There is an astonishing imagination, even in the science of mathematics. ... We repeat, there was far more imagination in the head of Archimedes than in that of Homer.
That Logic has advanced in this sure course, even from the earliest times, is apparent from the fact that, since Aristotle, it has been unable to advance a step, and thus to all appearance has reached its completion.
Twice two makes four seems to me simply a piece of insolence. Twice two makes four is a pert coxcomb who stands with arms akimbo barring your path and spitting. I admit that twice two makes four is an excellent thing, but if we are to give everything its due, twice two makes five is sometimes a very charming thing too.
The years of searching in the dark for a truth that one feels but cannot express, the intense desire and the alternations of confidence and misgiving until one breaks through to clarity and understanding, are known only to him who has experienced them himself.
Look, this is a man, he's got great numbers. He talks about numbers. I'm beginning to think not only did he invent the Internet, but he invented the calculator. It's fuzzy math. It's a scaring - trying to scare people in the voting booth. Under my tax plan, that he continues to criticize, I set a third - the federal government should take no more than a third of anybody's check.
We may discover resources on the moon or Mars that will boggle the imagination, that will test our limits to dream. And the fascination generated by further exploration will inspire our young people to study math, and science, and engineering and create a new generation of innovators and pioneers.
What's all this whining about the environment? They're always talking about 'stop the clearcuts.' I mean do the math people. If we were out of trees then we wouldn't have any clearcuts to be complaining about now would we?
Of all the intellectual faculties, judgment is the last to mature. A child under the age of fifteen should confine its attention either to subjects like mathematics, in which errors of judgment are impossible, or to subjects in which they are not very dangerous, like languages, natural science, history, etc.
But the creative principle resides in mathematics. In a certain sense, therefore, I hold true that pure thought can grasp reality, as the ancients dreamed.