A Quote by Edward Gibbon
The mathematics are distinguished by a particular privilege, that is, in the course of ages, they may always advance and can never recede.
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The point of mathematics is that in it we have always got rid of the particular instance, and even of any particular sorts of entities. So that for example, no mathematical truths apply merely to fish, or merely to stones, or merely to colours. So long as you are dealing with pure mathematics, you are in the realm of complete and absolute abstraction. . . . Mathematics is thought moving in the sphere of complete abstraction from any particular instance of what it is talking about.
In private enterprises men may advance or recede, whereas they who aim at empire have no alternative between the highest success and utter downfall.
Of course, the opposite of white privilege is not blackness, as many of us seemed to think then; the opposite of white privilege is working to dismantle that privilege. But my particular hip-hop generation proved to be very serious about figuring it all out and staying engaged.
Hold the old holding hand. Hold and be held. Plod on and never recede. Slowly with never a pause plod on and never recede.
But where do they find these lines in nature? I can only see luminous or obscure masses, planes that advance or planes that recede, reliefs or background. My eye never catches lines or details.
...mathematics is distinguished from all other sciences except only ethics, in standing in no need of ethics. Every other science, even logic, especially in its early stages, is in danger of evaporating into airy nothingness, degenerating, as the Germans say, into an arachnoid film, spun from the stuff that dreams are made of. There is no such danger for pure mathematics; for that is precisely what mathematics ought to be.
On foundations we believe in the reality of mathematics, but of course, when philosophers attack us with their paradoxes, we rush to hide behind formalism and say 'mathematics is just a combination of meaningless symbols,'... Finally we are left in peace to go back to our mathematics and do it as we have always done, with the feeling each mathematician has that he is working with something real. The sensation is probably an illusion, but it is very convenient.
Mystery is an inescapable ingredient of mathematics. Mathematics is full of unanswered questions, which far outnumber known theorems and results. It's the nature of mathematics to pose more problems than it can solve. Indeed, mathematics itself may be built on small islands of truth comprising the pieces of mathematics that can be validated by relatively short proofs. All else is speculation.
In fact, the answer to the question "What is mathematics?" has changed several times during the course of history... It was only in the last twenty years or so that a definition of mathematics emerged on which most mathematicians agree: mathematics is the science of patterns.
I have friends whose society is delightful to me; they are persons of all countries and of all ages; distinguished in war, in council, and in letters; easy to live with, always at my command.
May not music be described as the mathematics of the sense, mathematics as music of the reason? The musician feels mathematics, the mathematician thinks music: music the dream, mathematics the working life.
It is reasonable to have perfection in our eye that we may always advance toward it, though we know it can never be reached.
It is however, reasonable, to have perfection in our eye; that we may always advance towards it, though we know it never can be reached.
One may say that mathematics talks about the things which are of no concern to men. Mathematics has the inhuman quality of starlight - brilliant, sharp but cold ... thus we are clearest where knowledge matters least: in mathematics, especially number theory.
The revolution of ages may bring round the same calamities; but ages may revolve without producing a Tacitus to describe them.
But the origin of the American Republic is distinguished by peculiar circumstances. Other nations have been driven together by fear and necessity-the governments have generally been the result of a single man's observations; or the offspring of particular interests. In the formation of our constitution, the wisdom of all ages is collected-the legislators of antiquity are consulted-as well as the opinions and interests of the millions who are concerned. In short, it is an empire of reason.
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