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.
You expect far too much of a first sentence. Think of it as analagous to a good country breakfast: what we want is something simple, but nourishing to the imagination. Hold the philosophy, hold the adjectives, just give us a plain subject and verb and perhaps a wholesome, nonfattening adverb or two.
I think we have a great deal of mythology around writing. We believe that only a few people can really do it. I wrote a book called 'The Right to Write.' In it, I argued that all of us have the capacity to write. That it's as normal to write as it is to speak.
You will also find that help will always be given at Hogwarts to those who ask for it.
New insights fail to get put into practice because they conflict with deeply held internal images of how the world works...images that limit us to familiar ways of thinking and acting. That is why the discipline of managing mental models - surfacing, testing, and improving our internal pictures of how the world works - promises to be a major breakthrough for learning organizations.
Young children possess the ability to cut across the customary categories; to appreciate usually undiscerned links among realms, to respond effectively in a parallel manner to events which are usually categorized differently, and to capture these ori
My upbringing was in the church. We had to attend regularly. And, of course, the church provided a training ground for me, so to speak, as a young vocalist and certainly gave me all of the spiritual values that I needed as a young lady.
Subscribe for the occasional hand-picked quote. No noise.