Memorable Quotes (4 quotes)
If it were always necessary to reduce everything to intuitive knowledge, demonstration would often be insufferably prolix. This is why mathematicians have had the cleverness to divide the difficulties and to demonstrate separately the intervening propositions. And there is art also in this; for as the mediate truths (which are called lemmas, since they appear to be a digression) may be assigned in many ways, it is well, in order to aid the understanding and memory, to choose of them those which greatly shorten the process, and appear memorable and worthy in themselves of being demonstrated. But there is another obstacle, viz.: that it is not easy to demonstrate all the axioms, and to reduce demonstrations wholly to intuitive knowledge. And if we had chosen to wait for that, perhaps we should not yet have the science of geometry.
Of the many definitions of poetry, the simplest is still the best: “memorable speech.”
One of the memorable moments of my life was when Willard Libby came to Princeton with a little jar full of crystals of barium xenate. A stable compound, looking like common salt, but much heavier. This was the magic of chemistry, to see xenon trapped into a crystal.
The great upheavals which precede changes of civilisation, such as the fall of the Roman Empire and the founding of the Arabian Empire, for example, seem to have been determined mainly by considerable political transformations, invasions, or the overthrow of dynasties. But … most often, the real cause is … a profound modification in the ideas of the peoples. … The memorable events of history are the visible effects of the invisible changes of human thought. … The present epoch is one of these critical moments in which the thought of mankind is undergoing a process of transformation.