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.
Just what is it that academics have to fear if they stand up for common decency, instead of letting campus barbarians run amok?
Studies have shown that performance gets worse as group size increases ... If you have talented and motivated people, they should be encouraged to work alone when creativity or efficiency is the highest priority.
For that reason you can't write with music playing, and anyone who says he can is either writing badly, or not listening to the music, or lying. You need to hear what you're writing, and for that you need silence
The progress of the world depends almost entirely upon education.
Let the children...be carefully instructed in the principles and obligations of the Christian religion. This is the most essential part of education.
Those with a gift for action, for their part, often express contempt for those whose gifts are more reflective. Men of action like to say, 'Those who can, do, those who can't, teach,' forgetting that those who teach get to write the history books.
Subscribe for the occasional hand-picked quote. No noise.