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.
Interpretation
Understanding the source is crucial for accurate translation, whether in language or mathematics.
George Polya's quote emphasizes the importance of comprehension in the translation process, applicable both in linguistics and mathematics. To effectively translate a sentence from one language to another or to convert verbal conditions into mathematical symbols, one must first have a thorough understanding of the original content and then be adept at the specific forms of expression used in the target language or discipline. This underscores the broader principle that deep understanding is essential in any field of knowledge for clear and accurate communication.
In practice
This quote could be used in a lecture about the importance of understanding concepts before teaching them.
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
Mathematics is the cheapest science. Unlike physics or chemistry, it does not require any expensive equipment. All one needs for mathematics is a pencil and paper.
To believe in a child is to believe in the Future.
Books are to be distinguished by the grandeur of their topics even more than by the manner in which they are treated.
I am suspicious of writers who go looking for issues to address. Writers are neither preachers nor journalists. Journalists know much more than most writers about what's going on in the world. And if you want to change things, you do journalism.
Study history, study history. In history lies all the secrets of statecraft.
For me, literacy means freedom. For the individual and for society.
To read in bed is to draw around us invisible, noiseless curtains. Then at last we are in a room of our own and are ready to burrow back, back to that private life of the imagination we all led as a child and to whose secret satisfactions so many of us have mislaid the key.
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