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
Interpretation
Mathematics simplifies complex tasks by relying on established principles, allowing for efficiency in problem-solving.
George Polya's quote emphasizes the inherent efficiency in mathematics, suggesting that true mastery lies not in brute force or extensive effort, but in understanding and applying underlying principles. By leveraging these principles, one can solve problems with ease, illustrating the beauty of mathematics as a tool that reduces the labor involved in finding solutions.
In practice
A teacher might use this quote to inspire students to appreciate the problem-solving aspects of mathematics.
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!
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.
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.
It is intolerable that around 1 in 5 of the world's adults are illiterate. How can we build equitable information societies or thriving democracies if so many remain without the basic tools of literacy?
If you're going to binge, literature is definitely the way to do it.
Like all those possessing a library, Aurelian was aware that he was guilty of not knowing his in its entirety.
Oh, come off it,” said Ron, striding over to her and whipping her results out of her hand. “Yep— ten ‘Outstandings’ and one ‘Exceeds Expectations’ at Defense Against the Dark Arts.” He looked down at her, half-amused, half-exasperated. “You’re actually disappointed, aren’t you?
Children live in the same world we do. To kid ourselves that we can shelter them from it isn't just naive it's a vanity.
Universities are the cathedrals of the modern age. They shouldn't have to justify their existence by utilitarian criteria.
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