...the source of all great mathematics is the special case, the concrete example. It is frequent in mathematics that every instance of a concept of seemingly generality is, in essence, the same as a small and concrete special case.
Paul HalmosRead
In a way, math isn't the art of answering mathematical questions, it is the art of asking the right questions, the questions that give you insight, the ones that lead you in interesting directions, the ones that connect with lots of other interesting questions -the ones with beautiful answers.
Interpretation
Math is about asking the right questions rather than just finding answers.
This quote emphasizes that the true essence of mathematics lies not just in solving problems but in formulating the right questions that inspire exploration and curiosity. It suggests that significant insights in mathematics arise from inquiry, leading to a deeper understanding and connection with a broader range of concepts.
In practice
In a mathematics class focused on problem-solving, I shared this quote to inspire students to think critically.
...the source of all great mathematics is the special case, the concrete example. It is frequent in mathematics that every instance of a concept of seemingly generality is, in essence, the same as a small and concrete special case.
Upon the education of the people of this country the fate of this country depends.
Most of these students are so conditioned to success that they become afraid to take risks. They have been taught from a young age by zealous parents, schools, and institutional authorities what constitutes failure and success. They are socialized to obey. They obsess over grades and seek to please professors, even if what professors teach is fatuous. The point is to get ahead, and getting ahead means deference to authority. Challenging authority is never a career advancer.
I imagine a school system that recognizes learning is natural, that a love of learning is normal, and that real learning is passionate learning. A school curriculum that values questions above answers...creativity above fact regurgitation...individuality above conformity.. and excellence above standardized performance..... And we must reject all notions of 'reform' that serve up more of the same: more testing, more 'standards', more uniformity, more conformity, more bureaucracy.
By fully committing to our public education system and engaging holistically from cradle to career, we can guarantee that all of our children in Georgia, no matter their needs, have the kinds of teachers and neighbors in their lives that my mother had.
If you invest in a girl or a woman, you are investing in everybody else.
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