It is better to solve one problem five different ways, than to solve five problems one way.
Interpretation
Finding multiple solutions to a single problem is more effective than having one solution for multiple problems.
The quote by George Polya emphasizes the importance of diverse thinking and creativity in problem-solving. It suggests that exploring various approaches to a single challenge can yield better insights and innovations than applying a single method to multiple issues, encouraging flexibility and adaptability in our thought processes.
In practice
During a team meeting while brainstorming solutions to a project issue.
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.
It is not so easy to keep silent when the silence is a lie.
It's not the problem that causes our suffering; it's our thinking about the problem.
An intelligent mind is an inquiring mind. It is not satisfied with explanation, with conclusions. Nor is it a mind that believes, because belief is again another form of conclusion.
Not only does silence give us a chance to understand ourselves better, to get a truer and more balanced perspective on our own lives in relation to the lives of others: silence makes us whole if we let it. Silence helps draw together the scattered and dissipated energies of a fragmented existence.
Transient are conditioned things. Try to accomplish your aim with diligence.
If we treasure our own experience and regard it as real, we must also treasure other people's experience.
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