Mathematics consists in proving the most obvious thing in the least obvious way.
Interpretation
Mathematics involves demonstrating seemingly simple truths through complex reasoning.
George Polyaβs quote highlights the essence of mathematical thinking, where what appears to be evident often requires intricate proof and exploration. This reflects the beauty and challenge of mathematics, emphasizing that deeper understanding often lies beneath the surface of obviousness.
In practice
This quote can be used in a lecture to inspire students about the beauty of mathematical proofs.
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.
Bend your minds and wills to the education of the peoples and kindreds of the earth, that haply the dissensions that divide it may, through the power of the Most Great Name, be blotted out from its face, and all mankind become the upholders of one Order, and the inhabitants of one City.
Here's the teaching point, if you're teaching kids about intelligence and policy: Intelligence does not absolve policymakers of responsibility to ask tough questions, and it doesn't absolve them of having curiosity about the consequences of their actions.
By including children with different learning abilities in mainstream and specialized schools, we can change attitudes and promote respect. By creating suitable jobs for adults with autism, we integrate them into society.
When we make college more affordable, we make the American dream more achievable.
I have learned that, although I am a good teacher, I am a much better student, and I was blessed to learn valuable lessons from my students on a daily basis. They taught me the importance of teaching to a student - and not to a test.
Prescriptive grammar has spread linguistic insecurity like a plague among English speakers for centuries, numbs us to the aesthetic richness of non-standard speech, and distracts us from attending to genuine issues of linguistic style in writing.
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