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.
In all this world there is no substitute for personal integrity. It includes honor. It includes performance. It includes keeping one's word. It includes doing what is right regardless of the circumstances
Always remember that others may hate you but those who hate you don't win unless you hate them. And then you destroy yourself.
It's Hard to Stay Mad When There's So Much Beauty in the World
[In developing your potential] ... I don't develop; I am
It is sound judgment to put on a bold face and play your hand for a hundred times what it is worth; forty-nine times out of fifty nobody dares to call it, and you roll in the chips.
If you have done something meritorious, you experience pleasure and happiness; if wrong things, suffering. A happy or unhappy life is your own creation. Nobody else is responsible. If you remember this, you wonβt find fault with anybody. You are your own best friend as well as your worst enemy. (99)
Subscribe for the occasional hand-picked quote. No noise.