teachers of Mathematics, from the Curriculum and Evaluation Standards for School Mathematics
269
 
In 1977 there were 37 Elvis impersonators in the world. In 1993 there were 48,000. At this rate, by the year 2010 one out of every three people will be an Elvis impersonator.
National Institutes of Health, quoted in A Course in Mathematical Modeling by Douglas Mooney and Randall Swift.
1188
 
Virtually all young children like mathematics. They do mathematics naturally, discovering patterns and making conjectures based on observation. Natural curiosity is a powerful teacher, especially for mathematics. Unfortunately, as children become socialized by school and society, they begin to view mathematics as a rigid system of externally dictated rules governed by standards of accuracy, speed, and memory. Their view of mathematics shifts gradually from enthusiasm to apprehension, from confidence to fear. Eventually, most students leave mathematics under duress, convinced that only geniuses can learn it.
National Research Council, from Everybody Counts
1175
 
Sorrow shared is halved Joy shared is doubled.
Native American saying,
271
 
Tell me and I'll forget. Show me and I may not remember. Involve me, and I'll understand.
Native American saying,
270
 
Mathematics can be characterized as the science of patterns. Finding a pattern is a powerful problem-solving strategy. Recognizing and describing numerical patterns are foundational to the concept of functions. Patterns should be part of every mathematics course at all grade levels. The study of patterns provides both motivation and relevance to the elementary school child's involvement with mathematics.
NCTM, from Patterns: Addenda Series K - 6 of the Curriculum and Evaluation Standards, 1993, p. 1.
811
 
In a very broad sense the observation of patterns lies at the heard of acquiring understanding and knowledge in many disciplines such as science, history, economics, and social science. There is no area in which the study of patterns is as fundamental as it is in mathematics. Mathematicians observe patterns; they conjecture, test, discuss, verbalize, and generalize these patterns. Through this process they discover the salient features of the pattern, construct understandings of the concepts and relationships, develop a language to talk about the pattern, integrate, and discriminate between the pattern and other patterns. When relationships between quantities in a pattern are studied, knowledge about important mathematical relationships and functions emerges.
NCTM, from Patterns and Functions: Addenda Series 5 - 8 of the Curriculum and Evaluation Standards, 1991, p. 1.
810
 
Over the last hundred years the honor of visual reasoning in mathematics has been besmirched.
Tristan Needham, Visual Complex Analysis, p. vii.
1761
 
All trigonometric identities may be viewed as arising from the rule for complex multiplication… Every complex equation says two things at once.
Tristan Needham, Visual Complex Analysis, pp. 14-5.
1760
 
Only the joy of making love surpasses the joy of doing mathematics.
Edward Nelson,
1508
 
There is no evidence in all of creation that God chose to make a completed infinity. The notion is a human fabrication.
Edward Nelson,
1509
 
My joyful task is trying to show that contemporary mathematics is indeed inconsistent.
Edward Nelson,
1510
 
I attended first grade in fascist Italy and still have the notebook in which I wrote to dictation, "Mussolini ama I bambini." What a boon it was to know already in first grade that most of the things I was being taught simply were not so.
Edward Nelson,
1507
 
Unless we want mathematics to continue to be viewed as something distinct and separate from the mainstream of culture and consisting of a bag of clever tricks or skills, we must change the way we relate to the general public and the way we teach mathematics.
Harald M. Ness, Jr., in "Mathematics: an integral part of our culture," from Essays in Humanistic Mathematics.
505
 
I was told a story of a visit by John von Neumann to a well-known university where he lectured about his work to the mathematics students. He was schduled to speak in the evening to the general public. One of the students, wondering whether he should attend, asked whether he was going to say anything important. "Young Man", von Neumann replied, "What I am going to say this evening is far more important than anything I've said this afternoon."
Harald M. Ness, Jr., in "Mathematics: an integral part of our culture," from Essays in Humanistic Mathematics.
507
 
If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.
John von Neumann,
1723
 
The theory of Groups is a branch of mathematics in which one does something to something and then compares the results with the result of doing the same thing to something else, or something else to the same thing.
James Newman,
273
 
The problem - to cross the seven bridges in a continuous walk without recrossing any of them - was regarded as a small amusement of the Konigsberg townfolk. Euler, however, discovered an important scientific principle concealed in the puzzle... Thus began a vast and intricate theory, still young and growing, yet already one of the great forces in modern mathematics.
James Newman, quoted in Exploring Elementary Mathematics by Julian Weissglass.
272
 
…Number Theory. It is a field of almost pristine irrelevance to everything except the wondrous demonstration that pure numbers, no more substantial than Plato's shadows, conceal magical laws and orders that the mind can discover after all.
Newsweek, 5 July, 1993.
275
 
Pure mathematics is a sucker's game. It lures the curious and confident with its' seeming simplicity, only to make them look like fools. Now the inquisitive are hooked, like rubes in three-card monte.
Newsweek, 5 July, 1993.
274
 
I do not know what I may appear to the world, but to myself I seem to have been only a boy playing on the sea-shore, and diverting myself now and then finding a smoother pebble or a prettier sea-shell that ordinary, whilst the great ocean of truth lay all undiscovered before me.
Sir Isaac Newton,
277
 
Every body continues in its state of real, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed upon it.
Newton, First Law of Motion
276
 
I keep the subject constantly before me and wait till the first dawnings open little by little into the full light.
Sir Isaac Newton,
278
 
If I have seen farther than others, it is because I have stood on the shoulders of giants.
Sir Isaac Newton,
279
 
All this was in the two plague years of 1665 and 1666, for in those days I was in the prime of my age for invention, and minded mathematics and philosophy more than at any other time since.
Sir Isaac Newton, quoted in Analysis by Its History by E. Hairer and G. Wanner.
1101
 
First they came for the socialists, and I did not speak out -- because I was not a socialist. Then they came for the trade unionists, and I did not speak out -- because I was not a trade unionist. Then they came for the Jews, and I did not speak out -- because I was not a Jew. Then they came for me -- and there was no one left to speak for me.
Pastor Martin Niemoller, from the U.S. Holocaust Memorial Museum
967
 
Yea verily, I say unto you:
A man must have Chaos yet within him
To birth a dancing star.
I say unto you:
You have yet Chaos in you.
Friedrich Nietzsche, quoted in Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise, by Manfred Schroder.
565
 
Mathematics would certainly have not come into existence if one had known from the beginning that there was in nature no exactly straight line, no actual circle, no absolute magnitude.
Friedrich Nietzsche,
1662
 
We don't see things as they are; we see things as we are.
Anais Nin,
1743
 
Fools act on imagination without knowledge; pedants act on knowledge without imagination. The task of the university is to weld together imagination and experience.
Alfred North, "Universities and Their Function" in The Aims of Education and Other Essays, 1967.
1789
 

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