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.
The greatest investment a young person can make is in their own education, in their own mind. Because money comes and goes. Relationships come and go. But what you learn once stays with you forever.
The importance of a high moral code, which is at the foundation of the Scout movement, cannot be stressed too highly.
When the panting and thirsting soul first drinks the delicious waters of truth, when the moral and intellectual tastes and desires first seize the fragrant fruits that flourish in the garden of knowledge, then does the child catch a glimpse and foretaste of heaven.
The principle itself of dogmatic religion, dogmatic morality, dogmatic philosophy, is what requires to be rooted out; not any particular manifestation of that principle. The very corner-stone of an education intended to form great minds, must be the recognition of the principle, that the object is to call forth the greatest possible quantity of intellectual power, and to inspire the intensest love of truth.
I read books when I was a kid, lots of books. Books always seemed like magic to me. They took you to the most amazing places. When I got older, I realized that I couldn't find books that took me to all of the places I wanted to go. To go to those places, I had to write some books myself.
It is a good thing for an uneducated man to read books of quotations. Bartlett's Familiar Quotations is an admirable work, and I studied it intently. The quotations when engraved upon the memory give you good thoughts. They also make you anxious to read the authors and look for more.
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