If there is a problem you can't solve, then there is an easier problem you can't solve: find it.
Interpretation
This quote emphasizes the importance of simplifying problems to find solutions.
George Polya's quote suggests that when faced with a difficult problem, instead of becoming overwhelmed, one should look for a simpler aspect of the problem that can be addressed. This approach not only helps in problem-solving but also encourages a more systematic and less stressful way of thinking through challenges.
In practice
In a seminar on critical thinking, this quote can inspire participants to approach complex problems with clarity.
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.
I trust in the ebb and flow of the universe. I trust that life's bigger than what I can see. I trust that there is a divine order beyond my control. And I trust that no matter what happens, I will be all right.
One percent doubt is zero percent faith.
Go not to the Elves for counsel, for they will say both no and yes.
If empathy channels our optimism, we will see the empathy and the diseases and the poor school. We will answer with our innovations and we will surprise the pessimists.
Inflict not on an enemy every injury in your power, for he may afterwards become your friend.
There was madness in any direction, at any hour. You could strike sparks anywhere. There was a fantastic universal sense that whatever we were doing was right, that we were winning.
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