But just as much as it is easy to find the differential [derivative] of a given quantity, so it is difficult to find the integral of a given differential. Moreover, sometimes we cannot say with certainty whether the integral of a given quantity can be found or not.
Accordingly, we find Euler and D'Alembert devoting their talent and their patience to the establishment of the laws of rotation of the solid bodies. Lagrange has incorporated his own analysis of the problem with his general treatment of mechanics, and since his time M. Poinsôt has brought the subject under the power of a more searching analysis than that of the calculus, in which ideas take the place of symbols, and intelligent propositions supersede equations.
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.
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.
After years of finding mathematics easy, I finally reached integral calculus and came up against a barrier. I realized that this was as far as I could go, and to this day I have never successfully gone beyond it in any but the most superficial way.
Every one who understands the subject will agree that even the basis on which the scientific explanation of nature rests is intelligible only to those who have learned at least the elements of the differential and integral calculus, as well as analytical geometry.
I see with much pleasure that you are working on a large work on the integral Calculus ... The reconciliation of the methods which you are planning to make, serves to clarify them mutually, and what they have in common contains very often their true metaphysics; this is why that metaphysics is almost the last thing that one discovers. The spirit arrives at the results as if by instinct; it is only on reflecting upon the route that it and others have followed that it succeeds in generalising the methods and in discovering its metaphysics.
I would have I think made a bigger mistake if I had said, "Eh, chemical weapons. That doesn't really change my calculus." I think it was important for me as president of the United States to send a message that in fact there is something different about chemical weapons [in Syria].
I'd like to take some calculus, too. I have absolutely no ability in that direction and not much interest, either, but there's something going on in mathematics that I don't understand, and I'd like to find out what it is.
In the moral calculus of currently prevailing state capitalism, profits and bonuses in the next quarter greatly outweigh concern for the welfare of one’s grandchildren, and since these are institutional maladies, they will not be easy to overcome. While much remains uncertain, we can assure ourselves, with fair confidence, that future generations will not forgive us our silence and apathy.
If one looks at the different problems of the integral calculus which arise naturally when one wishes to go deep into the different parts of physics, it is impossible not to be struck by the analogies existing.
Science is the Differential Calculus of the mind. Art the Integral Calculus; they may be beautiful when apart, but are greatest only when combined.
Infinity converts the possible into the inevitable.
We can't exempt ourselves from the same moral calculus that we are willing to apply to others.
Looking at numbers as groups of rocks may seem unusual, but actually it's as old as math itself. The word "calculate" reflects that legacy - it comes from the Latin word calculus, meaning a pebble used for counting. To enjoy working with numbers you don't have to be Einstein (German for "one stone"), but it might help to have rocks in your head.
You know what speed is. You would not believe a man who claimed to walk at 5 miles an hour, but took 3 hours to walk 6 miles. You have only to apply the same common sense to stones rolling down hillsides, and the calculus is at your command.
History was easy, but I don't know about the Calculus. It seemed like it was making sense, so that probably means I failed.
Part of my job is to help other kids find books, because not everyone has a keenly organized mind. Some kids could wander the library for hours and still have no idea how to find anything. For them, the Dewey Decimal System might as well be advanced calculus.
Our First Amendment expresses a far different calculus for regulating speech than for regulating nonexpressive conduct and that is as it should be. The right to swing your fist should end at the tip of my nose, but your right to express your ideas should not necessarily end at the lobes of my ears.
When I was in school, my favorite subject was math. I took algebra and calculus. At an early age I grasped it and understood it quickly. I just enjoyed breaking the codes and solving problems.
The true Logic for this world is the Calculus of Probabilities, which takes account of the magnitude of the probability.
Computer science is to biology what calculus is to physics. It's the natural mathematical technique that best maps the character of the subject.
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.
In the calculus of good deeds you have the most to gain.
The theory of probabilities is at bottom nothing but common sense reduced to calculus; it enables us to appreciate with exactness that which accurate minds feel with a sort of instinct for which of times they are unable to account.
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