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It seems to me that the poet has only to perceive that which others do not perceive, to look deeper than others look. And the mathematician must do the same thing.
The elegance of a mathematical theorem is directly proportional to the number of independent ideas one can see in the theorem and inversely proportional to the effort it takes to see them.
Leibniz never married; he had considered it at the age of fifty; but the person he had in mind asked for time to reflect. This gave Leibniz time to reflect, too, and so he never married.
Physics is mathematical not because we know so much about the physical world, but because we know so little; it is only its mathematical properties that we can discover.
...the feeling of mathematical beauty, of the harmony of numbers and of forms, of geometric elegance. It is a genuinely aesthetic feeling, which all mathematicians know
Whoever despises the high wisdom of mathematics nourishes himself on delusion and will never still the sophistic sciences whose only product is an eternal uproar.
We need to tap the resource of current and retiring science and math professionals that have both content mastery and the practical experience to serve as effective teachers.
Calculus required continuity, and continuity was supposed to require the infinitely little; but nobody could discover what the infinitely little might be.
Mathematics, rightly viewed, possesses not only truth, but supreme beauty-a beauty cold and austere ... yet sublimely pure and capable of stern perfection such as only the greatest art can show.
At the fourth grade level, girls at the same percentages of boys say they're interested in careers in engineering or math or astrophysics, but by eighth grade that has dropped precipitously.
I am accustomed, as a professional mathematician, to living in a sort of vacuum, surrounded by people who declare with an odd sort of pride that they are mathematically illiterate.
The mathematician, carried along on his flood of symbols, dealing apparently with purely formal truths, may still reach results of endless importance for our description of the physical universe.