Calculators can only calculate - they cannot do mathematics.
Logic doesn't apply to the real world.
We are all concerned about the future of American education. But as I tell my students, you do not enter the future - you create the future. The future is created through hard work.
Mathematics, even in its present and most abstract state, is not detached from life. It is just the ideal handling of the problems of life.
The linear-programming was - and is - perhaps the single most important real-life problem.
One factor that has remained constant through all the twists and turns of the history of physical science is the decisive importance of the mathematical imagination.
Numerical precision is the very soul of science.
Think! Think and wonder. Wonder and think. How much water can 55 elephants drink?
"The most powerful single idea in mathematics is the notion of a variable."
I am persuaded that this method [for calculating the volume of a sphere] will be of no little service to mathematics. For I foresee that once it is understood and established, it will be used to discover other theorems which have not yet occurred to me, by other mathematicians, now living or yet unborn.
All of us are slaves to the prejudices of our own dimension.
Statistics are human beings with the tears wiped away.
The calculus is the greatest aid we have to the application of physical truth in the broadest sense of the word.
Who has not been amazed to learn that the function y = ex, like a phoenix rising from its own ashes, is its own derivative?
With an absurd oversimplification, the 'invention' of the calculus is sometimes ascribed to two men, Newton and Leibniz. In reality, the calculus is the product of a long evolution that was neither initiated nor terminated by Newton and Leibniz, but in which both played a decisive part.
The whole apparatus of the calculus takes on an entirely different form when developed for the complex numbers.
It is clear that Economics, if it is to be a science at all, must be a mathematical science ... simply because it deals with quantities... As the complete theory of almost every other science involves the use of calculus, so we cannot have a true theory of Economics without its aid.
The calculus is the story this [the Western] world first told itself as it became the modern world.
The definition of a limit is essentially his [Cauchy's] creation and is as much of a miracle as those fantastic Swiss clocks of the period in which hundreds of gleaming cogs are made to celebrate not only the time and date but the phases of the moon.
Starting in the seventeenth century, the general theory of extreme values - maxima and minima - has become one of the systematic integrating principles of science.
Everything tries to be round.
The Mean Value Theorem is the midwife of calculus - not very important or glamorous by itself, but often helping to deliver other theorems that are of major significance.
Among all of the mathematical disciplines the theory of differential equations is the most important... It furnishes the explanation of all those elementary manifestations of nature which involve time.
There is a very good saying that if triangles invented a god, they would make him three-sided.
Physics is an otherworld thing, it requires a taste for things unseen, even unheard of- a high degree of abstraction... These faculties die off somehow when you grow up... profound curiosity happens when children are young. I think physicists are the Peter Pans of the human race... Once you are sophisticated, you know too much- far too much. Pauli once said to me, "I know a great deal. I know too much. I am a quantum ancient.".
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