It is a capital mistake to theorize before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts.— Arthur Conan Doyle
Spectacular Math Problems quotations
Sometimes the easiest way to solve a problem is to stop participating in the problem.
It is better to solve one problem five different ways, than to solve five problems one way.
There are no solved problems; there are only problems that are more or less solved.
The biggest communication problem is we do not listen to undrstand. We listen to reply.
Science, in the very act of solving problems, creates more of them.
All the mathematical sciences are founded on relations between physical laws and laws of numbers.
If there is a problem you can't solve, then there is an easier problem you can't solve: find it.
The problem with the world is that the intelligent people are full of doubts while the stupid ones are full of confidence.
So what should we say when children complete a task—say, math problems—quickly and perfectly? Should we deny them the praise they have earned? Yes. When this happens, I say, “Whoops. I guess that was too easy. I apologize for wasting your time. Let’s do something you can really learn from!
One must acknowledge with cryptography no amount of violence will ever solve a math problem.
It is the duty of all teachers, and of teachers of mathematics in particular, to expose their students to problems much more than to facts.
Life is a journey to be experienced, not a problem to be solved.
Theorems are fun especially when you are the prover, but then the pleasure fades. What keeps us going are the unsolved problems.
The problem with cinema nowadays is that it's a math problem.
People can read a film mathematically; they know when this comes or that comes; in about 30 minutes, it's going to be over and have an ending. So film has become a mathematical solution. And that is boring, because art is not mathematical.
In mathematics, the art of asking questions is more valuable than solving problems.
Be selective in your battles, don't make every problem a war.
Dealing with failure is easy: Work hard to improve.
Success is also easy to handle: You've solved the wrong problem. Work hard to improve.
The aim (of education) must be the training of independently acting and thinking individuals who, however, see in the service to the community their highest life problem.
I think there are dozens or hundreds of different forms of creativity.
Pondering science and math problems for years is different from improvising jazz. Something which seems to me remarkable is how unconscious the creative process is. You encounter a problem, but can't solve it.
Running from your problems is just adding another one to the list.
Learning through the arts reinforces critical academic skills in reading, language arts and math, and provides students with the skills to creatively solve problems.
The life of a mathematician is dominated by an insatiable curiosity, a desire bordering on passion to solve the problems he is studying.
A GREAT discovery solves a great problem but there is a grain of discovery in any problem.
If it can be solved, theres no need to worry, and if it can't be solved, worry is of no use.
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.
Dear Math, please grow up and solve your own problems.
I'm tired of solving them for you. Always remember that you are absolutely unique. Just like everyone else.
From somewhere, back in my youth, heard Prof say, 'Manuel, when faced with a problem you do not understand, do any part of it you do understand, then look at it again.' He had been teaching me something he himself did not understand very well—something in math—but had taught me something far more important, a basic principle.
Anyone can run away, it's super easy. Facing problems and working through them, that's what makes you strong.
We've lost something that's been with us for so long, and something that drew a lot of us into mathematics. But perhaps that's always the way with math problems, and we just have to find new ones to capture our attention.
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 paper gives wrong solutions to trivial problems. The basic error,however, is not new.
Be grateful for small things, big things, and everything in between. Count your blessings, not your problems.
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.
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.
Mathematics may be defined as the economy of counting.
There is no problem in the whole of mathematics which cannot be solved by direct counting.
Stay away from negative people. They have a problem for every solution,
I hate the idea that, when it comes to books and learning, hard is often seen as the opposite of fun. It's strange to me that we should be so quick to give up on a book or a math problem when we are so willing to grapple, for centuries if necessary, with a single level of Angry Birds.
The value of a problem is not so much coming up with the answer as in the ideas and attempted ideas it forces on the would be solver.
Before the math and the momentum overwhelm us all, we are going to solve this nation's economic problems. And I'm going to level with you: We don't have that much time. But if we are serious, and smart, and we lead, we can do this.
There comes a point when you have to realize that you'll never be good enough for some people. The question is, is that your problem or theirs?
The measure of our intellectual capacity is the capacity to feel less and less satisfied with our answers to better and better problems.
Let's face it; by and large math is not easy, but that's what makes it so rewarding when you conquer a problem, and reach new heights of understanding.
Christians remind me of schoolboys who want to look up the answers to their math problems in the back of the book rather than work them through.
The Tour (de France) is essentially a math problem, a 2,000-mile race over three weeks that's sometimes won by a margin of a minute or less. How do you propel yourself through space on a bicycle, sometimes steeply uphill, at a speed sustainable for three weeks? Every second counts.
Environment-based education produces student gains in social studies, science, language arts, and math; improves standardized test scores and grade-point averages; and develops skills in problem-solving, critical thinking, and decision-making.