Mathematical Problems Quotes:

The tantalizing and compelling pursuit of mathematical problems offers mental absorption, peace of mind amid endless challenges, repose in activity, battle without conflict, refuge from the goading urgency of contingent happenings, and the sort of beauty changeless mountains present to senses tried by the present day kaleidoscope of events.

- Morris Kline

source: Morris Kline (1964). “Mathematics in Western Culture”, p.470, Oxford University Press

topic: Math, Challenges, Mind, Math And Love, Math Problems

One of the first and foremost duties of the teacher is not to give his students the impression that mathematical problems have little connection with each other, and no connection at all with anything else. We have a natural opportunity to investigate the connections of a problem when looking back at its solution.

- George Polya

topic: Teacher, Opportunity, Giving, Mathematical Problems

A mathematical problem should be difficult in order to entice us, yet not completely inaccessible, lest it mock at our efforts. It should be to us a guide post on the mazy paths to hidden truths, and ultimately a reminder of our pleasure in the successful solution.

- David Hilbert

source: "Mathematical Problems". Lecture delivered before the International Congress of Mathematicians at Paris, translated by Maby Winton Newson, mathcs.clarku.edu. 1900.

topic: Successful, Order, Effort, Mathematical Problems, Hidden Truth

Each problem that I solved became a rule, which served afterwards to solve other problems.

- Rene Descartes

topic: Success, Witty, Humorous, Math Education, Math Problems

Even fairly good students, when they have obtained the solution of the problem and written down neatly the argument, shut their books and look for something else. Doing so, they miss an important and instructive phase of the work. ... A good teacher should understand and impress on his students the view that no problem whatever is completely exhausted.

- George Polya

topic: Teacher, Book, Views, Mathematical Problems

One of the big misapprehensions about mathematics that we perpetrate in our classrooms is that the teacher always seems to know the answer to any problem that is discussed. This gives students the idea that there is a book somewhere with all the right answers to all of the interesting questions, and that teachers know those answers. And if one could get hold of the book, one would have everything settled. That's so unlike the true nature of mathematics.

- Leon Henkin

topic: Teacher, Book, Ideas, Math Problems, Mathematical Logic

It's not that I'm so smart, it's just that I stay with problems longer.

- Albert Einstein

topic: Inspirational, Motivational, Leadership, Pushing On, Solved Problems

If you think it's simple, then you have misunderstood the problem.

- Bjarne Stroustrup

topic: Simple, Thinking, Misunderstood, Mathematical Problems

All the mathematical sciences are founded on the relations between physical laws and laws of numbers.

- James Clerk Maxwell

source: "The Scientific Papers of James Clerk Maxwell".

topic: Math, Law, Numbers, Mathematical Problems, Exact Sciences

By relieving the brain of all unnecessary work, a good notation sets it free to concentrate on more advanced problems, and in effect increases the mental power of the race.

- Alfred North Whitehead

topic: Learning, Race, Brain, Mathematical Problems

The theory of numbers is particularly liable to the accusation that some of its problems are the wrong sort of questions to ask. I do not myself think the danger is serious; either a reasonable amount of concentration leads to new ideas or methods of obvious interest, or else one just leaves the problem alone. "Perfect numbers" certainly never did any good, but then they never did any particular harm.

- John Edensor Littlewood

source: John Edensor Littlewood, Béla Bollobás (1986). “Littlewood's Miscellany”, p.74, Cambridge University Press

topic: Thinking, Ideas, Numbers, Math Problems, Mathematical Problems

If I found any new truths in the sciences, I can say that they follow from, or depend on, five or six principal problems which I succeeded in solving and which I regard as so many battles where the fortunes of war were on my side.

- Rene Descartes

topic: War, Math, Battle, Mathematical Problems

It isn't that they can't see the solution. It is that they can't see the problem.

- Gilbert K. Chesterton

topic: Funny, Statistics, Problem, Solved Problems, Math Problems

This paper gives wrong solutions to trivial problems. The basic error,however, is not new.

- Clifford Truesdell

topic: Errors, Giving, Paper, Mathematical Problems

Since you are now studying geometry and trigonometry, I will give you a problem. A ship sails the ocean. It left Boston with a cargo of wool. It grosses 200 tons. It is bound for Le Havre. The mainmast is broken, the cabin boy is on deck, there are 12 passengers aboard, the wind is blowing East-North-East, the clock points to a quarter past three in the afternoon. It is the month of May. How old is the captain?

- Gustave Flaubert

topic: Ocean, Math, Boys, Mathematical Problems, Trigonometry

The bottom line for mathematicians is that the architecture has to be right. In all the mathematics that I did, the essential point was to find the right architecture. It's like building a bridge. Once the main lines of the structure are right, then the details miraculously fit. The problem is the overall design.

- Freeman Dyson

source: "Freeman Dyson: Mathematician, Physicist, and Writer". The College Mathematics Journal Interview with Donald J. Albers, January 1994.

topic: Math, Bridges, Design, Mathematical Problems

There are problems to whose solution I would attach an infinitely greater importance than to those of mathematics, for example touching ethics, or our relation to God, or concerning our destiny and our future; but their solution lies wholly beyond us and completely outside the province of science.

- Carl Friedrich Gauss

source: "The World of Mathematics". Book by J. R. Newman, 1956.

topic: Lying, Destiny, Touching, Math Problems, Mathematical Problems

The measure of our intellectual capacity is the capacity to feel less and less satisfied with our answers to better and better problems.

- C. West Churchman

topic: Math, Intellectual, Answers, Math Problems, Mathematical Problems

If there is a problem you can't solve, then there is an easier problem you can't solve: find it.

- George Polya

topic: Science, Problem, Easier, Math Problems, Mathematical Problems

When I am working on a problem, I never think about beauty but when I have finished, if the solution is not beautiful, I know it is wrong.

- R. Buckminster Fuller

topic: Beauty, Beautiful, Niece, Software Design, Solved Problems

Theorems are fun especially when you are the prover, but then the pleasure fades. What keeps us going are the unsolved problems.

- Carl Pomerance

topic: Fun, Science, Problem, Math Problems, Math Teacher

The older I get, the more I believe that at the bottom of most deep mathematical problems there is a combinatorial problem.

- Israel Gelfand

source: "Biography/ Personal Quotes". www.imdb.com.

topic: Believe, Statistics, Problem, Mathematical Problems

More people have access to education today than ever before. But I cannot help but feel that the modern educational experience is not preparing us adequately to attend the rich banquet of life. Certainly the young people of today have mastered the use of technology and are capable of solving complex scientific and mathematical problems, but who and what do these serve if they cannot think for themselves? If they have no understanding of the meaning and purpose of their own lives? If they do not know who they are as individuals?

- Matthew Kelly

topic: Education, Technology, Thinking, Mathematical Problems, Education Today

Even with the most stupid video games, kids learn more about learning than they ever did before, because they want to learn codes and moves before other kids figure them out. They're motivated to seek out someone or search the Net for help. A student who makes a video game has to solve mathematical problems to make special effects happen on the screen.

- Seymour Papert

source: "Sunday Interview - Seymour Papert/ Computers in the Lives of Our Children/ an Mit Mathematician and Philosopher Is Exploring How Technology Can Educate the Next Generation - and Their Parents". www.sfgate.com. February 2, 1997.

topic: Stupid, Moving, Kids, Mathematical Problems

By the time the average person finishes college, he or she will have taken over 2,600 tests, quizzes, and exams. The right answer approach becomes deeply ingrained in our thinking. This may be fine for some mathematical problems where there is in fact only one right answer. The difficulty is that most of life isn’t this way. Life is ambiguous; there are many right answers- all depending on what you’re looking for. But if you think there is only one right answer, then you’ll stop looking as soon as you find one.

- Roger von Oech

topic: Life, Taken, College, Mathematical Problems, Quiz

Music is a secret and unconscious mathematical problem of the soul.

- Gottfried Leibniz

topic: Soul, Secret, Problem, Mathematical Problems

I combat the errors of ages; I meet the violence of mobs; I cope with illegal proceedings from executive authority; I cut the gordian knot of powers, and I solve mathematical problems of universities, with truth-diamond truth; and God is my 'right hand man'.

- Joseph Smith, Jr.

topic: Cutting, Men, Errors, Mathematical Problems

An old French mathematician said: A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street. This clearness and ease of comprehension, here insisted on for a mathematical theory, I should still more demand for a mathematical problem if it is to be perfect; for what is clear and easily comprehended attracts, the complicated repels us.

- David Hilbert

topic: Men, Perfect, Ease, Clearness, Mathematical Problems

As a single atom man is an enigma: as a whole he is a mathematical problem. As an individual he is a free agent, as a species the offspring of necessity.

- William Winwood Reade

source: William Winwood Reade (1874). “The Martyrdom of Man”, p.186

topic: Men, Atoms, Agents, Mathematical Problems, Free Agents

Before a kid learns how to use a computer that can solve mathematical problems, he or she should know how to do arithmetic without a computer.

- Andy Rooney

topic: Kids, Use, Computer, Mathematical Problems

In fact, I barely missed being number one in France in both schools. In particular I did very well in mathematical problems.

- Benoit Mandelbrot

source: Source: bigthink.com

topic: School, Numbers, France, Mathematical Problems

Cell and tissue, shell and bone, leaf and flower, are so many portions of matter, and it is in obedience to the laws of physics that their particles have been moved, moulded and conformed. They are no exceptions to the rule that God always geometrizes. Their problems of form are in the first instance mathematical problems, their problems of growth are essentially physical problems, and the morphologist is, ipso facto, a student of physical science.

- D'Arcy Wentworth Thompson

topic: Flower, Math, Law, Mathematical Problems, Leaves And Flowers

If you attack a mathematical problem directly, very often you come to a dead end, nothing you do seems to work and you feel that if only you could peer round the corner there might be an easy solution. There is nothing like having somebody else beside you, because he can usually peer round the corner.

- Michael Atiyah

source: Michael Atiyah (1988). “Collected Works: Michael Atiyah Collected Works: Volume 1: Early Papers; General Papers”, p.214, Oxford University Press

topic: Peers, Might, Problem, Mathematical Problems

The definition of a good mathematical problem is the mathematics it generates rather than the problem itself.

- Andrew Wiles

source: "Andrew Wiles on Solving Fermat". The NOVA Interview, www.pbs.org. November 1, 2000.

topic: Definitions, Problem, Mathematics, Mathematical Problems