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.
My parents are both college professors, and it made me want to question authority, standards and traditions.
The Eeyore Educational System sees childhood as a waste of time, a luxury that society cannot afford . . . Put children in school at the earliest age possible; load them down with homework; take away their time, their creativity, their play, their power; then plug them into machines.
Across time and generations, books carry the thoughts and feelings, the essence, of the human spirit.
The student is half afraid to meet one of the great philosophers face to face. He feels himself inadequate and thinks he will not understand him. But if he only knew, the great man, just because of his greatness, is much more intelligible than his modern commentator. The simplest student will be able to understand, if not all, yet a very great deal of what Plato said; but hardly anyone can understand some modern books on Platonism.
There are only two kinds of books -- good books and the others. The good are winnowed from the bad through the democracy of time.
And books, they offer one hope -- that a whole universe might open up from between the covers, and falling into that universe, one is saved.
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