Nowadays group theoretical methods - especially those involving characters and representations, pervade all branches of quantum mechanics.
George Mackey, quoted in Contemporary Abstract Algebra, by J. Gallian.
245
 
ALGEBRA is a general Method of Computation by certain Signs and Symbols which have been contrived for this Purpose, and found convenient.
Maclaurin, quoted in Analysis by Its History by E. Hairer and G. Wanner.
1099
 
Knowledge will forever govern ignorance; and a people who mean to be their own governors must arm themselves with the power which knowledge gives.
James Madison,
1470
 
I'm intensely mixed.
Al Magid,
907
 
It is one of man's curious idiosyncrasies to create difficulties for the pleasure of resolving them.
Joseph de Maistre,
1253
 
I'm sorry to say that the subject I most disliked was mathematics. I have though about it. I think the reason was that matematics leaves no room for argument.
Malcolm X, quoted in The American Mathematical Monthly, vol. 102, no. 4, April 1995.
508
 
I have often reflected upon the new vistas that reading opened to me. I knew right there in prison that reading had changed forever the course of my life. As I see it today, the ability to read awoke in me some long dormant craving to be mentally alive.
Malcolm X,
1006
 
The structure of society, in its great features, will probably always remain unchanged.
Thomas Malthus, from "An Essay on the Principle of Population as It Effects he Future Improvement of Society..."
246
 
The Mandelbrot set is the most complex mathematical object known to mankind.
B. Mandelbrot,
247
 
The existence of these patterns [fractals] challenges us to study forms that Euclid leaves aside as being formless, to investigate the morphology of the amorphous. Mathematicians have disdained this challenge, however, and have increasingly chosen to flee from nature by devising theories unrelated to anything we can see or feel.
Benoit Mandelbrot,
480
 
Why is geometry often described as cold and dry? One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline, or a tree. Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line... Nature exhibits not simply a higher degree but an altogether different level of complexity.
Benoit Mandelbrot,
479
 
A good proof is one that makes us wiser.
Yu. I. Manin, from Proofs Without Words II
1210
 
Finally, in regard to those who possess the largest shares in the stock of worldly goods, could there, in your opinion, be any police so vigilant and effetive, for the protections of all the rights of person, property and character, as such a sound and comprehensive education and training, as our system of Common Schools could be made to impart; and would not the payment of a sufficient tax to make such education and traning universal, be the cheapest means of self-protection and insurance?
Horace Mann, from The Republic and the School, edited by Lawrence A. Cremin.
695
 
I tell them if they will occupy themselves with the study of mathematics they will find in it the best remedy against the lusts of the flesh.
Thomas Mann,
250
 
A house without books is like a room without windows.
Horace Mann,
852
 
There may be frugality which is not economy. A community, that withholds the means of education from its children, withholds the bread of life and starves their souls.
Horace Mann, quoted in A Teacher's Treasury of Quotations, by Bernard E. Farber.
249
 
The teacher who is attempting to teach without inspiring the pupil to learn is hammering on cold iron.
Horace Mann,
248
 
Education, then, beond all other devices of human origin, is the great equalizer of the conditions of men -- the balance-wheel of the social machinery.
Horace Mann, from The Republic and the School, edited by Lawrence A. Cremin.
699
 
Without undervaluing any other human agency, it may be safely affirmed that the Common School, improved and energized, as it can easily be, may become the most effective and benignant of all the forces of civilization. Two reasons sustain this position. In the first place, there is a universality in its operation, which can be affirmed of no other instituion whatever... And, in the second place, the materials upon which it operates are so pliant and ductile as to be susceptible of assuming a greater variety of forms than any other earthly work of the Creator.
Horace Mann, from The Republic and the School, edited by Lawrence A. Cremin.
698
 
As an innovation... the establishment of Free Schools was the boldest ever promulgated, since the commencement of the Christian era... Time has ratified its soundness. Two centuries proclaim it to be as wise as it was courageous, as beneficient as it was disinterested. It was one of those grand mental and moral experiments... The sincerity of our gratitude must be tested by our efforts to perpetuate and improve what they established. The gratitude of the lips only is an unholy offering.
Horace Mann, from The Republic and the School, edited by Lawrence A. Cremin.
696
 
Teachers should be able to teach subjects, not manuals merely.
Horace Mann, from The Republic and the School, edited by Lawrence A. Cremin.
694
 
When will society, like a mother, take care of all her children?
Horace Mann, quoted in The Horace Mann Centennial, issued by the Commonwealth of Massachusetts Department of Education in 1937.
687
 
If ever there can be a cause worthy to be upheld by all toil or sacrifice that the human heart can endure, it is the cause of education.
Horace Mann, quoted in The Horace Mann Centennial, issued by the Commonwealth of Massachusetts Department of Education in 1937.
686
 
Be ashamed to die until you have won some victory for humanity.
Horace Mann,
469
 
Under the Providence of God, our means of education are the grand machinery by which the "raw material" of human nature can be worked up into inventors and discoverers, into skilled artisans and scientific farmers, into scholars and jurists, into the founders of benevolent institutions, and the great expounders of ethical and theological science.
Horace Mann, from The Republic and the School, edited by Lawrence A. Cremin.
697
 
The greatest advantage to be derived from the study of geometry of more than three dimensions is a real understanding of the great science of geometry. Our plane and solid geometries are but the beginning of this science. The four-dimensional geometry is far more extensivve than the three-dimensional, and all the higher geometries are more extensive than the lower.
Henry Parker Manning, from Geometry of Four Dimensions.
573
 
The Biblical value of pi, by comparison, is exactly three, as is clear from a verse in 1 Kings vii 23: "and he made a molten sea, ten cubits from brim to brim, and his height was five cubit; and a line of thirty cubits did encompass him round about."
Eli Maor, from To Infinity and Beyond.
648
 
Thought that accepts reality as given is no thought at all.
Herbert Marcuse,
251
 
Challenges are what make life interesting; overcoming them is what makes life meaningful.
Joshua J. Marine,
1327
 
What Teacher Education Programs forget to tell their candidates:
A teacher cannot be all things to all people
You are not a "bad person" if you are not always able to meet all the needs of all your students
You are a powerful and compelling figure in the lives of your students
In recalling their school years, students mostly remember their teachers, and not the courses they took
You need to find a "critical friend" whom you can trust to serve as a sounding board
At times students can be very cruel, difficult, and mean-spirited
It is a mistake to personalize a student's unacceptable behavior
Teachers love their students as their parents love them--but in a different way and for a different reason
Few people will ever appreciate the amount of time and effort teachers give to their teaching
By choosing to be a teacher, you have entered an emotionally dangerous profession
You are both a role model and change agent
You need to pay attention to both your physical and emotional well-being
Teaching is not like inducing a chemical reaction, but more like creating a painting, or planting a garden, or writing a friendly letter.
Teaching is a complicated business because students are such unexpected blends of character, personality, and background
Most of the significant advances in civilization have been the result of the work of teachers
Teaching is an act of faith in the promise of the future
Teaching is a way of life
James Marran, Social Studies Dept. Chair New Trier High School, Winnetka, Ill.
1033
 
Taking an interest in what students are thinking and doing is often a much more powerful form of encouragement than praise.
Robert Martin, quoted in The Teacher's Quotation Book, edited by Wanda Lincoln and Murray Suid.
632
 
Thanksgiving Day comes, by statute, once a year; to the honest man it comes as frequently as the heart of gratitude will allow.
Edward Sandford Martin,
1429
 
By looking at the world through a lens of any single color, rather in light of the myriad colors and textures and shapes and sounds and smells that surround us, that are us, we destine ourselves to a world without rainbows. How finite.
Mary Hampton Mason, 18 September, 2008.
1359
 
Ever since there have been men, man has given himself over to too little joy. That alone, my brothers, is our original sin. I should believe only in a God who understood how to dance.
Henri Matisse, from Words I Wish I Wrote by Robert Fulgham
952
 
It is a great nuisance that knowledge can only be acquired by hard work.
W. Somerset Maugham, quoted in Excursions in Calculus, by Robert M. Young.
252
 
Every existence above a certain rank has its singular points; the higher the rank the more of them. At these points, influences whose physical magnitude is too small to be taken account of by a finite being, may produce results of the greatest importance....
James Clerk-Maxwell, from The World of Mathematics, by J.R. Newman.
253
 
We encourage children to read for enjoyment, yet we never encourage them to "math" for enjoyment. We teach kids that math is done fast, done only one way and if you don't get the answer right, there's something wrong with you. You would never teach reading this way.
Rachel McAnallen, from "Math? No Problem," The Hartford Courant, October, 1998.
747
 
That flower of modern mathematical thought, the notion of a function.
Thomas McCormack, quoted in Memorabilia Mathematica, by R.E. Moritz.
254
 
The Bible alone is the most dangerous thing I can think of.
Robert D. McFadden, Rev. Peter J. Gomes Is Dead at 68; A Leading Voice Against Intolerance. March 1, 2011, New York Times
1715
 
When it's third-and-10, you can take the milk drinkers and I'll take the whiskey drinkers every time.
Max McGee, Scored the first ever Superbowl Touchdown on a pass play in a game he was not started in because he had violated team curfew. Died 10/21/07 falling from his roof while clearing leaves at age 75.
1430
 
Well, mathematics is a hard subject. [On why there weren't many women mathematicians.]
Saunders McLane,
1412
 
Every society honors its live conformists, and its dead troublemakers.
Mignon McLaughlin,
1701
 
In the arithmetic of love, one plus one equals everything, and two minus one equals nothing.
Mignon McLaughlin,
1053
 
Never doubt that a small group of thoughtful, committed citizens can change the world. Indeed, it is the only thing that ever has.
Margaret Mead,
1276
 
As I was sitting in my chair,
I knew the bottom wasn't there,
Nor legs nor back, but I just sat,
Ignoring little things like that.
Hughes Mearns,
1635
 
Each field has its narrative, which contains its history, its culture, its assumptions, its people, and its life. Mathematics is no different. Each mathematician constructs his or her own life in mathematics, and each student--and we are all students at some level--needs to find him--or herself within this narrative. Writing and speaking mathematics are central to learning and doing mathematics.
John Meier and Thomas Rishel, from Writing in the Teaching and Learning of Mathematics.
731
 
She teaches the English at the American school;
She teaches imaginary numbers and the golden rule;
She says it's hard to worry about the future;
When your past is knocking at your door;
Sweet mistakes and information;
Have been her lovers before;
Hello, all you losers;
You've got nothing to fear;
This may not be the end of the world;
But you can see it from here.
John Mellencamp, from "This may not be the end of the world" from the album "Mr. Happy Go Lucky".
1187
 
The experimental verification of a theory concerning any natural phenomenon generally rests on the result of an integration.
J. W. Mellor, quoted in Memorabilia Mathematica, by R.E. Moritz.
255
 
Bridges would be safer if only people who knew the proper definition of a real number were allowed to design them.
Norman David Mermin, from "Topological Theory of Defects," in Review of Modern Physics, July 1979.
256
 
The mathematical community's approach to training a new generation of mathematicians is to have them run drills for sixteen years before they get to see the game. Students learn to recite the multiplication tables, to factor polynomials, to differentiate trigonometric functions, and to orthogonalize a basis for R^4. And after sixteen years of mathematics education most cannot name a living mathematician. They have no mathematical heroes. They do not know what takes place in the mathematics department at Bell Laboratories, about Falting's proof of Mordell's conjecture, or about the excitement and disappointment over the recent attempts to prove Fermat's "Last Theorem". Althout they have acquired some technical skills, they have not been made to feel part of something larger.
Craig B. Merow, from "Mathematics: A Wonderful Kind of Play", Mathematics Teacher, March 1990, pp. 172-175.
1293
 
In a time when much of the world's geography has been explored, and space exploration is restricted to astronauts, mathematics offers fertile ground for exploring the unknown.
Walter Meyer, from "Missing Dimensions of Mathematics," in the Humanistic Mathematics Network Journal, No. 11, Feb., 1995.
257
 
I am still learning.
Michelangelo,
1503
 
I saw the angel in the marble and carved until I set him free.
Michelangelo,
1505
 
Every block of stone has a statue inside it and it is the task of the sculptor to discover it.
Michelangelo,
1504
 
Upon this gifted age, in its dark hour,
Fall from the sky a meteor shower
Of facts... they lie unquestioned, uncombined.
Wisdom enough to leech us of our ill
Is daily spun; but there exists no loom
To weave it into fabric…
Edna St. Vincent Millay, quoted in "The Mathematics Framework" of the Massachusetts Curriculum Frameworks.
344
 
When a child has no hope, a nation has no future.
Zell Miller,
258
 
The mind is its own place, and in itself
Can make a heaven of hell, and a hell of heaven.
John Milton, from Paradise Lost
1770
 
Infinity is a dark illimitable ocean, without bound.
John Milton, quoted in To Infinity and Beyond by Eli Maor.
646
 
Heaven is angered by my arrogance; my proof [of the four-color theorem] is also defective.
Hermann Minkowski, quoted in From Here to Infinity, by Ian Stewart.
584
 
The world of learning is so broad, and the human soul is so limited in power! We reach forth and strain every nerve, but we seize only a bit of the curtain that hides the infinite from us.
Maria Mitchell, quoted in The Beacon Book of Quotations by Women, edited by Rosalie Maggio.
259
 
We must embrace pain and burn it as fuel for our journey.
Kenji Miyazawa,
1428
 
If we base our belief systems on the humble assumption that the complexities of the world are ontologically beyond our understanding, then maybe our belief systems will make more sense and end up causing less suffering.
Moby, from the linear notes to the album "Play."
960
 
The world is too big and too intricate to conform to our ideas of what it should be like... Just because we invent myths and theories to explain away the chaos we're still going to live in a world that's older and more complicated than we'll ever understand.
Moby, from the linear notes to the album "Play."
959
 
Any time we convey to a student that knowledge is the ability to give the expected response, we are propagating psychic stupidity. The same thing happens if we assign to the student interminable chores that neither demand nor repay thought... Algorithmic drill stands alone in the elementary curriculum: it is the only subject whose study ordinarily damages the mentality of the child.
Edwin E. Moise, quoted in Out of the Mouths of Mathematicians, by Rosemary Schmalz.
460
 
It seems quite unrealistic to judge a curriculum by its general outline, or to judge a course by its syllabus. We can "cover" very impressive material, if we are willing to turn the student into a spectator. But if you cast the student in a passive role, then saying that he has "studied" your course may mean no more than saying of a cat that he has looked at a king. Mathematics is something that one does.
Edwin E. Moise, quoted in Out of the Mouths of Mathematicians, by Rosemary Schmalz
448
 
I believe that the ultimate caricature of good mathematical teaching is linear error-free programming. Under this scheme, instead of taking care to insure that every student is provided with the most stimulating challenges that he can react to successfully, people use their best efforts to create a situation where nobody is faced with any challenge at all.
E. E. Moise, quoted in Out of the Mouths of Mathematicians, by R. Schmalz.
261
 
It is not only what we do, but also what we do not do, for which we are accountable.
Moliere,
800
 
...we discovered that education is not something which the teacher does, but that it is a natural process which develops spontaneously in the human being. It is not acquired by listening to words, but in virtue of experiences in which the child acts on his environment. The teacher's task is not to talk, but to prepare and arrange a series of motives for cultural activity in a special environment made for the child.
Dr. Maria Montessori,
1490
 
We teachers can only help the work going on, as servants wait upon a master.
Maria Montessori, quoted in The Beacon Book of Quotations by Women, edited by Rosalie Maggio.
263
 
The principal agent is the object itself and not the instruction given by the teacher. It is the child who uses the objects; it is the child who is active, and not the teacher.
Maria Montessori,
262
 
That student is taught the best who is told the least.
R.L. Moore, quoted in Essentials of Mathematics by Margie Hale.
956
 
We are just beginning to understand how geometry rules the universe.
Frank Morgan, from "Review: The Parsimonious Universe," American Mathematical Monthly, April, 1997.
741
 
The moving power of mathematical invention is not reasoning but imagination.
Augustus de Morgan,
264
 
A circle is a happy thing to be--
Think how the joyful perpendicular
Erected at the kiss of tangency
Must meet my central point, my avator.
And lovely as I am, yet only 3
Points are needed to determine me.
Christopher Morley, (1890-1957)
1549
 
Read, every day, something no one else is reading. Think, everyday, something no one else is thinking. Do, every day, something no one else would be silly enough to do. It is bad for the mind to continually be part of unanimity.
Christopher Morley,
1550
 
Passive learning, where a child sits still, with little activity except that of the ear and the eye and perhaps the hand marking the paper, is not wrong. Video, videotape, video games, computers-all are easily operated and produce interesting results with a modest amount of activity. But how much better if children learn how to make them behave? How much better if they learn that in order to find something out about a system, they must inquire of it, and that the best kind of evidence comes from scientific experiments and their confirmation.
Phylis Morrison, said in a presentation to the National Academy of Sciences in the late 1980s. http://www.setileague.org/admin/phylis.htm
1786
 
But mathematics is the sister, as well as the servant, of the arts and is touched by the same madness and genius.
Marston Morse, from A Dictionary of Quotations in Mathematics by Nowlan
1664
 
Immersing everyone in the process, insisting that everyone get in there and do it, accelerated the development of leadership [in the Civil Rights movement]. Here, you immerse the child in a physical event he understands, and show that child how to take from that event the mathematics he needs. It's the same process that raised someone like Fannie Lou Hamer until she could speak for the whole country.
Bob Moses, quoted in "Mississippi Learning", by Alexis Jetter, New York Times Magazine, February 21, 1993.
725
 
If they get these math tools then they will be in positions to demand access to the economic arrangements. These are the tools that are needed by people who are going to come to the table and act on their rights.
Bob Moses, from the program "Uncommon Americans" televised by the A&E network, July 1998.
727
 
Becoming literate in mathematics is a life-and-death issue for the black community. If we don't get it, we're headed for a new form of serfdom.
Bob Moses, quote in Math Literacy: Radical Equations, Time, 18 June, 2001.
938
 
[The Algebra Project is] our version of Civil Rights 1992. But this time, we're organizing around literacy -- not just reading and writing, but mathematical literacy.
Bob Moses, quoted in "Mississippi Learning", by Alexis Jetter, New York Times Magazine, February 21, 1993.
726
 
Everyone is entitled to his own opinion, but not his own facts.
Daniel Patrick Moynihan,
1566
 
Only dead fish swim with the stream.
Malcolm Muggeridge,
1771
 
When we try to pick anything by itself we find it hitched to everything else in the universe.
John Muir, quoted in The Magic of Mathematics, by Theoni Pappas.
490
 
What was the duty of the teacher if not to inspire?
Bharati Mukherjee, quoted in The Beacon Book of Quotations by Women, edited by Rosalie Maggio.
265
 
In my own experience, mathematics in general and pure mathematics in particular has always seems like secret gardens, special places where I could try to grow exotic and beautiful theories.
David Mumford,
1517
 
Ultimately formalism in its private aspect is an expression of fear. But fear can lend us wings and armor, and formalism can penetrate where intuition falters, leading her to places where she can again come into her own.
John Myhill, quoted in Godel Meets Einstein: Time Travel in the Godel Universe by Palle Yourgrau.
1056
 

87 quotes found and displayed.