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.
People say: idle curiosity. The one thing that curiosity cannot be is idle.
One way to learn to do something right is to do something wrong. Failure must teach us, or surely success will not reward us.
The true method of knowledge is experiment.
Convince yourself that you are working in clay, not marble, on paper not eternal bronze: Let that first sentence be as stupid as it wishes.
It's surprisingly nice out here, peaceful and pretty-strange to be standing in the middle of a little garden while enclosed by the massive stone walls of the prison, like being at the exact center of a hurricane, and finding peace and silence in the middle of so much shrieking damage.
Blind commitment to a theory is not an intellectual virtue: it is an intellectual crime.
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