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'm not by nature a terribly intuitive person; I need to build a situation in which I will behave more intuitively, and that has really changed the life of my work - I found a way to trick myself into being intuitive.
I think a lot of writers spend years just getting up the courage to write because it seems like such a fantasy of a profession. My dad saved me all that time by making me think, 'Oh, anyone can be a writer. It's like being a firefighter or a lawyer.'
What if desire wasn't an urge to be tamed, but a beacon of truth to be followed?
Failing to grapple with complexity actually turns out to be a pretty bad life strategy.
We live in a time when science is validating what humans have known throughout the ages: that compassion is not a luxury; it is a necessity for our well-being, resilience, and survival.
When I examine myself and my methods of thought, I come to the conclusion that the gift of fantasy has meant more to me than any talent for abstract, positive knowledge.
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