The best of ideas is hurt by uncritical acceptance and thrives on critical examination.
Interpretation
Ideas flourish under scrutiny and suffer from blind acceptance.
George Polya emphasizes the importance of critical thinking in the evaluation of ideas. Accepting ideas without question can lead to stagnation, while subjecting them to rigorous examination can enhance understanding and innovation.
In practice
During a team meeting, I reminded everyone that the best solutions come from questioning our assumptions.
Pedantry and mastery are opposite attitudes toward rules. To apply a rule to the letter, rigidly, unquestioningly, in cases where it fits and in cases where it does not fit, is pedantry. [...] To apply a rule with natural ease, with judgment, noticing the cases where it fits, and without ever letting the words of the rule obscure the purpose of the action or the opportunities of the situation, is mastery.
If you wish to learn swimming you have to go into the water and if you wish to become a problem solver you have to solve problems.
To teach effectively a teacher must develop a feeling for his subject; he cannot make his students sense its vitality if he does not sense it himself. He cannot share his enthusiasm when he has no enthusiasm to share. How he makes his point may be as important as the point he makes; he must personally feel it to be important.
Mathematics is not a spectator sport!
Mathematics is being lazy. Mathematics is letting the principles do the work for you so that you do not have to do the work for yourself
In order to translate a sentence from English into French two things are necessary. First, we must understand thoroughly the English sentence. Second, we must be familiar with the forms of expression peculiar to the French language. The situation is very similar when we attempt to express in mathematical symbols a condition proposed in words. First, we must understand thoroughly the condition. Second, we must be familiar with the forms of mathematical expression.
Never receive counsel from unproductive people. Never discuss your problems _x000D_ with someone incapable of contributing to the solution, because those who _x000D_ never succeed themselves are always first to tell you how. Not everyone has _x000D_ a right to speak into your life. You are certain to get the worst of the _x000D_ bargain when you exchange ideas with the wrong person. Don't follow anyone _x000D_ who's not going anywhere.
To be thrown upon one's own resources, is to be cast in the very lap of fortune.
I am anxious to give away information, for it is only by giving it away that you can keep it. When you have told it, you remember it. It is with information as it is with liberty, the only way to be dead sure of it is to give it to other people.
Yesterday you can't alter, but your reaction to yesterday you can. The past you cannot change, but your response to your past you can.
Knowledge must come through action. You can have no test which is not fanciful, save by trial.
Be generous with kindly words, especially about those who are absent.
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