A Quote by Stanislaw Ulam
Even the simplest calculation in the purest mathematics can have terrible consequences. Without the invention of the infinitesimal calculus most of our technology would have been impossible. Should we say therefore that calculus is bad?
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Foreshadowings of the principles and even of the language of [the infinitesimal] calculus can be found in the writings of Napier, Kepler, Cavalieri, Pascal, Fermat, Wallis, and Barrow. It was Newton's good luck to come at a time when everything was ripe for the discovery, and his ability enabled him to construct almost at once a complete calculus.
With an absurd oversimplification, the "invention" of calculus [method in mathematics] is sometimes ascribed to two men, Newton and Leibniz.
An announcement of [Christopher] Zeeman's lecture at Northwestern University in the spring of 1977 contains a quote describing catastrophe theory as the most important development in mathematics since the invention of calculus 300 years ago.
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.
Without calculation, economic activity is impossible. Since under Socialism economic calculation is impossible, under Socialism there can be no economic activity in our sense of the word All economic change, therefore, would involve operations the value of which could neither be predicted beforehand nor ascertained after they had taken place. Everything would be a leap in the dark. Socialism is the renunciation of rational economy.
Science is the Differential Calculus of the mind. Art the Integral Calculus; they may be beautiful when apart, but are greatest only when combined.
When I was about thirteen, the library was going to get 'Calculus for the Practical Man.' By this time I knew, from reading the encyclopedia, that calculus was an important and interesting subject, and I ought to learn it.
Ambition without knowledge is like a boat on dry land -movie - Karate kid"What is the calculus of innovation?" "The calculus of innovation is really quite simple: knowledge drives innovation, innovation drives productivity, productivity drives our economic growth."
Why do I think that we, the intellectuals, are able to help? Simply because we, the intellectuals, have done the most terrible harm for thousands of years. Mass murder in the name of an idea, a doctrine, a theory, a religion - that is all "our" doing, "our" invention: the invention of the intellectuals. If only we would stop setting man against man - often with the best intentions - much would be gained. Nobody can say that it is impossible for us to stop doing this.
If it's cynical, risky politics that brings a lighted match and a can of gas near the Democratic coalition, it should be named as such, and its consequences understood, and it should become part of the complex calculus we're all building to help us understand these campaigns.
I never failed in mathematics. Before I was fifteen I had mastered differential and integral calculus.
Arithmetic starts with the integers and proceeds by successively enlarging the number system by rational and negative numbers, irrational numbers, etc... But the next quite logical step after the reals, namely the introduction of infinitesimals, has simply been omitted. I think, in coming centuries it will be considered a great oddity in the history of mathematics that the first exact theory of infinitesimals was developed 300 years after the invention of the differential calculus.
If a nonnegative quantity was so small that it is smaller than any given one, then it certainly could not be anything but zero. To those who ask what the infinitely small quantity in mathematics is, we answer that it is actually zero. Hence there are not so many mysteries hidden in this concept as they are usually believed to be. These supposed mysteries have rendered the calculus of the infinitely small quite suspect to many people. Those doubts that remain we shall thoroughly remove in the following pages, where we shall explain this calculus.
The change began with John Stuart Mill and the Utopians . When Mill pointed out that economics had no ultimate solution to the problem of distribution , that society might do with the fruits of its toil as it saw fit, he introduced into the mechanical calculus of the market a conflicting calculus of moral judgment.
The teacher manages to get along still with the cumbersome algebraic analysis, in spite of its difficulties and imperfections, and avoids the smooth infinitesimal calculus, although the eighteenth century shyness toward it had long lost all point.
Imagine a life-form whose brainpower is to ours as ours is to a chimpanzee’s. To such a species, our highest mental achievements would be trivial. Their toddlers, instead of learning their ABCs on Sesame Street, would learn multivariable calculus on Boolean Boulevard. Our most complex theorems, our deepest philosophies, the cherished works of our most creative artists, would be projects their schoolkids bring home for Mom and Dad to display on the refrigerator door.
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