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.
Interpretation
Mathematics is an accessible science that requires minimal resources to practice.
This quote by George Polya emphasizes that mathematics is a unique field of study that can be pursued without the need for costly tools or labs, unlike other sciences such as physics or chemistry. It highlights the simplicity and accessibility of mathematics, suggesting that anyone can engage with it using just basic materials like a pencil and paper, thereby democratizing the knowledge and exploration of this essential discipline.
In practice
In a lecture on the importance of education, this quote can be used to emphasize the accessibility 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!
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.
I do not write for this generation. I am writing for other ages. If this could read me, they would burn my books, the work of my whole life. On the other hand, the generation which interprets these writings will be an educated generation; they will understand me and say: 'Not all were asleep in the nighttime of our grandparents.'
For most of us the rules of English grammar are at best a dimly remembered thing. But even for those who make the rules, grammatical correctitude sometimes proves easier to urge than to achieve. Among the errors cited in this book are a number committed by some of the leading authorities of this century. If men such as Fowler and Bernstein and Quirk and Howard cannot always get their English right, is it reasonable to expect the rest of us to?
Journalism largely consists of saying 'Lord Jones is Dead' to people who never knew that Lord Jones was alive.
When I was going for my graduate degree, I decided I was going to make a feature film as my thesis. That's what I was famous for-that I had my thesis film be a feature film, which was 'You're a Big Boy Now.'
True literacy is becoming an arcane art, and the nation is steadily "dumbing down."
But in the new (math) approach, the important thing is to understand what you're doing, rather than to get the right answer.
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