Mathematics is not a spectator sport!
Interpretation
Mathematics requires active participation and engagement, rather than passive observation.
The quote by George Polya emphasizes the importance of actively engaging with mathematical concepts instead of simply watching others perform calculations or problem-solving. It suggests that true understanding and mastery of mathematics come from hands-on practice, exploration, and participation, akin to how one must actively play a sport to appreciate and excel in it.
In practice
In a classroom setting, a teacher might say this quote to encourage students to participate in problem-solving activities.
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 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.
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.
All I hope, selfishly, is that there will be real books until the day I draw my last breath.
For a lot of us, awareness is merely realizing the extent to which we've been lied to all our lives. You start educating yourself. You become motivated; you follow your muse where it takes you. And you see the world in a different way. You start making decisions based on what you feel is right.
Books are for people who wish they were somewhere else.
I tell my students that the single most powerful thing that we have in this country - something that literally harbors no dissent and no questioning - is the all-powerful elite narrative.
The Indians seemed to be living in a place and in a way that was of immense importance to me. So I associate learning to read - English, oddly enough - with wanting to know about Indians. I'm still growing into it. I've never outgrown that.
There will always be places in the world where good schools don't exist and good teachers don't want to go, not just in the developing world but in places of socioeconomic hardship.
Subscribe for the occasional hand-picked quote. No noise.